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The energy-based dual-phase dynamics identification (EDDI) method is a new data-driven technique for the discovery of equations of motion (EOMs) of strongly nonlinear single-degree-of-freedom (SDOF) oscillators. This research uses the EDDI method to obtain mathematical models for SDOF systems with clearance nonlinearities. The first key aspect of the EDDI method is that it relates the kinetic energy of the system to the dissipated energy and the underlying non-conservative forces acting on the oscillator. The second key aspect is that the EOM is identified with only knowledge of the mass of the oscillator and the transient response. The first phase of the EDDI method constructs the dissipated energy from the kinetic energy, then identifies a mathematical model for the damping based on the dissipated energy. To achieve this, the moments in time when the displacements are zero, where the mechanical and kinetic energies are equal, are used to compute the energy dissipated by the damping of the system. The second phase begins by computing the conservative force acting on the oscillator from either a balance of the other forces in the system or through the Lagrange equation. Finally, the stiffness model is determined by solving a set of linear equations to construct a mathematical model for the conservative (elastic) force. The governing equations are discovered by incorporating both the damping and stiffness terms. The method is demonstrated by employing analytical and real measured responses of nonlinear SDOF systems with different clearances nonlinearities, which shows that the proposed approach is suitable for non-smooth mechanical systems as well as smooth systems.

Systems such as Wigner crystals and incommensurate charge density waves that spontaneously break a continuous translation symmetry have unusual transport properties arising from their ability to slide coherently in space. Recent experimental and theoretical studies suggest that spontaneous translation symmetry breaking in some two-dimensional materials with nontrivial quantum geometry (e.g., rhombohedral pentalayer graphene) leads to a topologically nontrivial electron crystal state called the anomalous Hall crystal and characterized by a vanishing linear-response dc longitudinal conductivity and a non-vanishing Hall conductivity. In this work we present a theoretical investigation of the sliding dynamics of this new type of electron crystal, taking into account the system's nontrivial quantum geometry. We find that when accelerated by an external electric field, the crystal acquires a transverse anomalous velocity that stems from not only the Berry curvature of the parent band but also the Galilean non-invariance of the crystal state (i.e., crystal states with different momenta are not related by simple momentum boosts). We further show that acceleration of the crystal modifies its internal current from the static crystal value that is determined by the Chern number of the crystal state. The net Hall conductance including contributions from center-of-mass motion and internal current is in general not quantized. As an experimentally relevant example, we present numerical results in rhombohedral pentalayer graphene and discuss possible experimental implications.

We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and nonlinear spectra, we borrow some ideas from filtering trajectory methods to obtain a novel semiclassical method for the dynamical propagation of density matrices. This new approximation is tested rigorously against standard multistate electronic models, spin-boson model, and models of the Fenna-Matthews-Olson complex. In all instances, the current method is significantly better or as good as many other semiclassical methods available, especially in low-temperature. All results are tested against the numerically exact Hierarchical Equations of Motion method. The new method shows excellent agreement across various parameter regimes with numerically exact results, highlighting the robustness and accuracy of our approach., Comment: 11 pages, 8 figures

The fractional AC Josephson effect is a discerning property of topological superconductivity in hybrid Josephson junctions. Recent experimental observations of missing odd Shapiro steps and half Josephson frequency emission in various materials have sparked significant debate regarding their potential origin in the effect. In this study, we present microwave emission measurements on a resistively shunted Josephson junction based on a HgTe quantum well. We demonstrate that, with significant spurious inductance in the shunt wiring, the experiment operates in a nonlinear dynamic regime characterized by period-doubling. This leads to additional microwave emission peaks at half of the Josephson frequency, $f_J/2$, which can mimic the $4\pi$-periodicity of topological Andreev states. The observed current-voltage characteristics and emission spectra are well-described by a simple RCLSJ model. Furthermore, we show that the nonlinear dynamics of the junction can be controlled using gate voltage, magnetic field, and temperature, with our model accurately reproducing these effects without incorporating any topological attributes. Our observations urge caution in interpreting emission at $f_J/2$ as evidence for gapless Andreev bound states in topological junctions and suggest the appropriate parameter range for future experiments., Comment: 13 pages, 8 figures

This paper investigates the dynamics of a deep neural network (DNN) learning interactions. Previous studies have discovered and mathematically proven that given each input sample, a well-trained DNN usually only encodes a small number of interactions (non-linear relationships) between input variables in the sample. A series of theorems have been derived to prove that we can consider the DNN's inference equivalent to using these interactions as primitive patterns for inference. In this paper, we discover the DNN learns interactions in two phases. The first phase mainly penalizes interactions of medium and high orders, and the second phase mainly learns interactions of gradually increasing orders. We can consider the two-phase phenomenon as the starting point of a DNN learning over-fitted features. Such a phenomenon has been widely shared by DNNs with various architectures trained for different tasks. Therefore, the discovery of the two-phase dynamics provides a detailed mechanism for how a DNN gradually learns different inference patterns (interactions). In particular, we have also verified the claim that high-order interactions have weaker generalization power than low-order interactions. Thus, the discovered two-phase dynamics also explains how the generalization power of a DNN changes during the training process.

