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We present an approximate semiclassical (SC) framework for mixed quantized dynamics in Wigner phase space in a two-part series. In the first article, we introduced the Adiabatic Hybrid Wigner Dynamics (AHWD) method that allows for a few important "system" degrees of freedom to be quantized using high-level double Herman–Kluk SC theory while describing the rest (the "bath") using classical-limit linearized SC theory. In this second article, we extend our hybrid Wigner dynamics to nonadiabatic processes. The resulting Nonadiabatic Hybrid Wigner Dynamics (NHWD) has two variants that differ in the choice of degrees of freedom to be quantized. Specifically, we introduce NHWD(E) where only the electronic state variables are quantized and the NHWD(V) where both electronic state variables and a handful of strongly coupled nuclear modes are quantized. We show that while NHWD(E) proves accurate for a wide range of scattering models and spin-boson models, systems where a few nuclear modes are strongly coupled to electronic states require NHWD(V) to accurately capture the long-time dynamics. Taken together, we show that AHWD and NHWD represent a new framework for SC simulations of high-dimensional systems with significant quantum effects. [ABSTRACT FROM AUTHOR]

The Wigner phase space formulation of quantum mechanics is a complete framework for quantum dynamic calculations that elegantly highlights connections with classical dynamics. In this series of two articles, building upon previous efforts, we derive the full hierarchy of approximate semiclassical (SC) dynamic methods for adiabatic and non-adiabatic problems in Wigner phase space. In Paper I, focusing on adiabatic single surface processes, we derive the well-known double Herman–Kluk (DHK) approximation for real-time correlation functions in Wigner phase space and connect it to the linearized SC (LSC) approximation through a stationary phase approximation. We exploit this relationship to introduce a new hybrid SC method, termed Adiabatic Hybrid Wigner Dynamics (AHWD) that allows for a few important "system" degrees of freedom (dofs) to be treated at the DHK level, while treating the rest of the dofs (the "bath") at the LSC level. AHWD is shown to accurately capture quantum interference effects in models of coupled oscillators and the decoherence of vibrational probability density of a model I2 Morse oscillator coupled to an Ohmic thermal bath. We show that AHWD significantly mitigates the sign problem and employs reduced dimensional prefactors bringing calculations of complex system–bath problems within the reach of SC methods. Paper II focuses on extending this hybrid SC dynamics to nonadiabatic processes. [ABSTRACT FROM AUTHOR]

Developing phase diagrams for inhomogeneous systems in thermodynamics is difficult, in part, due to the large phase space and the possibility of unstable and metastable solutions arising from first-order phase transitions. Pseudo-arclength continuation (PAC) is a method that allows one to trace out stable and unstable solutions of nonlinear systems. Typically, PAC utilizes the Jacobian in order to implement Newton (or quasi-Newton) steps. In this work, we present a Jacobian-free PAC method that is amenable to the usual workflows in inhomogeneous thermodynamics. We demonstrate our method in systems that have first-order phase transitions, including a novel example of polyelectrolyte complex coacervation in confinement, where multiple surface phase transitions occur and can overlap with one another. [ABSTRACT FROM AUTHOR]

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or −1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case. [ABSTRACT FROM AUTHOR]

We investigate roaming in the photodissociation of acetaldehyde (CH3CHO), providing insights into the contrasting roaming dynamics observed for this molecule compared to formaldehyde. We carry out trajectory studies for full-dimensional acetaldehyde, supplemented with an analysis of a two-degree-of-freedom restricted model and obtain evidence for two distinct roaming pathways. Trajectories exhibit roaming at both shorter (9–11.5 au) and larger (14.5–22.9 au) maximum CH3–HCO separations, characterized by differing amounts of HCO rotation. No roaming trajectories were found in the intervening gap region. The roaming dynamics near 14.5–22.9 au are well-reproduced by the restricted model and involve passage through a centrifugal barrier, analogous to formaldehyde roaming. However, the shorter-range 9–11.5 au roaming appears unique to acetaldehyde and is likely facilitated by repulsive interactions absent in the simplified models. Phase space analysis reveals that this additional roaming pathway is inaccessible in the reduced dimensionality system. The findings suggest that acetaldehyde's increased propensity for roaming compared to formaldehyde may arise from the presence of multiple distinct roaming mechanisms rather than solely the higher roaming fragment mass. [ABSTRACT FROM AUTHOR]

For microscale gaps, DC breakdown voltage is described theoretically and through simulation by accounting for field emission generated electrons and the subsequent ionization of neutral gas and ion-induced secondary electron emission. Here, we extend DC microscale breakdown theory to AC. Particle-in-cell (PIC) simulations show that breakdown voltage V varies linearly with gap distance d independent of frequency and the ion-induced secondary electron coefficient γ S E for d ≲ 4 μ m , where field emission dominates breakdown over ionization and avalanche. For d ≳ 4 μ m and γ S E = 0 , DC breakdown voltage increases linearly with d; for γ S E = 0.05 , DC breakdown voltage decreases to a minimum before beginning to increase at larger gap distances. For AC fields with γ S E = 0.05 , V behaves similarly to the DC case with the decrease corresponding to secondary emission occurring at higher voltages and larger gap distances with increasing frequency. At 10 GHz and γ S E = 0.05 , V resembles that of the DC case with γ S E = 0 up to ∼8 μm, suggesting that increasing the frequency effectively changes the number of ions striking the electrodes and the resulting electrons released. Phase space plots showing electron and ion velocities as a function of position across the gap show that electrons and ions are increasingly trapped within the gap with increasing frequency, reducing the number of ions that can strike the cathode and the subsequent secondary emission. Incorporating the resulting effective secondary emission coefficient for AC microscale gaps yields a simple phenomenologically based modification of the DC microscale gas breakdown equation. [ABSTRACT FROM AUTHOR]

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system–bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu–Planck potentials as entropic potentials and the Helmholtz–Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker–Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system–bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions. [ABSTRACT FROM AUTHOR]

