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We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications. [ABSTRACT FROM AUTHOR]

Since the development of generalized gradient approximations in the 1990s, approximations based on density functional theory have dominated electronic structure theory calculations. Modern approximations can yield energy differences that are precise enough to be predictive in many instances, as validated by large- and small-scale benchmarking efforts. However, assessing the quality of densities has been the subject of far less attention, in part because reliable error measures are difficult to define. To this end, this work introduces the mean-field error, which directly assesses the quality of densities from approximations. The mean-field error is contextualized within existing frameworks of density functional error analysis and understanding and shown to be part of the density-driven error. It is demonstrated in several illustrative examples. Its potential use in future benchmarking protocols is discussed, and some conclusions are drawn. [ABSTRACT FROM AUTHOR]

Based on the variational field theory framework, we extend our previous mean-field formalism [Y. A. Budkov and A. L. Kolesnikov, JStatMech 2022, 053205.2022], taking into account the electrostatic correlations of the ions. We employ a general covariant approach and derive a total stress tensor that considers the electrostatic correlations of ions. This is accomplished through an additional term that depends on the autocorrelation function of the local electric field fluctuations. Utilizing the derived total stress tensor and applying the mechanical equilibrium condition, we establish a general expression for the disjoining pressure of the Coulomb fluids, confined in a pore with a slit-like geometry. Using this equation, we derive an asymptotic expression for the disjoining pressure in a slit-like pore with non-electrified conductive walls. Present theory is the basis for future modeling of the mechanical stresses that occur in electrode pores with conductive charged walls, immersed in liquid phase electrolytes beyond the mean-field theory. [ABSTRACT FROM AUTHOR]

The absence of chain ends makes ring polymers distinctly different from their linear analogues. The intrinsic viscosity, complex viscosity and the dielectric relaxation of ring polymers are investigated within the tenets of the optimized Rouse–Zimm theory. The distance dependent excluded volume interactions (EVIs) are obtained from Flory's mean field theory. The hydrodynamic interactions (HIs) between the pairs of monomers are estimated using the preaveraged Oseen tensor. The intrinsic viscosity of linear and ring polymers both with and without EVI are compared as a function of ring size. A monotonically increasing trend of the intrinsic viscosity is observed in both cases. The intrinsic viscosity of both linear and ring polymers both with and without EVI show a very good agreement with the experimental results of polystyrene over a wide range of molecular weights in both good and theta solvents, respectively. The fractal dimensions of the ring polymers with EVI lie between that of a random walk and a self-avoiding walk model of linear polymers in three dimensions. The ring size increases with EVI and the effect of EVI is stronger on larger rings than that on smaller rings. The dielectric relaxation follow a connectivity independent universal scaling behavior at low and high frequency regions. The imaginary part of the complex dielectric susceptibility displays a local maxima in the intermediate frequency region, which reveals a structure dependent behavior of the rings. The theoretically calculated dielectric loss of ring polymers with HI matches well with those obtained from experiments. [ABSTRACT FROM AUTHOR]

We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 − J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work. [ABSTRACT FROM AUTHOR]

The Robeson bound is a theoretical limit that applies to kinetics-driven membrane separations of gas mixtures. However, this bound does not apply to sorption-driven membrane processes such as CO2/N2 separation, which lacks a theoretical explanation. As a result, we are uncertain about the factors that control the limiting behavior of sorption-driven separations. To address this issue, we employed a simple lattice model and dynamic mean field theory to examine the transport properties of disordered model structures, isolating sorption effects from purely kinetic effects. Our findings indicate that transport effects play a crucial role in sorption-driven processes, and perm-selectivity is consistently lower than sorption selectivity, which is an unattainable limit. We used basic geometric fragments of the structure to explain how transport effects emerge and manifest themselves in sorption-driven processes. [ABSTRACT FROM AUTHOR]

We systematically examine the influence of varying temperature (T) over a large range in model poly(vinyl acetate) gels swollen in isopropyl alcohol. The theta temperature Θ, at which the second virial coefficient A2 vanishes, is found to be equal to within numerical uncertainty to the corresponding high molecular mass polymer solution value without cross-links, and we quantify the swelling and deswelling of our model gels relative to their size at T = Θ, as customary for individual flexible polymer chains in solutions. We also quantify the "solvent quality" dependence of the shear modulus G relative to G(T = Θ) and compare to the gel swelling factor, α. We find that all our network swelling and deswelling data can be reduced to a scaling equation of the same general form as derived from renormalization group theory for flexible linear polymer chains in solutions so that it is not necessary to invoke either the Flory–Huggins mean field theory or the Flory–Rehner hypothesis that the elastic and mixing contributions to the free energy of network swelling are separable to describe our data. We also find that changes of G relative to G(T = Θ) are directly related to α. At the same time, we find that classical rubber elasticity theory describes many aspects of these semi-dilute solution cross-linked networks, regardless of the solvent quality, although the prefactor clearly reflects the existence of network defects whose concentration depends on the initial polymer concentration of the polymer solution from which the networks were synthesized. [ABSTRACT FROM AUTHOR]