By measuring the current-voltage characteristics and the switching current distributions as a function of temperature, we have investigated the phase dynamics of Al tunnel ferromagnetic Josephson junctions (JJs), designed to fall in the typical range of parameters of state-of-the-art transmons, providing evidence of phase diffusion processes. The comparison with the experimental outcomes on non-magnetic JJs with nominally the same electrodynamical parameters demonstrates that the introduction of ferromagnetic barriers does not cause any sizeable detrimental effect, and supports the notion of including tunnel ferromagnetic JJs in qubit architectures., Comment: Accepted Manuscript Version. Please cite this article as DOI: 10.1063/5.0211006

In this article, we explore the connection between the heating phase of periodically driven CFTs and the Modular Hamiltonian of a subregion in the vacuum state. We show that the heating phase Hamiltonian corresponds to the Modular Hamiltonian, with the fixed points mapping to the endpoints of the subregion. In the bulk dual, we find that these fixed points correspond to the Ryu-Takayanagi surface of the AdS-Rindler wedge. Consequently, the entanglement entropy associated to the boundary interval within two fixed points exactly matches with the Rindler entropy of AdS-Rindler. We observe the emergent Virasoro algebra in the boundary quantization of the Modular Hamiltonian has a striking similarity with the emergent near Horizon Virasoro algebra. This is a consequence of the fact that while obtaining the boundary Virasoro algebra, a cut-off with conformal boundary condition around the fixed point is introduced, which in the bulk is related to a stretched horizon, with an emergent two-dimensional conformal symmetry. We also argue that as one tunes the parameter space of Floquet Hamiltonians to transition from the non-heating to the heating phase the operator algebra type changes from Von Neumann type $I$ to $III_1$ factor, providing a non-equilibrium analogue of the Hawking-Page transition., Comment: 22 pages, 3 figures, references added and typos corrected

In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math., 48,1995]) in view of the numerical approximation of conservation laws. Given any entropy solution consists of two different families of shocks interacting at some positive time for the standard two-phase compressible Euler equations, it is proved that such entropy solution is the sharp interface limit for a family global strong solutions of the modified Jin-Xin relaxation scheme for Navier-Stokes/Allen-Cahn system, here the relaxation time is selected as the thickness of the interface, weighted estimation and improved antiderivative method are used in the proof. Moreover, the simulation results are given by this modified Jin-Xin relaxation scheme method. Both numerical and theoretical results show that, the interacting shock waves can pass through the interface without any effect., Comment: 25 pages, 9 figures

The dynamics of two-phase flow within the cathode of a proton exchange membrane fuel cell, particularly in Gas Diffusion Layers (GDLs) with varying fiber curvatures, remain underexplored. Using a periodic surface model, we stochastically reconstruct three GDL types with different fiber curvatures, incorporating vital parameters derived from a physical GDL. Considering the randomness in reconstruction, the structure generation process is iterated four times for each GDL type, enabling an ensemble average analysis. Pore network models are adopted to reveal disparities in these GDL porous structures. The subsequent two-phase simulations are conducted to explore liquid transport through these GDLs and interfaces to assembled gas channels. Time-varying GDL total, local water saturation, and capillary pressure are investigated. Results show stochastic reconstructions exhibit similar frequency peak ranges in pore and throat diameters, and coordination numbers, but diverge from the physical GDL. Bigger fiber curvature tends to enhance pore network connectivity by increasing smaller pores, leading to heightened water saturation and capillary pressure. Straight-fiber GDLs, compared to curved-fiber GDLs, show greater potential proximity to the physical GDL in terms of overall water saturation and capillary pressure but are also accompanied by increased uncertainty. Despite similar layer porosity, water saturation in the same layer of all samples differs increasingly from the inlet to the outlet. Water breakthrough and detachment near the GDL can induce significant water saturation instability at the GDL and gas channel interface. Detached droplets in gas channels connected with straight-fiber GDLs exhibit larger sizes and slower movement than those in channels assembled with curved-fiber GDLs. These findings can be utilized in future GDL design and optimization.