This study focuses on conducting an ab initio evolutionary investigation to search for stable polymorphs of iron diborocarbides with the formula FeB 2 C 2. We also examined other forms of C contents, including FeB 3 C and FeBC 3. Our findings reveal that the lowest energetic structure of FeB 2 C 2 is a semimetallic monoclinic phase with a space group (s.g.) of C2/m and a metastable metallic phase of FeB 2 C 2 is an orthorhombic structure with s.g. of Pmmm. In addition, structural and relative properties of FeB 3 C and FeBC 3 are performed and discussed to compare with FeB 2 C 2. All predicted structures are dynamically and elastically stable, verified without negative phonon frequency and Born criteria, respectively. We also analyzed the energetic stability through calculated cohesive and formation energies, which showed that C2/m- FeB 2 C 2 is stable at low pressure. Interestingly, the C2/m and Pmmm phases of FeB 2 C 2 are hard materials with Vickers hardness ( H v) of 22.40 and 27.52 GPa, respectively. Additionally, we examined the electron–phonon coupling of both FeB 2 C 2 phases. Unexpectedly, we found that the semimetallic C2/m- FeB 2 C 2 phase is a superconductor with a significant superconducting temperature ( T c) exceeding 6 K. These findings provide some novel results for the Fe–B–C system and pave the way for investigating other metal borocarbides and related ternary compounds. [ABSTRACT FROM AUTHOR]

Modern electronic structure theory is built around the Born–Oppenheimer approximation and the construction of an electronic Hamiltonian H ̂ e l (X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ′) and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, H ̂ P S (X , P). While classical Born–Oppenheimer dynamics that run along the eigensurfaces of the operator H ̂ e l (X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of H ̂ P S (X , P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general. [ABSTRACT FROM AUTHOR]

Time-Resolved Serial Femtosecond Crystallography (TR-SFX) conducted at X-ray Free Electron Lasers (XFELs) has become a powerful tool for capturing macromolecular structural movies of light-initiated processes. As the capabilities of XFELs advance, we anticipate that a new range of coherent control and structural Raman measurements will become achievable. Shorter optical and x-ray pulse durations and increasingly more exotic pulse regimes are becoming available at free electron lasers. Moreover, with high repetition enabled by the superconducting technology of European XFEL (EuXFEL) and Linac Coherent Light Source (LCLS-II) , it will be possible to improve the signal-to-noise ratio of the light-induced differences, allowing for the observation of vibronic motion on the sub-Angstrom level. To predict and assign this coherent motion, which is measurable with a structural technique, new theoretical approaches must be developed. In this paper, we present a theoretical density matrix approach to model the various population and coherent dynamics of a system, which considers molecular system parameters and excitation conditions. We emphasize the use of the Wigner transform of the time-dependent density matrix, which provides a phase space representation that can be directly compared to the experimental positional displacements measured in a TR-SFX experiment. Here, we extend the results from simple models to include more realistic schemes that include large relaxation terms. We explore a variety of pulse schemes using multiple model systems using realistic parameters. An open-source software package is provided to perform the density matrix simulation and Wigner transformations. The open-source software allows us to define any arbitrary level schemes as well as any arbitrary electric field in the interaction Hamiltonian. [ABSTRACT FROM AUTHOR]

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π, vi = 1, 3, ji = 0, 1) → H + NO+(X1Σ+) has been studied based on the recently constructed diabatic potential energy matrix. It was found that the vibrational excitation of reactant NO inhibits the reactivity, while the rotational excitation of reactant NO has little effect on the reaction probability. These attributes were also observed in the semi-classical trajectory calculations employed in the adiabatic representation. Such an inhibitory effect of the vibrational excitation of reactant NO was owing to lower accessibility of the conical intersection and avoided crossing regions, which are located in the wells with respect to the Π diabat, as evidenced by the analysis of the population of the time-independent wave functions. Calculated vibrational state distributions of the product show that the decrease of the reaction mainly leads to the less formation of low vibrational states (vf < 6), and the product vibrational state distributions are more evenly populated for vi = 1 and 3, suggesting a non-statistical behavior. However, the overall shapes of the product rotational distributions remain unchanged, indicating that the redistribution of energy into the rotation of product NO is sufficient in the charge transfer process between H+ and NO. While the reaction is dominated by the forward and backward scattering in differential cross sections (DCSs), consistent with the complex-forming mechanism, a clear forward bias in the DCSs appears, indicating that the occurrence of the reaction is not sufficiently long to undergo the whole phase space of the interaction configurations. [ABSTRACT FROM AUTHOR]

The effect of ring stiffness and pressure on the glassy dynamics of a thermal assembly of two-dimensional ring polymers is investigated using extensive coarse-grained molecular dynamics simulations. In all cases, dynamical slowing down is observed with increasing pressure, and thereby, a phase space for equilibrium dynamics is identified in the plane of the obtained monomer density and ring stiffness. When the rings are highly flexible, i.e., have low ring stiffness, glassiness sets in via the crowding of crumpled polymers, which take on a globular form. In contrast, at large ring stiffness, when the rings tend to have large asphericity under compaction, we observe the emergence of local domains having orientational ordering at high pressures. Therefore, our simulations highlight how varying the deformability of rings leads to contrasting mechanisms in driving the system toward the glassy regime. [ABSTRACT FROM AUTHOR]

As an optimal one-dimensional reaction coordinate, the committor function not only describes the probability of a trajectory initiated at a phase space point first reaching the product state before reaching the reactant state but also preserves the kinetics when utilized to run a reduced dynamics model. However, calculating the committor function in high-dimensional systems poses significant challenges. In this paper, within the framework of milestoning, exact expressions for committor functions at two levels of coarse graining are given, including committor functions of phase space point to point (CFPP) and milestone to milestone (CFMM). When combined with transition kernels obtained from trajectory analysis, these expressions can be utilized to accurately and efficiently compute the committor functions. Furthermore, based on the calculated committor functions, an adaptive algorithm is developed to gradually refine the transition state region. Finally, two model examples are employed to assess the accuracy of these different formulations of committor functions. [ABSTRACT FROM AUTHOR]

The performance of Hamiltonian Monte Carlo simulations crucially depends on both the integration timestep and the number of integration steps. We present an adaptive general-purpose framework to automatically tune such parameters based on a local loss function that promotes the fast exploration of phase space. We show that a good correspondence between loss and autocorrelation time can be established, allowing for gradient-based optimization using a fully differentiable set-up. The loss is constructed in such a way that it also allows for gradient-driven learning of a distribution over the number of integration steps. Our approach is demonstrated for the one-dimensional harmonic oscillator and alanine dipeptide, a small protein commonly used as a test case for simulation methods. Through the application to the harmonic oscillator, we highlight the importance of not using a fixed timestep to avoid a rugged loss surface with many local minima, otherwise trapping the optimization. In the case of alanine dipeptide, by tuning the only free parameter of our loss definition, we find a good correspondence between it and the autocorrelation times, resulting in a > 100 fold speedup in the optimization of simulation parameters compared to a grid search. For this system, we also extend the integrator to allow for atom-dependent timesteps, providing a further reduction of 25% in autocorrelation times. [ABSTRACT FROM AUTHOR]