Polarization plays a crucial role in understanding the interaction of fluorescent molecules in a light field. We report the study on the effect of a field–dipole interaction under polarization light-sheet fluorescence microscopy using the vectorial theory of light. The molecule is suitably modeled as a radiating electric dipole in a polarized electric field (both linear and random), and the system point spread function (PSF) is determined for different orientations of the dipole (both fixed and random). PSF analysis and contour plots suggest distinct nature of a field distribution in each case, indicating the importance of a field–dipole interaction for high-quality fluorescence imaging. The analysis suggests that the field spreads gradually along the polarization axis at a high numerical aperture (NA) of the objective lens, whereas it is more isotropic and homogeneous at low NA. Moreover, fast changes are not observed at low NA (i.e., far from the central lobe in the field contour plots), suggesting the absence of high-frequency components. However, sidelobes are prominent for linear polarized (along x) light. On the other hand, rapid variations are evident for randomly polarized light, depicting the presence of high spatial frequencies in the system optical transfer function. The other significant observation is the distinct frequency spectrum (both k x and k y) for random and fixed dipoles, indicating the significance of dipole orientation in a light-sheet field. Compared to the point-illumination-based fluorescence microscopy, sheet based polarization technique provides a high signal-to-noise ratio, a uniform field, an order large field of view, and critical information (related to the micro-environment of a dipole and its short-range interactions). The study is expected to facilitate polarization-sensitive investigation of large biological specimens (both fixed and live). [ABSTRACT FROM AUTHOR]

Hybrid particle–field molecular dynamics is a molecular simulation strategy, wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle–field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle–field method and particle–particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle–field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form, in particular, we demonstrate the ability of the Hamiltonian hybrid particle–field model to recover all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle–field filtering length scale on the emergent particle–particle correlations. [ABSTRACT FROM AUTHOR]

Solar, stellar and galactic large-scale magnetic fields are originated due to a combined action of non-uniform (differential) rotation and helical motions of plasma via mean-field dynamos. Usually, non-linear mean-field dynamo theories take into account algebraic and dynamic quenching of alpha effect and algebraic quenching of turbulent magnetic diffusivity. However, the theories of the algebraic quenching do not take into account the effect of modification of the source of turbulence by the growing large-scale magnetic field. This phenomenon is due to the dissipation of the strong large-scale magnetic field resulting in an increase of the total turbulent energy. This effect has been studied using the budget equation for the total turbulent energy (which takes into account the feedback of the generated large-scale magnetic field on the background turbulence) for (i) a forced turbulence, (ii) a shear-produced turbulence, and (iii) a convective turbulence. As the result of this effect, a non-linear dynamo number decreases with increase of the large-scale magnetic field, so that that the mean-field αΩ, α2, and α2Ω dynamo instabilities are always saturated by the strong large-scale magnetic field. [ABSTRACT FROM AUTHOR]

Measurements of neutron star mass and radius or tidal deformability deliver unique insight into the equation of state (EOS) of cold dense matter. EOS inference is very often done using generalized parametric or non-parametric models, which deliver no information on composition. In this paper, we consider a microscopic nuclear EOS model based on a field theoretical approach. We show that current measurements from NICER and gravitational wave observations constrain primarily the symmetric nuclear matter EOS. We then explore what could be delivered by measurements of mass and radius at the level anticipated for future large-area X-ray timing telescopes. These should be able to place very strong limits on the symmetric nuclear matter EOS, in addition to constraining the nuclear symmetry energy that determines the proton fraction inside the neutron star. [ABSTRACT FROM AUTHOR]

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations with a nonlocal self-generated drift. We establish the localisation limit, that is the convergence of nonlocal to local systems, when the range of interaction tends to 0. These theoretical results are sustained by numerical simulations. The major new feature in our analysis is that we do not need diffusion to gain compactness, but rely on a full rank assumption on the interaction kernels. In turn, we prove existence of weak solutions for the resulting system, a cross-diffusion system of quadratic type. [ABSTRACT FROM AUTHOR]