Methanol is one of the most abundant interstellar Complex Organic Molecules (iCOMs) and it represents a major building block for the synthesis of increasingly complex oxygen-containing molecules. The reaction between protonated methanol and its neutral counterpart, giving protonated dimethyl ether, (CH$_3$)$_2$OH$^+$, along with the ejection of a water molecule, has been proposed as a key reaction in the synthesis of dimethyl ether in space. Here, gas phase vibrational spectra of the (CH$_3$)$_2$OH$^+$ reaction product and of the [C$_2$H$_9$O$_2$]$^+$ intermediate complex(es), formed under different pressure and temperature conditions, are presented. The widely tunable free electron laser for infrared experiments, FELIX, was employed to record their vibrational fingerprint spectra using different types of infrared action spectroscopy in the $600-1700$ cm$^{-1}$ frequency range, complemented with measurements using an OPO/OPA system to cover the O-H stretching region $3400-3700$ cm$^{-1}$. The formation of protonated dimethyl ether as a product of the reaction is spectroscopically confirmed, providing the first gas-phase vibrational spectrum of this potentially relevant astrochemical ion., Comment: 15 pages, 6 figures, Molecular Physics, Published online: 22 Jun 2023, for associated data files see Zenodo repository at https://doi.org/10.5281/zenodo.7868559

A comprehensive study of the vortex phases and vortex dynamics is presented for a recently discovered high-temperature superconductor YH$_6$ with T$_C$ (onset) of 215 K under pressure of 200 GPa.Thermal activation energy (U$_0$) is derived in the framework of thermally activated flux flow (TAFF) theory. The activation energy yields a power law dependence U$_0$ $\propto$ H$^\alpha$ on magnetic field with a possible crossover at a field around 8-10 Tesla. Furthermore, we have depicted the vortex phase transition from vortex-glass to vortex-liquid state according to the vortex-glass theory. Finally, vortex phase diagram is constructed for the first time for superhydrides. Very high estimated values of flux flow barriers U$_0$(H) = 1.5-7*10$^4$ K together with high crossover fields makes YH$_6$ a rather outstanding superconductor as compared to most cuprates and iron-based systems. The Ginzburg number for YH$_6$ Gi = 3-7*10$^{-3}$ indicates that thermal fluctuations are not so strong and cannot broaden superconducting transitions in weak magnetic fields.

The CALPHAD system of fundamental phase-level databases, now known as the Materials Genome, has enabled a mature technology of computational materials design and qualification that has already met the acceleration goals of the national Materials Genome Initiative. As first commercialized by QuesTek Innovations, the methodology combines efficient genomic-level parametric design of new material composition and process specifications with multidisciplinary simulation-based forecasting of manufacturing variation, integrating efficient uncertainty management. Recent projects demonstrated under the multi-institutional CHiMaD Design Center notably include novel alloys designed specifically for the new technology of additive manufacturing. With the proven success of the CALPHAD-based Materials Genome technology, current university research emphasizes new methodologies for affordable accelerated expansion of more accurate CALPHAD databases. Rapid adoption of these new capabilities by US apex corporations has compressed the materials design and development cycle to under 2 years, enabling a new "materials concurrency" integrated into a new level of concurrent engineering supporting an unprecedented level of manufacturing innovation.

Many learning algorithms used as normative models in neuroscience or as candidate approaches for learning on neuromorphic chips learn by contrasting one set of network states with another. These Contrastive Learning (CL) algorithms are traditionally implemented with rigid, temporally non-local, and periodic learning dynamics that could limit the range of physical systems capable of harnessing CL. In this study, we build on recent work exploring how CL might be implemented by biological or neurmorphic systems and show that this form of learning can be made temporally local, and can still function even if many of the dynamical requirements of standard training procedures are relaxed. Thanks to a set of general theorems corroborated by numerical experiments across several CL models, our results provide theoretical foundations for the study and development of CL methods for biological and neuromorphic neural networks., Comment: 23 pages, 4 figures. Paper accepted to ICML and update includes changes made based on reviewer feedback

We propose a novel method to reconstruct phase dynamics equations from responses in macroscopic variables to weak inputs. Developing linear and nonlinear response theories in coupled phase-oscillators, we derive formulae which connect the responses with the system parameters including the time delay in interactions. We examine our method by applying it to two phase models, one of which describes a mean-field network of the Hodgkin--Huxley type neurons with a nonzero time delay. The method does not require much invasiveness nor microscopic observations, and these advantages highlight its broad applicability in various fields., Comment: 12 pages, 5 figures

We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamics eventually leads to an asymmetric Laplace distribution of wealth (conjectured in [22] and shown formally in a recent work [18]). In this manuscript, we carry out a formal mean-field limit as the number of agents goes to infinity where we uncover a two-phase (ODE) dynamics. Convergence towards the unique equilibrium (two-sided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well., Comment: 25 pages, 7 figures

In the presence of an AC drive, multiterminal Josephson junctions exhibit the inverse AC Josephson effect, where the oscillations of the superconducting phase of each junction can lock onto one another or onto the external drive. The competition between these different phase locked states results in a complex array of quantized voltage plateaus whose stability strongly depend on the circuit parameters of the shunted junctions. This phase diagram cannot be explored with low temperature transport experiments alone, given the breadth of the parameter space, so we present an easily tunable analog circuit whose dynamical properties emulate those of a three terminal junction. We focus on the observation of the multiterminal inverse AC Josephson effect, and we discuss how to identify Shapiro steps associated with each of the three junctions as well as their quartet states. We only observe integer phase locked states in strongly overdamped networks, but fractional Shapiro steps appear as well when the quality factor of the junctions increases. Finally, we discuss the role of transverse coupling in the synchronization of the junctions., Comment: 11 pages, 7 figures

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature $T^{*}$ is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, $T^*$ is also tuned by a magnetic flux.