Preparation of atomic Bose–Einstein condensate (BEC) with tunable interactions in a quasi-one-dimensional (quasi-1D) optical trap is essential for both the observation of bright matter-wave solitons and the quantum simulation based on the discrete atomic momentum states. However, the quasi-1D BEC has been obtained by a complex process, which includes the creation of a three-dimensional BEC and its adiabatic transform into a quasi-1D trap. Here, we report the direct creation of a quasi-1D BEC of 133 Cs atoms by the fast evaporative cooling of ultracold atoms prepared by the degenerated Raman sideband cooling. We produce the pure BEC of up to 5.5 × 10 4 atoms in a quasi-1D optical trap with an evaporative time of 6 s. We demonstrate the anisotropic expansion of the atomic cloud after the release from the quasi-1D trap and study the dependence of both the phase space density and the temperature on the number of atoms in the trap during the evaporative cooling. Our study facilitates the promising applications of quasi-1D interacting atomic gases. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

We have reanalyzed the rich plethora of ground state configurations of the asymmetric Wigner bilayer system that we had recently published in a related diagram of states [Antlanger et al., Phys. Rev. Lett. 117, 118002 (2016)], comprising roughly 60 000 state points in the phase space spanned by the distance between the plates and the charge asymmetry parameter of the system. In contrast to this preceding contribution where the classification of the emerging structures was carried out "by hand," we have used for the present contribution machine learning concepts, notably based on a principal component analysis and a k-means clustering approach: using a 30-dimensional feature vector for each emerging structure (containing relevant information, such as the composition of the configuration as well as the most relevant order parameters), we were able to reanalyze these ground state configurations in a considerably more systematic and comprehensive manner than we could possibly do in the previously published classification scheme. Indeed, we were now able to identify new structures in previously unclassified regions of the parameter space and could considerably refine the previous classification scheme, thereby identifying a rich wealth of new emerging ground state configurations. Thorough consistency checks confirm the validity of the newly defined diagram of states. [ABSTRACT FROM AUTHOR]

We simulate the nonadiabatic dynamics of photo-induced isomerization and dissociation in ethylene using ab initio classical trajectories in an extended phase space of nuclear and electronic variables. This is achieved by employing the linearized semiclassical initial value representation method for nonadiabatic dynamics, where discrete electronic states are mapped to continuous classical variables using either the Meyer–Miller–Stock–Thoss representation or a more recently introduced spin mapping approach. Trajectory initial conditions are sampled by constraining electronic state variables to a single initial excited state and by drawing nuclear phase space configurations from a Wigner distribution at a finite temperature. An ensemble of classical ab initio trajectories is then generated to compute thermal population correlation functions and analyze the mechanisms of isomerization and dissociation. Our results serve as a demonstration that this parameter-free semiclassical approach is computationally efficient and accurate, identifying mechanistic pathways in agreement with previous theoretical studies and also uncovering dissociation pathways observed experimentally. [ABSTRACT FROM AUTHOR]

The effect of the presence of Ar on the isomerization reaction HCN ⇄ CNH is investigated via machine learning. After the potential energy surface function is developed based on the CCSD(T)/aug-cc-pVQZ level ab initio calculations, classical trajectory simulations are performed. Subsequently, with the aim of extracting insights into the reaction dynamics, the obtained reactivity, that is, whether the reaction occurs or not under a given initial condition, is learned as a function of the initial positions and momenta of all the atoms in the system. The prediction accuracy of the trained model is greater than 95%, indicating that machine learning captures the features of the phase space that affect reactivity. Machine learning models are shown to successfully reproduce reactivity boundaries without any prior knowledge of classical reaction dynamics theory. Subsequent analyses reveal that the Ar atom affects the reaction by displacing the effective saddle point. When the Ar atom is positioned close to the N atom (resp. the C atom), the saddle point shifts to the CNH (HCN) region, which disfavors the forward (backward) reaction. The results imply that analyses aided by machine learning are promising tools for enhancing the understanding of reaction dynamics. [ABSTRACT FROM AUTHOR]

The importance of microwave device reliability and performance for microscale devices motivates a more fundamental understanding of breakdown mechanisms in this regime. Microwave breakdown theories predict breakdown when electron production balances electron loss. Electron production depends strongly on the ionization rate ν i ; however, previous studies either used the measured ν i in macroscale gaps or the empirical formula for DC voltage, inaccurately predicting ν i in microscale gaps. Alternatively, this work characterizes ν i in microwave microplasmas by using particle-in-cell simulations. We calculated ν i in argon gas at atmospheric pressure for 2–10 μm gaps under AC fields ranging from 1 to 1000 GHz. The behavior of ν i may be separated into two regimes by defining a critical frequency f c r that depends on the amplitude of the applied voltage, gap distance, and pressure. For frequency f < f c r , the electrodes collect the electrons during each cycle and the electron number oscillates with the electric field, causing ν i / f to roughly scale with the reduced effective field E e f f / p. For f > --> f c r , the phase-space plots indicate that the electrons are confined inside the gap, causing the electron number to grow exponentially and v i / p to become a function of E e f f / p. These results elucidate the ionization mechanism for AC fields at microscale gap distances and may be incorporated into field emission-driven microwave breakdown theories to improve their predictive capability. [ABSTRACT FROM AUTHOR]

Explanation for the modification of rates and mechanism of reactions carried out in optical cavities still eludes us. Several studies indicate that the cavity-mediated changes in the nature of vibrational energy flow within a molecule may play a significant role. Here, we study a model polaritonic system, proposed and analyzed earlier by Fischer et al., J. Chem. Phys. 156, 154305 (2022), comprising a one-dimensional isomerization mode coupled to a single photon mode in a lossless cavity. We show that the isomerization probability in the presence of virtual photons, for specific cavity–system coupling strengths and cavity frequencies, can exhibit suppression or enhancement for different choices of the initial reactant vibropolariton wavepacket. We observe a qualitative agreement between the classical and quantum average isomerization probabilities in the virtual photon case. A significant part of the effects due to coupling to the cavity can be rationalized in terms of a "chaos–order–chaos" transition of the classical phase space and the phase space localization nature of the polariton states that dominantly participate in the quantum isomerization dynamics. On the other hand, for initial states with zero photons (i.e., a "dark cavity"), the isomerization probability is suppressed when the cavity frequency is tuned near to the fundamental frequency of the reactive mode. The classical–quantum correspondence in the zero photon case is unsatisfactory. In this simple model, we find that the suppression or enhancement of isomerization arises due to the interplay between cavity–system energy flow dynamics and quantum tunneling. [ABSTRACT FROM AUTHOR]