Commonly encountered shapes in nuclei are spherical, prolate and oblate. The shape of a nucleus is decided by the residual interactions among its nucleons. In our current investigation, we incorporate both axial and triaxial degrees of freedom to study how the shape of thorium nuclei changes within the boundaries of the drip lines. We employed the relativistic mean-field theory and utilized density-dependent meson-exchange as the functional throughout our calculations. We calculated the total binding energy as it varies with the deformation parameter β2 and subsequently depicted the resulting binding energy curves. Furthermore, we examined the self-consistent energy surface for thorium isotopes with triaxial quadrupole deformations. The emergence of potential energy minima can be attributed to the presence of gaps or regions with reduced density of single-particle energy levels around the Fermi surface, as the nucleus undergoes deformation. The nuclear shape evolution of thorium isotopes ranging from 204Th to 280Th was investigated, 216Th and 274Th are spherical in shape and the nearby isotopes are less deformed and nearly spherical. Isotopes ranging from 220Th to 264Th exhibit a higher level of deformation. The most deformed nucleus is 240Th and is prolate. The weak triaxial behavior is observed within the region associated with shape phase transition. [ABSTRACT FROM AUTHOR]

Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control. Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure. However, these algorithms do not consider network state changes. We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity. By using mean field theory and information entropy to calculate node activity, we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance. We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C. elegans neural network. We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers. [ABSTRACT FROM AUTHOR]

Microbial fuel cells and their related microfluidic systems have emerged as promising greener energy alternatives for the exploitation of avenues related to combined power and wastewater treatment operations. Moreover, the potential for their application in biosensing technology is large. However, while the fundamental principles of science that govern the design and operation of microbial fuel cells (MFCs) and microfluidic microbial fuel cells (MMFCs) are similar to those found in colloid science, the literature shows that current research lacks sufficient reference to the electrostatic and electrokinetic aspects, focusing mostly on aspects related to the architecture, design, anodes, microbial growth and metabolism, and electron transfer mechanisms. In this regard, research is yet to consider MFCs and MMFCs in the context of electrostatic and electrokinetic aspects. In this extensive review, we show, for the first time, the interrelationship of MFCs and MMFCs with electric double layer theory. Consequently, we show how the analytical solution to the mean field Poisson–Boltzmann theory relates to these systems. Moreover, we show the interrelationship between MFC and MMFCs' performance and the electric double layer and the associated electrostatic and electrokinetic phenomena. This extensive review will likely motivate research in this direction. [ABSTRACT FROM AUTHOR]

This paper concerns a two-fluid Euler-Maxwell system for plasmas with two small parameters. We study the non-relativistic quasi-neutral limit for smooth solutions of the system in whole space R 3. When the initial data are smooth and sufficiently close to constant equilibrium states, we give a rigorous justification of the limit for all time. The limit system is governed by a compressible Euler system. The proof is based on uniform energy estimates and various dissipative estimates of smooth solutions with respect to the parameters and time. A key step in these estimates is to control the quasi-neutrality of the velocities by using a projection operator. [ABSTRACT FROM AUTHOR]

This paper presents a semi-analytical model for calculating the mean deformation of a cylindrical or quasi-spheroidal liquid object placed in standing acoustic waves under the near-field approach. The interaction between the waves and the object is characterized by the angular distribution of the radiation pressure P rad (θ) over the object surface. The key parameters of the model are the Helmholtz number, α, and the object shape aspect ratio, called ϵ for elliptic shapes and ϵg for arbitrary shapes. For elliptic cross-sectional rigid objects, effects are globally dominated by suction for small α or compression for large α, whatever ϵ. When suction predominates, two opposed compression maxima and two opposed suction minima are observed. When compression predominates, an interference pattern with several extrema is observed. For potentially deformable objects, a potential flattening is found whatever α, which is all the more important as ϵ decreases. A general deformation model is developed to quantify the action/reaction loop between the acoustic field and the deformable object of the aspect ratio, ϵg. The acoustic Bond number Boa and a curvature-based parameter, ϵ κ , are introduced. As Boa increases, the object flattens whatever α. For small α, convex deformation is observed until a maximum Bond number is reached when ϵg = ϵ κ = 0. There, an abrupt change occurs from a convex shape to a planar liquid sheet. Otherwise, a local transition from a convex to a concave shape occurs, for which ϵ κ = 0, while ϵ g ≠ 0. Our model successfully predicts numerical and experimental results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a natural learning rule for mean field games with finite state and action space, the so-called myopic adjustment process. The main motivation for these considerations is the complexity of the computations necessary to determine dynamic mean field equilibria, which makes it seem questionable whether agents are indeed able to play these equilibria. We prove that the myopic adjustment process converges locally towards strict stationary equilibria under rather broad conditions. Moreover, we also obtain a global convergence result under stronger, yet intuitive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient and flexible algorithm to solve dynamic mean-field planning problems based on an accelerated proximal gradient method. Besides an easy-to-implement gradient descent step in this algorithm, a crucial projection step becomes solving an elliptic equation whose solution can be obtained by conventional methods efficiently. By induction on iterations used in the algorithm, we theoretically show that the proposed discrete solution converges to the underlying continuous solution as the grid becomes finer. Furthermore, we generalize our algorithm to mean-field game problems and accelerate it using multilevel and multigrid strategies. We conduct comprehensive numerical experiments to confirm the convergence analysis of the proposed algorithm, to show its efficiency and mass preservation property by comparing it with state-of-the-art methods, and to illustrate its flexibility for handling various mean-field variational problems. [ABSTRACT FROM AUTHOR]