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopies provides access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

The Josephson equations predict remarkable effects concerning the phase state of a superconducting junction with an oscillating current induced by a static voltage. Whether the paradigm can be twisted by yielding an oscillating voltage without making use of harmonic drives is a fundamentally relevant problem yet not fully settled. Here, we demonstrate that a dynamical regime with an oscillating phase evolution is a general hallmark of driven Josephson systems exhibiting sign competition in the Josephson couplings. We show that in frustrated Josephson systems an oscillating phase dynamics gets switched on by driving the changeover among different ground states, which can be induced by varying the parameters that set the phase state. Remarkably, the character of the transitions in the Josephson phase space allows different types of dynamics, with few or several harmonics. This result sets out a characteristic mark of any superconducting system with frustrated Josephson couplings and can be exploited to disentangle the complexity of the underlying phases., Comment: 11 pages, 7 figures

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase reduction of the hybrid system to derive an effective, dimensionality-reduced phase equation. We apply the reduced phase model to a periodically forced excitable system and two-coupled excitable systems, both undergoing noise-induced oscillations. The reduced phase model can quantitatively predict the entrainment of a single system to the periodic force and the mutual synchronization of two coupled systems, including the phase slipping behavior due to noise, as verified by Monte Carlo simulations. The derived phase model gives a simple and efficient description of noise-induced oscillations and can be applied to the analysis of more general cases.

Many systems, classical or quantum, closed or open, exhibit universal statistical properties. Exciton-polariton condensates, being intrinsically driven-dissipative, offer a promising platform for observing non-equilibrium universal features. By conducting extensive numerical simulations of an incoherently pumped and interacting condensate coupled to an exciton reservoir we show that the effective nonlinearity of the condensate phase dynamics can be finely adjusted across a broad range, by varying the exciton-polariton interaction strength, allowing one to probe three main universal regimes with parameters accessible in current experiments: the weakly nonlinear Edwards-Wilkinson (EW) regime, where the phase fluctuations dominate, but the phase profile does not become rough, the strongly non-linear Kardar-Parisi-Zhang regime, where the condensate phase fluctuations grow in a superdiffusive manner leading to roughening of the phase, and a vortex-dominated phase emerging at stronger interactions, where both density and phase dynamics play significant roles. Our results provide a unified picture of the phase diagram of 2d exciton-polariton condensates under incoherent pumping, and shed light on recent experimental and numerical observations., Comment: 17 pages, 10 figures

This study proves the two-phase dynamics of a deep neural network (DNN) learning interactions. Despite the long disappointing view of the faithfulness of post-hoc explanation of a DNN, a series of theorems have been proven in recent years to show that for a given input sample, a small set of interactions between input variables can be considered as primitive inference patterns that faithfully represent a DNN's detailed inference logic on that sample. Particularly, Zhang et al. have observed that various DNNs all learn interactions of different complexities in two distinct phases, and this two-phase dynamics well explains how a DNN changes from under-fitting to over-fitting. Therefore, in this study, we mathematically prove the two-phase dynamics of interactions, providing a theoretical mechanism for how the generalization power of a DNN changes during the training process. Experiments show that our theory well predicts the real dynamics of interactions on different DNNs trained for various tasks.

Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for phase analysis, using the osculating circle to construct a co-moving coordinate system, which allows us to define a unique phase of the system. This coordinate independent, geometrical technique allows dissecting intricate local phase dynamics, even in regimes where traditional methods fail. Our methodology enables the analysis of a wider range of complex systems which were previously deemed intractable., Comment: 12 pages, 14 figures

We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic expansion for an embedding of the perturbed invariant torus, as well as for the reduced phase dynamics in local coordinates. Both can be determined to arbitrary degrees of accuracy, and we show that the phase dynamics may directly be obtained in normal form. We apply the method to predict remote synchronisation in a chain of coupled Stuart-Landau oscillators., Comment: 29 pages, 3 figures

Partial synchronization is characteristic phase dynamics of coupled oscillators on various natural and artificial networks, which can remain undetected due to the complexity of the systems. With an analogy between pairwise asynchrony of oscillators and topological defects, i.e., vortices, in the two-dimensional XY spin model, we propose a robust and data-driven method to identify the partial synchronization on complex networks. The proposed method is based on an integer matrix whose element is pseudo-vorticity that discretely quantifies asynchronous phase dynamics in every two oscillators, which results in graphical and entropic representations of partial synchrony. As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a complex small-world network. Partially synchronized chimera states are revealed by discriminating synchronized states even with phase lags. Such phase lags also appear in partial synchronization in chimera states. Our topological, graphical, and entropic method is implemented solely with measurable phase dynamics data, which will lead to a straightforward application to general oscillatory networks including neural networks in the brain., Comment: 9 pages, 5 figures