Accurate tool wear state identification models are essential to ensure manufacturing reliability and efficiency. Tool wear state recognition systems establish a mapping relationship with the tool state by extracting signal features. Therefore, this paper proposes an architecture for identifying the actual wear state of data unbalanced machining tools by applying the power of minimalism in deep learning networks, namely, VanillaNet, combined with recurrence plot encoding technology (RP). In this paper, the signal is preprocessed by RP, and the nonlinear one-dimensional time-sequential digital signal embedded in variable time-lag delay coordinate space in the phase space is converted into a two-dimensional (2D) color texture image, thereby achieving the feature extraction of tool wear. Then, the data-enhanced 2D recurrence coded image is used as the input to VanillaNet, and its minimalist network architecture is applied to establish the mapping relationship between tool wear states and wear features. This process reduces the state recognition time and achieves the fast recognition of tool wear states. The model in this paper achieves more than 95 % on all four classification metrics: accuracy, recall, F1 score, and precision in three sets of crossover experiments while reducing misclassification in the sharp wear phase. The proposed model also outperforms three DL-based methods, namely, CNN-Attention, AlexNet, and ResNet. [ABSTRACT FROM AUTHOR]

This study proposes an innovative expert system that uses exclusively EEG signals to diagnose schizophrenia in its early stages. For diagnosing psychiatric/neurological disorders, electroencephalogram (EEG) testing is considered a financially viable, safe, and reliable alternative. Using the reconstructed phase space (RPS) and the continuous wavelet transform, the researchers maximized the differences between the EEG nonstationary signals of normal and schizophrenia individuals, which cannot be observed in the time, frequency, or time-frequency domains. This reveals significant information, highlighting more distinguishable features. Then, a deep learning network was trained to enhance the accuracy of the resulting image classification. The algorithm's efficacy was confirmed through three distinct methods: employing 70% of the dataset for training, 15% for validation, and the remaining 15% for testing. This was followed by a 5-fold cross-validation technique and a leave-one-out classification approach. Each method was iterated 100 times to ascertain the algorithm's robustness. The performance metrics derived from these tests — accuracy, precision, sensitivity, F1 score, Matthews correlation coefficient, and Kappa — indicated remarkable outcomes. The algorithm demonstrated steady performance across all evaluation strategies, underscoring its relevance and reliability. The outcomes validate the system's accuracy, precision, sensitivity, and robustness by showcasing its capability to autonomously differentiate individuals diagnosed with schizophrenia from those in a state of normal health. [ABSTRACT FROM AUTHOR]

High Q (Hf1−xSnx)O2 ceramics were prepared via a standard solid‐state reaction route, and the microwave dielectric characteristics were investigated systematically together with the structure evolution. With increasing x, the structure changed from HfO2 (monoclinic in space group P21/c, x = 0 and 0.03) to Hf0.77Sn0.23O2 (orthorhombic in space group Pbcn, x = 0.23), while the two‐phase structure: HfO2 major phase and Hf0.77Sn0.23O2 secondary phase, was determined for x = 0.05–0.21, and Hf0.77Sn0.23O2 major phase combined with SnO2 tetragonal secondary phase in space group P42/mnm was confirmed for x = 0.30–0.40. The Qf value was significantly increased from 24,500 to 167,650 GHz by Sn‐substitution, and the best combination of microwave dielectric characteristics was obtained in Hf0.77Sn0.23O2 ceramics: εr = 17.2, Qf = 167 650 GHz at 9.6 GHz and 230 710 GHz at 26.1 GHz, and τf = −52.6 ppm/°C. The dielectric loss was deeply linked with the structure stability and lattice‐distortion. Also, the phase composition, the bond strength, as well as the degree of covalency, had a tight connection with dielectric loss. The present ceramics were expected to be the promising candidates as low‐εr microwave dielectric ceramics. [ABSTRACT FROM AUTHOR]

In ITER, disruption-born runaway electrons (REs), unless mitigated, are expected to form a several Mega-Ampere beam that ultimately intercepts the first wall leading to melting of the plasma facing components. Developing a successful mitigation strategy therefore requires modeling that takes into account the coupling between REs and the MHD during the formation and termination of the beam, along with estimates for the wall loads that can be compared to design values. Using the JOREK code, this work aims to provide the latter by presenting a novel model for collisions between REs and the wall and applying it to a beam termination scenario in ITER. To this end, the transport of REs is modeled by tracing particles in the fields calculated by preceding simulations of the disruption event where REs were treated in the fluid picture and self-consistently coupled to the MHD. The resulting heat loads are found to be highly localized in both the poloidal and toroidal directions, with 3D features also playing an important role in the appearance of hot spots. Peak loads were on the order of 10 7 − 10 8 J m 2 . The load distribution was found to only be weakly sensitive to the initial phase space distribution of the REs when decoupled from the fields, while modifying properties of the underlying MHD yielded notable differences in wetted area and peak loads, in particular for cases with higher resistivity. [ABSTRACT FROM AUTHOR]

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator–prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, promising but simple schemes are investigated to enhance the micro-bunching of relativistic electron beams for coherent harmonic generation (CHG) by using phase merging effects. In contrast to the standard CHG scheme, two specially designed dispersion sections (DSs) are adopted with the DS-modulator–DS configuration. The phase space of the e beam is appropriately coupled in the first DS, and the electrons within one seed wavelength can merge to the same phase with a matched second DS. Micro-bunching of the e beam can thus be enhanced by a large margin with much higher-harmonic components. Taking e beams from laser wakefield accelerators (LWFAs) as an example, start-to-end simulations are performed to show the effectiveness and robustness of the proposed schemes with several configurations. The beam current can be optimized to several tens to hundreds of kiloamperes, and the radiation power reaches hundreds of megawatts in the extreme ultraviolet regime within a 3.5 m-long beamline. The proposed schemes offer new opportunities for future compact free-electron lasers driven by LWFAs and provides prospects for truly compact and widely applicable systems. [ABSTRACT FROM AUTHOR]