The fully correlated frequency-independent Dirac–Coulomb–Breit Hamiltonian provides the most accurate description of electron–electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac–Coulomb–Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac–Coulomb–Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation. [ABSTRACT FROM AUTHOR]

While the effect of relativity in the electronic density has been widely studied, the effect on the pair probability, intracule, and extracule densities has not been studied before. Thus, in this work, we unveil new insights related to changes in the electronic structure caused by relativistic effects. Our numerical results suggest that the mean inter-electronic distance is reduced (mostly) due to scalar-relativistic effects. As a consequence, an increase in the electron–electron repulsion energy is observed. Preliminary results suggest that this observation is also valid when electronic correlation effects are considered. [ABSTRACT FROM AUTHOR]

Multiferroic MnTiO3 (MTO) is made up of alternate Mn2+ (3 d 5) and Ti4+ (3 d 0) layers along the c -axis. It undergoes a magnetic spin-flop driven ferroelectric polarization flop beyond ∼ 6 T below T N ∼ 64 K. MTO also exhibits a weak negative thermal expansion along the c -axis below ∼ 90 K. We demonstrate that doping Mn ions at non-magnetic Ti layers acts as a very effective microscopic control parameter to systematically tune both these functional responses. Tuning of c/a lattice parameters in MnTi 1 − x Mn x O3 leads to significant reduction in the spin-flop critical magnetic field from ∼ 6 T to more easily accessible fields (< 2 T for x = 0.05). Simultaneously, the controlled tuning of magnetic frustration due to Mn-doping at Ti sites also helps in a systematic enhancement of anomalous thermal expansion in regard to increasing the onset temperature for anomalous expansion to higher values (by ∼ 40 K for x = 0.10) and also strengthening its magnitude (by ∼ 30 % at 15 K for x = 0.10 in comparison to x = 0.00). Increase in the c/a ratio with Mn doping in MnTiO3 likely causes reduction in the effective magnetocrystalline anisotropy, which leads to a decrease in the value of the spin-flop magnetic field. Detailed temperature-dependent structural analyses shed light on the critical role of exchange striction mechanism in tuning the negative thermal expansion in doped MnTiO3. [ABSTRACT FROM AUTHOR]

We present a simple mean-field theory to describe the polymer-mediated depletion attraction between colloidal particles that accounts for the polymer's chain stiffness. We find that for fixed polymer radius of gyration and volume fraction, the strength of this attraction increases with increasing chain stiffness in both dilute and semidilute concentration regimes. In contrast, the range of attraction monotonically decreases with chain stiffness in the dilute regime, while it attains a maximum in the semidilute regime. The obtained analytical expressions for the depletion interaction were compared with numerical self-consistent field lattice computations and shown to be in quantitative agreement. From the interaction potential between two spheres, we calculated the second osmotic virial coefficient B2, which appears to be a convex function of chain stiffness. A minimum of B2 as a function of chain stiffness was observed both in the numerical self-consistent field computations and the analytical theory. These findings help explain the general observation that semiflexible polymers are more effective depletants than flexible polymers and give insight into the phase behavior of mixtures containing spherical colloids and semiflexible polymers. [ABSTRACT FROM AUTHOR]