In this letter, we demonstrate the cyclically symmetric Thomas oscillators as swarmalators and describe their possible collective dynamics. We achieve this by sewing Kuromoto-type phase dynamics to particle dynamics represented by the Thomas model. More precisely, this is equivalent to a non-linear particle aggregation model with cyclic symmetry of coordinates and position-dependent phase dynamics. The non-linear equations describe spatiotemporal patterns of crystalline order and chaotic randomness at two extreme values of the system parameter. This pattern is the outcome of non-linear self-organization, which leads to a new class of turbulent flow - active turbulence. We claim that this model can capture the dynamics of many naturally occurring microorganisms and micro-swimmers. The model described in this letter can be a prototypical model for understanding active systems and may shed light on the possibility of making novel materials(active matter) with exciting biomedical and industrial applications. The key to this is the understanding and control over the complex dynamics of active systems, an out-of-equilibrium system, which is potentially helpful in making functional materials, nano and micromachines., Comment: 13 pages, 40 figures

In this paper, we delve into the issue of Quantum Synchronization in a driven two-level (qubit) system situated within a structured environment. Our findings have practical implications as we discover that adding a time-dependent periodic modulation to the transition frequency of the qubit can significantly enhance quantum synchronization. We first discovered the phase preference and, consequently, the phase locking conditions in our system using the Husimi Q-function. It is revealed that combining frequency modulation and non-Markovian effects enables us to achieve a stable phase-locking for the system. We show that tuning the amplitude-tofrequency ratio of the modulation process on the zeros of the zeroth-order Bessel function led to phase locking and, thus, surprisingly enhances quantum synchronization in the system. These results provide new insights into efficiently understanding phase dynamics in quantum environments., Comment: 10 pages, 8 figures

We consider the two-phase dynamics of two incompressible and immiscible fluids. As a mathematical model we rely on the Navier-Stokes-Cahn-Hilliard system that belongs to the class of diffuse-interface models. Solutions of the Navier-Stokes-Cahn-Hilliard system exhibit strong non-local effects due to the velocity divergence constraint and the fourth-order Cahn-Hilliard operator. We suggest a new first-order approximative system for the inviscid sub-system. It relies on the artificial-compressibility ansatz for the Navier-Stokes equations, a friction-type approximation for the Cahn-Hilliard equation and a relaxation of a third-order capillarity term. We show under reasonable assumptions that the first-order operator within the approximative system is hyperbolic; precisely we prove for the spatially one-dimensional case that it is equipped with an entropy-entropy flux pair with convex (mathematical) entropy. For specific states we present a numerical characteristic analysis. Thanks to the hyperbolicity of the system, we can employ all standard numerical methods from the field of hyperbolic conservation laws. We conclude the paper with preliminary numerical results in one spatial dimension., Comment: 24 pages

The phase-locking of transverse higher-order resonator modes results in a beam with rapidly oscillating spatial intensity profile. To complete the description of such transverse mode-locked (TML) beams, their spatiotemporal phase dynamics are explored in this work. The analysis of the phase terms of TML beams reveals oscillating wavevectors, which are experimentally verified by exploiting the mode-matching requirement of a single-mode fiber. The wavevector oscillation is further quantified by exploring its dependence on beam size. The findings have to be considered in potential future applications of TML beams in phase-sensitive processes.

We present the first model aimed at understanding how the Meissner effect in a young neutron star affects its macroscopic magnetic field. In this model, field expulsion occurs on a dynamical timescale, and is realised through two processes that occur at the onset of superconductivity: fluid motions causing the dragging of field lines, followed by magnetic reconnection. Focussing on magnetic fields weaker than the superconducting critical field, we show that complete Meissner expulsion is but one of four possible generic scenarios for the magnetic-field geometry, and can never expel magnetic flux from the centre of the star. Reconnection causes the release of up to $\sim 5\times 10^{46}\,\mathrm{erg}$ of energy at the onset of superconductivity, and is only possible for certain favourable early-phase dynamics and for pre-condensation fields $10^{12}\,\mathrm{G}\lesssim B\lesssim 5\times 10^{14}\,\mathrm{G}$. Fields weaker or stronger than this are predicted to thread the whole star., Comment: 24 pages, 12 figures. Accepted for publication in MNRAS