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We report an isothermal electric field-induced first-order phase transition from a Mott insulator to the metallic state in the epitaxial thin film of V 2 O 3 in the temperature regime below its Mott transition temperature of ≈ 180 K. This isothermal electric field-induced transition is accompanied by interesting electrothermal history effects, which depend on the measurement paths followed in the electric field–temperature phase space. These interesting properties result in tuneable resistive switching and distinct memristive behaviour in V 2 O 3 . A generalized framework of disorder-influenced first-order phase transition in combination with a resistor network model has been used to explain the observed experimental features. These findings promise possibilities for Mott insulators to be used as highly energy-efficient switches in novel technologies such as neuromorphic computing. [ABSTRACT FROM AUTHOR]

Single-cell omics technologies can measure millions of cells for up to thousands of biomolecular features, enabling data-driven studies of complex biological networks. However, these high-throughput experimental techniques often cannot track individual cells over time, thus complicating the understanding of dynamics such as time trajectories of cell states. These "dynamical phenotypes" are key to understanding biological phenomena such as differentiation fates. We show by mathematical analysis that, in spite of high dimensionality and lack of individual cell traces, three time-points of single-cell omics data are theoretically necessary and sufficient to uniquely determine the network interaction matrix and associated dynamics. Moreover, we show through numerical simulations that an interaction matrix can be accurately determined with three or more time-points even in the presence of sampling and measurement noise typical of single-cell omics. Our results can guide the design of single-cell omics time-course experiments, and provide a tool for data-driven phase-space analysis. [ABSTRACT FROM AUTHOR]

Overdensities in the radial phase space |$(r,v_{\rm r})$| of the Milky Way's halo have previously been associated with the phase-mixed debris of a highly radial merger event such as Gaia Sausage–Enceladus. We present and test an alternative theory in which the overdense 'chevrons' are instead composed of stars trapped in resonances with the Galactic bar. We develop an analytic model of resonant orbits in the isochrone potential, and complement this with a test particle simulation of a stellar halo in a realistic barred Milky Way potential. These models are used to predict the appearance of action space |$(J_\phi ,J_{\rm r})$| and radial phase space in the Solar neighbourhood. They are able to reproduce almost all salient features of the observed chevrons. In particular, both the analytic model and simulation predict that the chevrons are more prominent at |$v_{\rm r}\ \lt\ 0$| when viewed near the Sun, as is observed by Gaia. This is inconsistent with formation by an ancient merger event. We also associate individual chevrons with specific resonances. At a bar pattern speed of |$\Omega _\mathrm{b}=35$| km s |$^{-1}$|  kpc |$^{-1}$|⁠ , the two most prominent prograde chevrons align very closely with the corotation and outer Lindblad resonances. The former can be viewed as a highly eccentric extension of the Hercules stream. Finally, our model predicts that the |$v_{\rm r}$| asymmetry changes sign as a function of Galactic radius and azimuth, and we find evidence that this is indeed the case in the Milky Way. [ABSTRACT FROM AUTHOR]

Abstract\nHighlightsThe calcium ferrite nanoparticles were made by the sol–gel process. X-ray diffraction, a scanning electron microscope, and UV–vis spectroscopy were used to analyze the material. There is an orthorhombic phase in the space group Pnma. There were four techniques used to calculate the average crystallite size. Using ImageJ software, the particles were aggregated and their size was ascertained. Using energy-dispersive X-ray (EDX) analysis, the composition of the material was ascertained. 2.29 eV was determined to be the band gap. Vibrating test magnetometer (VSM) provided an explanation for the materials’ magnetic property. A decreased band gap energy is responsible for the 90% degradation of malachite green dye at a concentration of 15 mg/L in 150 min, with a four-cycle reusability.Calcium ferrite nanoparticles were successfully synthesized by sol–gel assisted combustion method using leaf extract of Brassica oleracea as fuel.To the best of the author’s knowledge, no such case study that reports the synthesis of calcium ferrite nanoparticles by using leaf extract of Brassica oleracea is previously reported in academic literature.The method is cost-effective and convenient without the use of any chemical fuel agents.The synthesized prepared material efficiently removes malachite green dye, commonly used in industries for dyeing silk and nylon, from the solution.More than 90 % removal efficiency for MB.The material displayed excellent stability and reusability for dyes adsorption.Results were validated with pseudo-first-order kinetic model.Calcium ferrite nanoparticles were successfully synthesized by sol–gel assisted combustion method using leaf extract of Brassica oleracea as fuel.To the best of the author’s knowledge, no such case study that reports the synthesis of calcium ferrite nanoparticles by using leaf extract of Brassica oleracea is previously reported in academic literature.The method is cost-effective and convenient without the use of any chemical fuel agents.The synthesized prepared material efficiently removes malachite green dye, commonly used in industries for dyeing silk and nylon, from the solution.More than 90 % removal efficiency for MB.The material displayed excellent stability and reusability for dyes adsorption.Results were validated with pseudo-first-order kinetic model. [ABSTRACT FROM AUTHOR]

Electrical triggering of a metal-insulator transition (MIT) often results in the formation of characteristic spatial patterns such as a metallic filament percolating through an insulating matrix or an insulating barrier splitting a conducting matrix. When MIT triggering is driven by electrothermal effects, the temperature of the filament or barrier can be substantially higher than the rest of the material. Using X-ray microdiffraction and dark-field X-ray microscopy, we show that electrothermal MIT triggering leads to the development of an inhomogeneous strain profile across the switching device, even when the material does not undergo a pronounced, discontinuous structural transition coinciding with the MIT. Diffraction measurements further reveal evidence of unique features associated with MIT triggering including lattice distortions, tilting, and twinning, which indicate structural nonuniformity of both low-and high-resistance regions inside the switching device. Such lattice deformations do not occur under equilibrium, zero-voltage conditions, highlighting the qualitative difference between states achieved through increasing temperature and applying voltage in nonlinear electrothermal materials. Electrically induced strain, lattice distortions, and twinning could have important contributions in the MIT triggering process and drive the material into nonequilibrium states, providing an unconventional pathway to explore the phase space in strongly correlated electronic systems. [ABSTRACT FROM AUTHOR]