There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom of the particle evolve according to a hybrid stochastic differential equation whose drift term depends on a discrete internal or environmental state that switches according to a continuous time Markov chain. Examples include Brownian motion in a randomly switching environment, membrane voltage fluctuations in neurons, protein synthesis in gene networks, bacterial run-and-tumble motion, and motor-driven intracellular transport. In this paper we derive generalized Dean–Kawasaki (DK) equations for a population of actively switching particles, either independently switching or subject to a common randomly switching environment. In the case of a random environment, we show that the global particle density evolves according to a hybrid DK equation. Averaging with respect to the Gaussian noise processes in the absence of particle interactions yields a hybrid partial differential equation for the one-particle density. We use this to show how a randomly switching environment induces statistical correlations between the particles. We also discuss methods for handling the moment closure problem for interacting particles, including dynamical density functional theory and mean field theory. We then develop the analogous constructions for independently switching particles. In order to derive a DK equation, we introduce a discrete set of global densities that are indexed by the single-particle internal states, and take expectations with respect to the switching process. However, the resulting DK equation is no longer closed when particle interactions are included. We conclude by deriving Martin–Siggia–Rose–Janssen–de Dominicis path integrals for the global density equations in the absence of interactions, and relate this to recent field theoretic studies of Brownian gases and run-and-tumble particles. [ABSTRACT FROM AUTHOR]

For decades, the difficulty of tackling a strong coupling model with a perturbative approach remained despite numerous inquiries. In this work, a typical mean field theory procedure transforms a strong coupling Hamiltonian into a weak one, which can be solved with a perturbative approach. The Hamiltonian of two-dimensional free electron gas with Hubbard on-site interaction is calculated as a test of the new procedure. Consequently, the spectral characteristics of the cuprates "peak-dip-hump" are reproduced. The result is compared with the past theoretical investigations, e.g., quantum Monte Carlo method, density matrix renormalization group, tensor network methods, etc. which agree well with the spectral curve. [ABSTRACT FROM AUTHOR]

The unrestricted Hartree‐Fock method is extended to correlation calculation within the density‐matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin‐orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi‐Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O2. [ABSTRACT FROM AUTHOR]

Magnetars are the neutron stars with the highest magnetic fields up to 1015–1016 G. It has been proposed that they are also responsible for a variety of extra‐galactic phenomena, ranging from giant flares in nearby galaxies to fast radio bursts. Utilizing a relativistic mean field model and a variable magnetic field configuration, we investigate the effects of strong magnetic fields on the equation of state and anisotropy of pressure of magnetars. It is found that the mass and radius of low‐mass magnetars are weakly enhanced under the action of the strong magnetic field, and the anisotropy of pressure can be ignored. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars. [ABSTRACT FROM AUTHOR]

The integrity of heat exchanger (HE) tubes is essential for power plant safety and efficiency. Numerous tube assessment techniques have been proposed, including eddy current inspection and the guided wave method. However, they mainly evaluate from the inside of the tubes. Hence, when the interior region of a tube wall is not accessible, inspection is difficult. To overcome this issue, a new guided wave device is fabricated that inspects from the exterior of the heat exchanger tubes. Using this device, a few sample heat exchanger tubes are selected and inspected in a field evaluation during an overhaul period. Furthermore, the feasibility of the device is evaluated. This new approach is expected to contribute to the efficient evaluation of heat exchanger tubes. [ABSTRACT FROM AUTHOR]

Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein--Uhlenbeck (OU) correlated noise poses challenges beyond the white noise assumptions and is yet to be done.Here, we resort to the mean-field approximation of a spatially extended system perturbed with OU noise and obtain the stationary probability density function deriving the Fokker--Planck equation for the same. This allows us to determine the role of diffusion and noise on the resilience of the spatial system. While the theoretical analysis guides us on the landscape of tipping thresholds of the system, critical transitions customary to a variety of systems, require a priori prediction. Here, we propose a probabilistic information-based indicator--spatial mutual information--that can successfully forecast tippings, complementing the previously developed spatial indicators. Further, validating its reliability on empirical data, we show that spatial mutual information serves as a robust indicator capturing information characteristic to an imminent tipping reaching peaks in its vicinity. [ABSTRACT FROM AUTHOR]