This study numerically investigates the influence of the taper on the flow-induced vibrations of an elastically mounted circular cylinder under Vortex-induced vibrations. The dynamic response of three different taper ratios defined as 12 (highly tapered cylinder), 20 (medium tapered cylinder), and 40 (low tapered cylinder))is studied at a fixed Reynolds number, defined based on the averaged cylinder diameter, of 150. The amplitude and frequency response of the tapered cylinder is characterized by a low mass ratio (defined as the ratio of the total oscillating mass to the displaced fluid mass) = 2 over the wide range of reduced velocity covering the full amplitude-response spectrum (based on the oscillation amplitude) of the VIV. The results show the existence of difference in the spanwise shedding of vortices owing to the poor spanwise pressure correlation. The flow field analysis in the wake of the oscillating cylinder reveals the dominance of the three-dimensional structures in the wake (near the top end with the larger diameter) behind the cylinder with the increase in the taper ratio (even at such low where the uniform cylinder exhibits the two-dimensional wake). Also, the tapered cylinder exhibits a wide range of frequency synchronization (i.e. wide lock-in area) compared to the uniform cylinder. Tapering the cylinder results in the shift of the peak of the max oscillation amplitude or, in turn, the shift in the transitioning of the response branches. Further, force decomposition, energy transfer, and phase dynamics are also discussed for the taper cylinders.

Persistent currents--inviscid quantized flow around an atomic circuit--are a crucial building block of atomtronic devices. We investigate how acceleration influences the transfer of persistent currents between two density-connected, ring-shaped atomic Bose-Einstein condensates, joined by a tunable weak link that controls system topology. We find that the acceleration of this system modifies both the density and phase dynamics between the rings, leading to a bias in the periodic vortex oscillations studied in T. Bland et al., Phys. Rev. Research 4, 043171 (2022). Accounting for dissipation suppressing such vortex oscillations, the acceleration facilitates a unilateral vortex transfer to the leading ring. We analyze how this transfer depends on the weak-link amplitude, the initial persistent current configuration, and the acceleration strength and direction. Characterization of the sensitivity to these parameters paves the way for a new platform for acceleration measurements.

Determining the underlying equations of motion and parameter values for vibrating structures is of great concern in science and engineering. This work introduces a new data-driven approach called the energy-based dual-phase dynamics identification (EDDI) method for identifying the nonlinear dynamics of single-degree-of-freedom oscillators. The EDDI method leverages the energies of the system to identify the governing dynamics through the forces acting on the oscillator. The approach consists of two phases: a model-dissipative and model-stiffness identification. In the first phase, the fact that kinetic and mechanical energies are equivalent when the displacement is zero is leveraged to compute the energy dissipated and a corresponding model for the nonlinear damping of the system. In the second phase, the energy dissipated is used to compute the mechanical energy (ME), which is then used to obtain a reformulated Lagrangian. The conservative forces acting on the oscillator are then computed by taking the derivative the Lagrangian, then a model for the nonlinear stiffness is identified by solving a system of linear equations. The resulting governing equations are identified by including both the nonlinear damping and stiffness terms. A key novelty of the EDDI method is that the only thing required to perform the identification is free-response measurements and the mass of the oscillator. No prior understanding of the dynamics of the system is necessary to identify the underlying dynamics, such that the EDDI method is a truly data-driven method. The method is demonstrated using simulated and measured responses of nonlinear single-degree-of-freedom systems with a variety of nonlinear mechanisms.

For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the other stable. In this paper we show that these two families can be joined by a heteroclinic connection, which manifests in the fluid as a travelling front. By shifting the analysis to the setting of Whitham modulation theory, this front is in wavenumber and frequency space. An implication of this jump is that a permanent frequency downshift of the Stokes wave can occur in the absence of viscous effects. This argument, which is built on a sequence of asymptotic expansions of the phase dynamics, is confirmed via energetic arguments, with additional corroboration obtained by numerical simulations of a reduced model based on the Benney-Roskes equation.

Reinforcement learning (RL) often necessitates a meticulous Markov Decision Process (MDP) design tailored to each task. This work aims to address this challenge by proposing a systematic approach to behavior synthesis and control for multi-contact loco-manipulation tasks, such as navigating spring-loaded doors and manipulating heavy dishwashers. We define a task-independent MDP to train RL policies using only a single demonstration per task generated from a model-based trajectory optimizer. Our approach incorporates an adaptive phase dynamics formulation to robustly track the demonstrations while accommodating dynamic uncertainties and external disturbances. We compare our method against prior motion imitation RL works and show that the learned policies achieve higher success rates across all considered tasks. These policies learn recovery maneuvers that are not present in the demonstration, such as re-grasping objects during execution or dealing with slippages. Finally, we successfully transfer the policies to a real robot, demonstrating the practical viability of our approach., Comment: J. P. Sleiman and M. Mittal contributed equally. Accepted for CoRL 2024 (Oral). Project website: https://leggedrobotics.github.io/guided-rl-locoma/