This work continues the review and illustrative application to energy systems of the "Fourth-Order Best-Estimate Results with Reduced Uncertainties Predictive Modeling" (4th-BERRU-PM) methodology. The 4th-BERRU-PM methodology uses the Maximum Entropy (MaxEnt) principle to incorporate fourth-order experimental and computational information, including fourth (and higher) order sensitivities of computed model responses with respect to model parameters. The 4th-BERRU-PM methodology yields the fourth-order MaxEnt posterior distribution of experimentally measured and computed model responses and parameters in the combined phase space of model responses and parameters. The 4th-BERRU-PM methodology encompasses fourth-order sensitivity analysis (SA) and uncertainty quantification (UQ), which were reviewed in the accompanying work (Part 1), as well as fourth-order data assimilation (DA) and model calibration (MC) capabilities, which will be reviewed and illustrated in this work (Part 2). The applicability of the 4th-BERRU-PM methodology to energy systems is illustrated by using the Polyethylene-Reflected Plutonium (acronym: PERP) OECD/NEA reactor physics benchmark, which is modeled using the linear neutron transport Boltzmann equation, involving 21,976 imprecisely known parameters. This benchmark is representative of "large-scale computations" such as those involved in the modeling of energy systems. The result ("response") of interest for the PERP benchmark is the leakage of neutrons through the outer surface of this spherical benchmark, which can be computed numerically and measured experimentally. The impact of the high-order sensitivities of the response with respect to the PERP model parameters is quantified for "high-precision" parameters (2% standard deviations) and "typical-precision" parameters (5% standard deviations). Analyzing the best-estimate results with reduced uncertainties for the 1st—through 4th-order moments (mean values, covariance, skewness, and kurtosis) produced by the 4th-BERRU-PM methodology for the PERP benchmark indicates that, even for systems modeled by linear equations (e.g., the PERP benchmark), retaining only first-order sensitivities is insufficient for reliable predictive modeling (including SA, UQ, DA, and MC). At least second-order sensitivities should be retained in order to obtain reliable predictions. [ABSTRACT FROM AUTHOR]

The pressure-induced structural changes in the perovskite-type (ABO 3 ) ferroelectric solid solution (1-x)Na 0.5 Bi 0.5 TiO 3 -xBaTiO 3 (NBT-xBT) at the morphotropic phase boundary (MPB) ( x MPB = 0.048 ) have been analyzed up to 12.3 GPa by single-crystal x-ray diffraction with synchrotron radiation. A pressure-induced phase transition takes place between 4.4 and 5.0 GPa, where the pseudocubic low-pressure phase transforms into an orthorhombic high-pressure phase with space group Pnma. The high-pressure phase is comprised of mixed BO 6 tilts and anti-polar A-cation displacements, without exhibiting coherent off-centered shifts of the B-site Ti 4 + cations that can be detected by synchrotron x-ray diffraction. Our results reveal that at ambient pressure and room temperature the NBT- x MPB BT structure possesses anti-phase BO 6 tilts with a relatively large correlation length and the same type of polar distortions as those present in pure NBT, but with strongly violated correlation length due to Ba 2 + -induced local elastic-stress fields. For x MPB the effect of Ba on the mesoscopic-scale structure is compensated by a mild external pressure of only 0.7 GPa, resulting in structural features resembling those of pure NBT at ambient conditions. [ABSTRACT FROM AUTHOR]

Due to the lack of field monitoring points, the monitoring data is incomplete, making it difficult to obtain more complete characteristics of mining subsidence. To address this issue, a novel method for interpolating missing subsidence points is proposed. Firstly, the subsidence data are decomposed into multi-frequency domains utilizing the empirical mode decomposition (EMD) method. Subsequently, the missing subsidence data are reconstructed by combining the radial basis function (RBF) with phase space reconstruction technology. The interpolation accuracy is then analyzed under various conditions, including different mining degrees, sample numbers, and observation point locations. The results indicate that the interpolation accuracy increases with the mining degree coefficient. During the active stage of surface subsidence, a larger sample number correlates positively with higher interpolation accuracy. However, in the recession stage, the impact of sample number on interpolation accuracy is less pronounced compared to the timeliness of sample acquisition. The location of observation points has minimal effect on interpolation accuracy. By applying this method to the 833 working face in the Shanjiacun coal mine, the mean absolute percentage error (MAPE) is less than 20%, and the mean squared error (MSE) is below 0.5 mm, objectively demonstrating the method's effectiveness and engineering applicability. These research findings offer valuable technical support for mine safety production and ecological environment protection. [ABSTRACT FROM AUTHOR]

Possible squeezed states generated in a three-waveguide nonlinear coupler operating with second harmonic generation is discussed. This study is carried out using two well-known techniques; the phase space method (based on positive-P representation) and the Heisenberg-based analytical perturbative (AP) method. The effects of key design parameters were investigated under various conditions, including full frequency matching, symmetrical and asymmetrical waveguide initialization, and both codirectional and contr-adirectional propagation. The system consistently produced long-lasting oscillatory squeezed states across all three waveguides, even when only one waveguide was pumped with coherent light while the others were in a vacuum state. Also, the performance and capacities of both methods are critically evaluated. For low levels of key design parameters and in the early stages of evolution, a high level of agreement between the two methods is noticed. In the new era of quantum-based technology, the proposed system opens a new avenue for utilising nonlinear couplers in nonclassical light generation. [ABSTRACT FROM AUTHOR]

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding simulations, and inherent uncertainties in the system. We propose a two-step unsupervised deep learning framework named as Conditional Latent Autoregressive Recurrent Model (CLARM) for learning the spatiotemporal dynamics of charged particles in accelerators. CLARM consists of a Conditional Variational Autoencoder transforming six-dimensional phase space into a lower-dimensional latent distribution and a Long Short-Term Memory network capturing temporal dynamics in an autoregressive manner. The CLARM can generate projections at various accelerator modules by sampling and decoding the latent space representation. The model also forecasts future states (downstream locations) of charged particles from past states (upstream locations). The results demonstrate that the generative and forecasting ability of the proposed approach is promising when tested against a variety of evaluation metrics. [ABSTRACT FROM AUTHOR]

Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks. [ABSTRACT FROM AUTHOR]