We study the small mass limit in mean field theory for an interacting particle system with non-Gaussian Lévy noise. When the Lévy noise has a finite second moment, we obtain the limit equation with convergence rate ε + 1 / ε N , by taking first the mean field limit N → ∞ and then the small mass limit ε → 0. If the order of the two limits is exchanged, the limit equation remains the same but has a different convergence rate ε + 1 / N. However, when the Lévy noise is α -stable, which has an infinite second moment, we can only obtain the limit equation by taking first the small mass limit and then the mean field limit, with the convergence rate 1 / N α − 1 + 1 / N p 2 + ε p / α where p ∈ (1 , α). This provides an effectively limit model for an interacting particle system under a non-Gaussian Lévy fluctuation, with rigorous error estimates. [ABSTRACT FROM AUTHOR]

In this paper, by treating the cosmological constant as a thermodynamic pressure, we study the thermodynamics and phase transitions of the dyonic AdS black holes in Gauss-Bonnet-Scalar gravity, where the conformal scalar field is considered. In a more general extended phase space, we first verified the first law of black hole thermodynamics, and find that it is always true. Meanwhile, the corresponding Smarr relation is also obtained. Then, we found that this black hole exhibits interesting critical behaviors in six dimensions, i.e., two swallowtails can be observed simultaneously. Interestingly, in a specific parameter space, we observed the small/intermediate/large black hole phase transitions, with the triple point naturally appearing. Additionally, the small/large black hole phase transition, similar to the liquid/gas phase transition of the van der Waals fluids, can also be found in other parameter regions. Moreover, we note that the novel phase structure composed of two separate coexistence curves discovered in the dyonic AdS black holes in Einstein-Born-Infeld gravity disappears in Gauss-Bonnet-Scalar gravity. This suggests that this novel phase structure may be related to gravity theory, and importantly, it is generally observed that the triple point is a universal property of dyonic AdS black holes. On the other hand, we calculated the critical exponents near the critical points and found that they share the same values as in mean field theory. Finally, it is true that these results will provide some deep insights into the interesting thermodynamic properties of the dyonic AdS black holes in the background of conformal scalar fields. [ABSTRACT FROM AUTHOR]

This article presents a framework for annular finite‐time H∞$$ {H}_{\infty } $$ filtering problem for discrete‐time mean‐field stochastic systems with state‐ and disturbance‐dependent noise. Both static and dynamic event‐triggered mechanisms are introduced, which are related to two different thresholds and internal variables, respectively. Based on mean‐field theory and the Lyapunov functional method, two groups of sufficient conditions are derived to ensure the filtering error systems have annular finite‐time boundedness under an H∞$$ {H}_{\infty } $$ performance level. Then, the desired filter gains can be obtained by solving two convex optimization problems. Finally, two numerical examples are given to show the validity of the proposed results. [ABSTRACT FROM AUTHOR]

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus 1 5 4 Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection Λ ̃ and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei. [ABSTRACT FROM AUTHOR]

In this note we prove the uniqueness of solutions to a class of mean field games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general nonseparable Hamiltonians that satisfy a so-called displacement monotonicity condition. This monotonicity condition that we propose for nonseparable Hamiltonians is sharper and more general than the one proposed in the work [W. Gangbo et al., Ann. Probab., 50 (2022), pp. 2178-2217]. The displacement monotonicity assumptions imposed on the data actually provide not only uniqueness, but also the existence and regularity of the solutions. Our analysis uses elementary arguments and does not rely on the well-posedness of the corresponding master equations. [ABSTRACT FROM AUTHOR]

This paper proposes a new mathematical paradigm to analyze discrete-time meanfield games. It is shown that finding Nash equilibrium solutions for a general class of discretetime mean-field games is equivalent to solving an optimization problem with bounded variables and simple convex constraints, called MF-OMO. This equivalence framework enables finding multiple (and possibly all) Nash equilibrium solutions of mean-field games by standard algorithms. For instance, projected gradient descent is shown to be capable of retrieving all possible Nash equilibrium solutions when there are finitely many of them, with proper initializations. Moreover, analyzing mean-field games with linear rewards and mean-field independent dynamics is reduced to solving a finite number of linear programs, hence solvable in finite time. This framework does not rely on the contractive and the monotone assumptions and the uniqueness of the Nash equilibrium. [ABSTRACT FROM AUTHOR]