The low-energy effective action of String Theory introduces corrections to the dilaton-graviton sector, resulting in deformed black holes beyond general relativity. We analyze extreme mass-ratio inspiral systems (EMRIs), where a stellar-mass object spirals into a slowly rotating supermassive black hole including a distinct deviation parameter. This study examines the effects of this deformation on gravitational wave fluxes, orbital evolution, and phase dynamics, incorporating leading-order post-Newtonian corrections. With one-year observations of EMRIs, we employ the Fisher information matrix method to evaluate the potential for detecting deviations from general relativity through space-based gravitational wave detectors that utilize time-delay interferometry to suppress laser noise. The constraint on modified black holes, $\Delta\alpha \preceq 10^{-5}$, is almost the same with and without the time-delay interferometry combination. This analysis enhances our understanding and underscores the crucial role of observations in advancing gravitational phenomena within String Theory., Comment: 19 pages, 4 figures; Added some references and revised some sentences; Comments are welcome

The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize and evolve into chaos. Two distinct transitions into chaotic behaviour were identified as energy levels increased. The initial transition occurs through bifurcations following the Feigenbaum sequence. The subsequent transition, at higher energy levels, shows a shift from quasi-periodic states to chaotic regimes. The first chaotic state is mainly due to inertial forces governing nonlinear interactions. The second chaotic state arises from the increased significance of free surface elevation in the dynamics. A novel reformulation using phase and amplitude representations for each truncated variable revealed that phase components exhibit a temporal piece-wise locking behaviour, maintaining a constant value for a prolonged interval before an abrupt transition of $\pm\pi$, while amplitudes remain chaotic. It was observed that phase stability duration decreases with increased energy, leading to chaos in phase components at high energy levels. This is attributed to the nonlinear term in the equations, where phase components are introduced through linear combinations of triads with different modes. When locking durations vary across modes, the dynamics result in a stochastic interplay of multiple $\pi$ phase shifts, creating a stochastic dynamic within the coupled phase triads, observable even at minimal energy injections., Comment: 31 pages, 13 figures, 55 references, 2 appendices

Multiterminal Josephson junctions are a promising platform to host synthetic topological phases of matter and Floquet states. However, the energy scales governing topological protection in these devices are on the order of the spacing between Andreev bound states. Recent theories suggest that similar phenomena may instead be explored in circuits composed of two-terminal Josephson junctions, allowing for the topological protection to be controlled by the comparatively large Josephson energy. Here, we explore a Josephson circuit, in which three superconducting electrodes are connected through Josephson junctions to a common superconducting island. We demonstrate the dynamic generation of multiplet resonances, which have previously been observed in multiterminal Josephson junctions. The multiplets are found to be robust to elevated temperatures and are confirmed by exhibiting the expected Shapiro step quantization under a microwave drive. We also find an unexpected novel supercurrent, which couples a pair of contacts that are both voltage-biased with respect to the common superconducting island. We show that this supercurrent results from synchronization of the phase dynamics and pose the question whether it should also carry a topological contribution.

Starting with the overall wave function expression for the electron in an Aharonov-Bohm potential, we derive a version of the Kuramoto Model describing the phase dynamics of the bound state of the quantum mechanical system., Comment: 14 pages, 6 figures, 1 table

This study aimed to utilize bibliometric methods to analyze trends in international Magnetoencephalography (MEG) research from 2013 to 2022. Due to the limited volume of domestic literature on MEG, this analysis focuses solely on the global research landscape, providing insights from the past decade as a representative sample. This study utilized bibliometric methods to explore and analyze the progress, hotspots and developmental trends in international MEG research spanning from 1995 to 2022. The results indicated a dynamic and steady growth trend in the overall number of publications in MEG. Ryusuke Kakigi emerged as the most prolific author, while Neuroimage led as the most prolific journal. Current hotspots in MEG research encompass resting state, networks, functional connectivity, phase dynamics, oscillation, and more. Future trends in MEG research are poised to advance across three key aspects: disease treatment and practical applications, experimental foundations and technical advancements, and fundamental and advanced human cognition. In the future, there should be a focus on enhancing cross-integration and utilization of MEG with other instruments to diversify research methodologies in this field

This article explores the application of the path integral formalism in describing synchronization phenomena in entangled networks, cavities, and reservoirs. We discuss the concept of using Lagrangian mechanics for systems undergoing synchronization and its connection to least-action principles. By replacing the concept of least action with a least signaling term, we investigate how the path integral representation can be applied to study synchronization dynamics in entangled networks, drawing parallels with coupled oscillators in phase space models such as the Kuramoto model, as well as its relation to algorithms, such as the firefly algorithm for potential use in optimization in networks. This article also illustrates how entanglement signals themselves can interact strongly with ordered systems of harmonic oscillators that reach thresholds of classical synchronization with potential therefore for using entangled signals as weak measurement probes where phase dynamics is of interest., Comment: 8 pages, 8 figures

We consider the simultaneous control of the relative phase and populations of two-level quantum systems by an external field. We apply a reverse engineering approach, which allows obtaining an analytical expression for the control field depending upon two user-defined functions that dictate the population and the relative phase dynamics. We show that, in general, the prescribed functions for the dynamics cannot be chosen arbitrarily. We implement the reverse engineering technique to reach several target states using different kinds of functions to specify the system dynamics. We show that by adjusting these dynamical functions, we can produce different kinds of control fields. These controls can be easily build, needing, apart from the dynamical function themselves, only their derivatives. The methodology presented here will certainly find many applications that go beyond simple two-level systems.