Understanding flame-acoustics interaction (FAI) that can potentially trigger thermoacoustic instabilities is of critical importance to mitigate the serious side effects of pressure oscillations. While FAI has been studied extensively in premixed flames, comparatively less analysis has been conducted to explore FAI mechanisms in non-premixed flames, especially under high-pressure conditions. This study aims to numerically investigate FAI in high-pressure hydrogen/air counterflow diffusion flames, with special attention on the impact of pressure on FAI. To this end, a fully compressible unsteady counterflow solver combined with Navier-Stokes Characteristic Boundary Conditions (NSCBC) is employed to capture the reflection of the acoustic waves at the boundaries. The results show that for all ambient pressures ( $ 1\leq P_a\leq 60 $ 1 ≤ P a ≤ 60 bar) considered here, real-gas effects on flame structures are negligible and that increasing $ P_a $ P a would lead to a power-law dependence of density gradient on $ P_a $ P a with an exponent of 1.5. Furthermore, all tested cases show acoustic growth with time under fully reflecting boundary conditions, which is found to be pressure dependent. The flames become less resilient to FAI when the pressure (or density gradient) is increased. The results from the spectral analysis show that for all ambient pressures, there is only a single dominant frequency at the low-density fuel side and two dominant frequencies at the high-density oxidiser side. This indicates that the pressure oscillation is more sinusoidal at the H $ _2 $ 2 side than that at the air side. Moreover, the phase space portraits of pressure signals indicate that the dynamics of the system are becoming periodic and approaching a limit cycle. It is found that the integrated heat release rate and the pressure fluctuations are partially in phase, which is responsible for the growth of high-frequency acoustic waves at both fuel and oxidiser sides. On the other hand, the significant density gradient contributes to the growth of low-frequency acoustic waves at the oxidiser side due to the high degree of acoustic reflectivity at the density boundary. [ABSTRACT FROM AUTHOR]

La0.6Sr0.4CoO3 (LSC) coatings with a thickness of 50–100 µm were deposited on Fe-25Cr ferritic stainless steel (DIN 50049) via screen printing. The required suspension had been prepared using fine LSC powders synthesised using EDTA gel processes. In its bulk form, the LSC consisted entirely of the rhombohedral phase with space group R-3c, and it exhibited high electrical conductivity (~144 S·cm−1). LSC-coated steel was oxidised in air at 1073 K, i.e., under conditions corresponding to SOFC cathode operation, for times of up to 144 h. The in situ electrical resistance of the steel/La0.6Sr0.4CoO3 layered system during oxidation was measured. The products formed on the samples after the oxidation reaction resulting from exposure to the corrosive medium were investigated using XRD, SEM-EDS, and TEM-SAD. The microstructural, nanostructural, phase, and chemical analysis of films was performed with a focus on the film/substrate interface. It was determined that the LSC coating interacts with the oxidised steel in the applied conditions, and a multi-layer interfacial zone is formed. Detailed TEM-SAD observations indicated the formation of a main layer consisting of SrCrO4, which was the reaction product of (La,Sr)CoO3, and the Cr2O3 scale formed on the metal surface. The formation of the SrCrO4 phase resulted in improved electrical conductivity of the investigated metal/ceramics layered composite material, as demonstrated by the low area-specific resistance values of 5 mΩ·cm2, thus making it potentially useful as a SOFC interconnect material operating at the tested temperature. In addition, the evaporation rate of chromium measured for the uncoated steel and the steel/La0.6Sr0.4CoO3 layered system likewise indicates that the coating is capable of acting as an effective barrier against the formation of volatile compounds of chromium. [ABSTRACT FROM AUTHOR]

In prior studies [0, Katsanikas & Wiggins, 0, 2021a, 0, 2021b, 0, 2023a, 0, 2023b], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored specifically for Hamiltonian systems with three or more degrees of freedom. These approaches, as described in the aforementioned papers, were applied to a quadratic Hamiltonian system in its normal form with three degrees of freedom. Within this framework, we provide a more intricate geometric characterization of this entity within the family of 4D toratopes which elucidates the structure of the dividing surfaces discussed in these works. Our analysis affirmed the nature of this construction as a dividing surface with the property of no-recrossing. These insights were derived from analytical findings tailored to the Hamiltonian system discussed in these publications. In this series of papers, we extend our previous findings to quartic Hamiltonian systems with three degrees of freedom. We establish the no-recrossing property of the PODS for this class of Hamiltonian systems and explore their structural aspects. Additionally, we undertake the computation and examination of the PODS in a coupled scenario of quartic Hamiltonian systems with three degrees of freedom. In the initial paper [Gonzalez Montoya et al., 2024], we employed the first methodology for constructing PODS, while in this paper, we utilize the second methodology for the same purpose. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of periodic orbit-dividing surfaces (PODS) to rotating Hamiltonian systems with two degrees of freedom. First, we present a method that enables us to apply the classical algorithm for the construction of PODS [Pechukas & McLafferty, 1973; Pechukas, 1981; Pollak & Pechukas, 1978; Pollak, 1985] in rotating Hamiltonian systems with two degrees of freedom. Then we study the structure of these surfaces in a rotating quadratic normal-form Hamiltonian system with two degrees of freedom. [ABSTRACT FROM AUTHOR]

Bifurcations of nonlinear and supernonlinear ion-acoustic waves (IAWs) are studied in an electron-ion plasmas with generalized (r, q)-distributed electrons. The IAWs are examined under the Zakharov–Kuznetsov (ZK) and modified ZK equations using the reductive perturbation technique. Transforming both the ZK and mZK equations into their corresponding dynamical systems, all possible phase spaces and potential energy functions are analyzed. The nonlinear periodic and solitary wave solutions are obtained under the ZK and mZK equations. A newly discovered supernonlinear wave, in particular, supernonlinear periodic wave under the modified ZK equation in electron-ion magnetized plasma with (r, q)-distributed electrons is reported for the first time in the literature. Nonlinear and supernonlinear wave solutions are shown under the influence of physical parameters. The proposed study contributes to new wave motions in slow solar wind streams and astrophysical plasmas. [ABSTRACT FROM AUTHOR]