In the present work, we constrain the equations of the state of asymmetric dense matter in consideration of the heaviest observed neutron star mass M max = 2.35 ± 0.17 M ⊙ for the black widow pulsar PSR J0952-0607, finite and bulk nuclear properties. We propose four interactions for the relativistic mean field model which include different combinations of non-linear, self, and cross-couplings among isoscalar–scalar σ , isoscalar–vector ω , isovector–vector ρ and isovector–scalar meson δ meson fields up to the quartic order. These interactions harmonize with the finite nuclei and bulk nuclear matter properties. It is observed that interactions obtained with the inclusion of δ meson coupling with nucleons have a significant effect on the slope of symmetry energy (L), radius (R 1.4 ) , and dimensionless tidal deformability (Λ 1.4) corresponding to a canonical mass neutron star. The radius of 2.08 M ⊙ neutron star mass is predicted to be in the range R 2.08 = 12.98–13.34 km which also satisfies the NICER observations Miller et al. (Astrophys. J. Lett. 918, L28 (2021). [ABSTRACT FROM AUTHOR]

Layered honeycomb magnets with strong atomic spin–orbit coupling at transition metal sites have been intensively studied for the search of Kitaev magnetism and the resulting non-Abelian braiding statistics. α -RuCl 3 has been the most promising candidate, and there have been several reports on the realization of sibling compounds α -RuBr 3 and α -RuI 3 with the same crystal structure. Here, we investigate correlated electronic structures of α -RuCl 3 and α -RuI 3 by employing first-principles dynamical mean-field theory. Our result provides a valuable insight into the discrepancy between experimental and theoretical reports on transport properties of α -RuI 3 , and suggests a potential realization of correlated flat bands with strong spin–orbit coupling and a quantum spin-Hall insulating phase in α -RuI 3 . [ABSTRACT FROM AUTHOR]

We consider a time varying delayed Cucker-Smale system in a harmonic potential field and analyze its long time collective behavior. Under appropriate assumptions on the initial data, we show the asymptotic collective behavior when the time varying delay is uniformly bounded by a sufficiently small constant. Our strategies are based on the Lyapunov functional approach, forward-backward estimate and the continuity argument. Finally, some numerical tests are performed to illustrate the theoretical result. [ABSTRACT FROM AUTHOR]

The morphology of superstructures formed by bottlebrush block copolymers in the melt can be tuned by changing the side chain length or/and their grafting density at constant volume fractions of the blocks. This feature enables fabrication of microphase separated bulk structures and mesoporous materials thereof with spherical or cylindrical domains (precursors of the mesopores), with high porosity unattainable for materials produced from conventional linear block copolymers. These paradigms are proven by DPD simulations that allow constructing morphological phase diagrams of the melt of block copolymers comprising one linear and one bottlebrush block and comparing the simulation results to the predictions of the mean field analytical theory. While the binodal lines separating the stability regions of spherical and cylindrical domains predicted by the theory perfectly match the simulation results, the simulation indicates appearance of a gyroid phase around the theoretical binodal separating the stability ranges of cylinders and lamellae. The results of our work provide guidelines for macromolecular design of novel composite and mesoporous materials with a wide spectrum of potential applications. [ABSTRACT FROM AUTHOR]

The quest to comprehend the nature of consciousness has spurred the development of many theories that seek to explain its underlying mechanisms and account for its neural correlates. In this paper, I compare my own conscious electromagnetic information field (cemi field) theory with integrated information theory (IIT) and global workspace theory (GWT) for their ability to 'carve nature at its joints' in the sense of predicting the entities, structures, states and dynamics that are conventionally recognized as being conscious or nonconscious. I go on to argue that, though the cemi field theory shares features of both integrated information theory and global workspace theory, it is more successful at carving nature at its conventionally accepted joints between conscious and nonconscious systems, and is thereby a more successful theory of consciousness. [ABSTRACT FROM AUTHOR]

The recognition of human activities from video sequences and their transformation into a machine-readable form is a challenging task, which is the subject of many studies. The goal of this project is to develop an automated method for analyzing, identifying and processing motion capture data into a planning language. This is performed in a cooking scenario by recording the pose of the acting hand. First, predefined side actions are detected in the dataset using classification. The remaining frames are then clustered into main actions. Using this information, the known initial positions and virtual object tracking, a machine-readable planning domain definition language (PDDL) is generated. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and stability of singular patterns in a fractional Ginzburg–Landau equation with a mean field. We prove the existence of three types of singular steady-state patterns (double fronts, single spikes, and double spikes) by solving their respective consistency conditions. In the case of single spikes, we prove the stability of single small spike solution for sufficiently large spatial period by studying an explicit non-local eigenvalue problem which is equivalent to the original eigenvalue problem. For the other solutions, we prove the instability by using the variational characterisation of eigenvalues. Finally, we present the results of some numerical computations of spike solutions based on the finite difference methods of Crank–Nicolson and Adams–Bashforth. [ABSTRACT FROM AUTHOR]

As gas atomisation has been the main method for producing high-performance spherical powders in the past decades, its application in the production of metallic powders has become one of the main research subjects in this field. Since it is challenging to directly observe the atomising gas and to investigate melt flow states by experiments, numerical simulation is attracting increasing interest in studying the gas atomisation process. In this work, various computational fluid dynamics models were implemented to simulate the gas atomisation process. With the models, the droplet breakup, cooling, and solidification within the coupled process were investigated. The final mean particle size was predicted through numerical simulations and compared with the statistics extracted from the gas atomisation process, which shows that a reasonable mass median diameter of the particle can be predicted numerically. The results also show a clear relationship between the breakup trajectory and the resulting particle size. [ABSTRACT FROM AUTHOR]

The modeling and control of epidemics, such as the novel Coronavirus, have become crucial on a global scale, for effective management of epidemic situations. This paper is focused on using the mean field approach for modeling and control of epidemics. The mean field approach is an effective alternative to the classical approach of using continuous time Markov decision process (CTMDP) models, which suffer from the curse of dimensionality and entail knowledge of global state information. The mean field approach captures the collective behavior of a dynamic system consisting of numerous interacting nodes representing individuals in the population. The objectives of this paper are twofold: (a) to provide an overview of the mean field approach to epidemic modeling and control, and (b) to present recent advances in this area. Emphasizing the importance of containing and suppressing epidemic spread through non-pharmaceutical interventions, the paper highlights the need to minimize loss of lives, reduce suffering, and alleviate the burden on the public healthcare system. A potential challenge here is the presence of a section of the population who act on their free will and deviate from recommended best practices, which could lead to a potential public health crisis. Motivated by this, the paper explores two specific threads to modeling and control. The first thread assumes that individual nodes comply with a socially optimal control policy mandated by a regulatory authority. The second thread allows for independent and strategic behavior by the individual nodes, modeled as a mean field game, where the strategies of rational agents are based on mean field Nash equilibria. The paper begins by discussing the modeling of epidemics using an extended SIVR (Susceptible-Infected-Vaccinated-Recovered) compartmental model, accompanied by an illustrative example. Next, a literature review is provided, focusing on the mean field approach for socially optimal control of epidemics and how a regulatory authority can effectively contain the spread. Subsequently, the paper presents an update on the use of mean field game-based approaches in studying epidemic spread and control. Finally, future research directions in this important area are discussed. [ABSTRACT FROM AUTHOR]

In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model results in a non-linear mean-field Fokker-Planck equation and we show the existence of steady states via a Schauder fixed point argument. Our proof relies on the study of a related linear equation using hypocoercivity techniques. [ABSTRACT FROM AUTHOR]

Many physical properties behave differently in disorder systems from the order one. The effects of atomic disorder on the magnetic properties have been explored on Co2TiSi and Co2TiAl full Heusler alloys. Co2TiSi crystallizes in an ordered L21 crystal symmetry, and Co2TiAl mainly possesses a B2 structure. The B2 disorder affects not only the magnetic ordering but also the saturation magnetization, causing the deviation from the Slater-Pauling prediction for Co2TiAl. The critical exponents of the magnetic phase transition have been analyzed by employing different techniques like, the Arrott plot, Kouvel–Fisher plot, critical isotherm analysis, scaling magnetic behavior, and magnetocaloric analysis as well. The calculated critical exponents are close to the mean field theory which implies long-range ferromagnetic ordering in Co2TiSi. However, the exchange interaction in Co2TiAl deviates from the long-range mean field theory. This may be due to the magnetic contribution of the B2-disordered phase. In addition to the magnetic ordering, the magnetocaloric analysis provides the applicability of Co2TiSi alloy as a low-cost, hysteresis-free magnetic refrigerant with a large working temperature near room temperature. [ABSTRACT FROM AUTHOR]

We formulate a Majorana mean-field theory for the extended JKΓ Kitaev model in a magnetic Zeeman field of arbitrary direction, and apply it for studying spatially inhomogeneous states harboring vortices. This mean-field theory is exact in the pure Kitaev limit and captures the essential physics throughout the Kitaev spin liquid phase. We determine the charge profile around vortices and the corresponding quadrupole tensor. The quadrupole-quadrupole interaction between distant vortices is shown to be either repulsive or attractive, depending on parameters. We predict that electrically biased scanning probe tips enable the creation of vortices at preselected positions. Our results paves the way for the electric manipulation of Ising anyons in Kitaev spin liquids. [ABSTRACT FROM AUTHOR]