In this paper, we report the discovery of some novel dynamical scenarios for quasi-periodic shrimp-shaped structures embedded within chaotic phases in bi-parameter space of a discrete predator–prey system. By constructing high-resolution, two-dimensional stability diagrams based on Lyapunov exponents, we observe the abundance of both periodic and quasi-periodic shrimp-shaped organized domains in a certain parameter space of the system. A comprehensive comparative analysis is conducted to elucidate the similarities and differences between these two types of shrimps. Our analysis reveals that, unlike periodic shrimp, quasi-periodic shrimp induces (i) torus bubbling transition to chaos and (ii) multistability with multi-tori, torus-chaotic, and multi-chaotic coexisting attractors, resulting from the crossing of its two inner antennae. The basin sets of the coexisting attractors are analyzed, and we observe the presence of intriguing basin boundaries. We also verify that, akin to periodic shrimp structures, quasi-periodic shrimps also maintain the three-times self-similarity scaling. Furthermore, we encounter the occurrence of spiral organization for the self-distribution of quasi-periodic shrimps within a large chaotic domain. We believe that these novel findings will significantly enhance our understanding of shrimp-shaped structures and the intricate dynamics exhibited by their distribution in chaotic regimes. [ABSTRACT FROM AUTHOR]

This research aims to investigate the mechanisms of multistability in chaotic maps. The study commences by examining the fundamental principles governing the development of homogeneous multistability using a basic one-dimensional chain-climbing map. Findings suggest that the phase space can be segmented into distinct uniform mediums where particles exhibit consistent movement. As critical parameter values are reached, channels emerge between these mediums, resulting in deterministic chaotic diffusion. Additionally, the study delves into the topic of introducing heterogeneous factors on the formation of heterogeneous multistability in the one-dimensional map. A thorough examination of phenomena such as multistate intermittency highlights the intimate connection between specific phase transition occurrences and channel formation. Finally, by analyzing two instances—a memristive chaotic map and a hyperchaotic map—the underlying factors contributing to the emergence of multistability are scrutinized. This study offers an alternative perspective for verifying the fundamental principles of homogenous and heterogeneous multistability in complex high-dimensional chaotic maps. [ABSTRACT FROM AUTHOR]

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N ≫ 1 , as it undergoes a free expansion doubling its volume. The microstate of the system changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ α . The initial and final macrostates of the system are thermal equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ α . The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ α . Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δ v : it produces entropy at a rate proportional to Δ v . This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δ v and is given by the Boltzmann equation for the limit Δ v → 0 . We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes. [ABSTRACT FROM AUTHOR]

This study proposes deterministic and stochastic energy‐aware hybrid models that should enable simulations of idealized and primitive‐equations Geophysical Fluid Dynamics (GFD) models at low resolutions without compromising on quality compared with high‐resolution runs. Such hybrid models bridge the data‐driven and physics‐driven modeling paradigms by combining regional stability and classical GFD models at low resolution that cannot reproduce high‐resolution reference flow features (large‐scale flows and small‐scale vortices) which are, however, resolved. Hybrid models use an energy‐aware correction of advection velocity and extra forcing compensating for the drift of the low‐resolution model away from the reference phase space. The main advantages of hybrid models are that they allow for physics‐driven flow recombination within the reference energy band, reproduce resolved reference flow features, and produce more accurate ensemble forecasts than their classical GFD counterparts. Hybrid models offer appealing benefits and flexibility to the modeling and forecasting communities, as they are computationally cheap and can use both numerically‐computed flows and observations from different sources. All these suggest that the hybrid approach has the potential to exploit low‐resolution models for long‐term weather forecasts and climate projections thus offering a new cost effective way of GFD modeling. The proposed hybrid approach has been tested on a three‐layer quasi‐geostrophic model for a beta‐plane Gulf Stream flow configuration. The results show that the low‐resolution hybrid model reproduces the reference flow features that are resolved on the coarse grid and also gives a more accurate ensemble forecast than the physics‐driven model. Plain Language Summary: Reliable weather forecast and climate prediction are crucial for socio‐economic sectors, decision making, and strategic planning for mitigating risks and impacts of natural disasters. In order to forecast weather and climate, observations and numerical models are used. A necessary ingredient for these forecasts is the ocean‐atmospheric model that resolves mesoscale oceanic eddies and can use large ensembles (hundred of members). Supercomputers can run eddy‐resolving simulations but only for single runs or use large ensembles but in non‐eddy‐resolving regimes. Applying the large ensemble approach with eddy‐resolving simulations is far beyond what supercomputers will be able to compute for the next decades, while it is urgently needed. This study offers deterministic and stochastic energy‐aware hybrid models that enable simulations of Geophysical Fluid Dynamics models at low resolutions without compromising on quality compared with high‐resolution runs. The use of low resolutions makes hybrid models much faster than high‐resolution physics‐driven runs. This acceleration can be translated into the use of larger ensembles. Thus, the proposed hybrid approach has the potential to exploit large ensembles of high‐quality solutions for long‐term weather forecasts and climate projections for the very first time. Key Points: Deterministic and stochastic energy‐aware hybrid models have been proposedHybrid models allow low‐resolution simulations without compromising on quality compared with high‐resolution runsHybrid approach produce more accurate ensemble predictions than their classical Geophysical Fluid Dynamics counterparts [ABSTRACT FROM AUTHOR]

Background: Simulations, ludic or otherwise, have so far struggled to gain a foothold in mainstream historiography. Some authors suggest there may be fundamental incompatibilities between history and the language of simulations and scholarly games. Others believe that designing, employing, and validating historical simulations may be simply too costly and/or labor-intensive to justify their widespread adoption. Intervention: This paper intends to identify points of friction between historiography and simulation-based research and suggest practical solutions to these issues. Methods: My discussion is based on the description and analysis of a case study, the ThomondSim/ The Triumphs of Turlough research project. The initiative consisted of the development and application of an agent-based computational model (ABM) and a scholarly board game to investigate the possible associations between economic, environmental, and military hazards in 13th and 14th centuries Ireland. Results and Discussion: Ensuring the simulations matched historical evidence to a standard deemed acceptable by the historiographical community limited their phase space, compromising their capacity to explore emergent phenomena. The intricacy of the underlying conceptual model suited the ABM better than the board game, which struggled to reconcile complexity with good game design practices. The board game, however, proved to be an effective validating tool for the ABM. Limitations and Suggestions for Further Research: The project espoused an overt simulation- and game-centric approach, paying little attention to unguided play. Recent literature suggests that fostering, rather than hindering, playful exploration could address some of the pitfalls identified by this project. Conclusion: Play could be a means of reconciliation between simulational, ludic, and historiographical practices. However, to ensure that projects adhere to epistemic standards, it is recommended that a methodology is developed to integrate it into research in ways that can be tested and evaluated. [ABSTRACT FROM AUTHOR]