The fundamental process of detecting and examining the polarization modes of gravitational waves plays a pivotal role in enhancing our grasp on the precise mechanisms behind their generation. A thorough investigation is essential for delving deeper into the essence of gravitational waves and rigorously evaluating and validating the range of modified gravity theories. In this line of interest, a general description of black holes in theories beyond general relativity can serve a meaningful purpose where distinct deviation parameters can be mapped to solutions representing distinct theories. Employing a refined version of the deformed Kerr geometry, which is free from pathological behaviours such as unphysical divergences in the metric, we explore an extreme mass-ratio inspiral system, wherein a stellar-mass object perturbs a supermassive black hole. We compute the effects of deformation parameters on the rate of change of orbital energy and angular momentum, orbital evolution and phase dynamics with leading order post-Newtonian corrections. With the waveform analysis, we assess the plausibility of detecting deviations from general relativity through observations facilitated by the Laser Interferometer Space Antenna (LISA), simultaneously constraining the extent of these deviations. Therefore, this analysis provides an understanding while highlighting the essential role of observations in advancing gravitational phenomena beyond general relativity., Comment: 34 pages, 5 Figures, Texts modified, Version to appear in JCAP

Optical vector analysis (OVA) is an enabling technology for comprehensively characterizing both amplitude and phase responses of optical devices or systems. Conventional OVA technologies are mostly based on discrete optoelectronic components, leading to unsatisfactory system sizes, complexity, and stability. They also encounter challenges in revealing the on-chip characteristics of integrated photonic devices, which are often overwhelmed by the substantial coupling loss and extra spectral response at chip facets. In this work, we demonstrate a miniaturized OVA system for integrated photonics devices based on broadband single sideband (SSB) modulators on a thin-film lithium niobate (LN) platform. The OVA could provide a direct probe of both amplitude and phase responses of photonic devices with kHz-level resolution and tens of terahertz measurement bandwidth. We perform in-situ characterizations of single and coupled microring resonators fabricated on the same chip as the OVA, unfolding their intrinsic loss and coupling states unambiguously. Furthermore, we achieve the direct measurement of collective phase dynamics and density of states of the Bloch modes in a synthetic frequency crystal, by in-situ OVA of a dynamically modulated microring resonator. Our in-situ OVA system provides a compact, high-precision, and broadband solution for characterizing future integrated photonic devices and circuits, with potential applications ranging from optical communications, biosensing, neuromorphic computing, to quantum information processing.

The ability to understand and ultimately control the transformations and properties of various nanoscale systems, from proteins to synthetic nanomaterial assemblies, hinges on the ability to uncover their dynamics on their characteristic length and time scales. Here, we use MHz X-ray photon correlation spectroscopy (XPCS) to directly elucidate the characteristic microsecond-dynamics of density fluctuations of semiconductor nanocrystals (NCs), not only in a colloidal dispersion but also in a liquid phase consisting of densely packed, yet mobile, NCs with no long-range order. We find the wavevector-dependent fluctuation rates in the liquid phase are suppressed relative to those in the colloidal phase and relative to observations of densely packed repulsive particles. We show that the suppressed rates are due to a substantial decrease in the self-diffusion of NCs in the liquid phase, which we attribute to explicit attractive interactions. Using coarse-grained simulations, we find that the extracted shape and strength of the interparticle potential explains the stability of the liquid phase, in contrast to the gelation observed via XPCS in many other charged colloidal systems. This work opens the door to elucidating fast, condensed phase dynamics in complex fluids and other nanoscale soft matter, such as densely packed proteins and non-equilibrium self-assembly processes, in addition to designing microscopic strategies to avert gelation., Comment: 7 pages, 4 figures

We use three-dimensional direct numerical simulations of homogeneous isotropic turbulence in a cubic domain to investigate the dynamics of heavy, chiral, finite-size inertial particles and their effects on the flow. Using an immersed-boundary method and a complex collision model, four-way coupled simulations have been performed, and the effects of particle-to-fluid density ratio, turbulence strength and particle volume fraction have been analysed. We find that freely falling particles on the one hand add energy to the turbulent flow but, on the other hand, they also enhance the flow dissipation: depending on the combination of flow parameters, the former or the latter mechanism prevails, thus yielding enhanced or weakened turbulence. Furthermore, particle chirality entails a preferential angular velocity which induces a net vorticity in the fluid phase. As turbulence strengthens, the energy introduced by the falling particles becomes less relevant and stronger velocity fluctuations alter the solid phase dynamics, making the effect of chirality irrelevant for the large-scale features of the flow. Moreover, comparing the time history of collision events for chiral particles and spheres (at the same volume fraction) suggests that the former tend to entangle, in contrast to the latter which rebound impulsively.

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling, these transitions can be understood in terms of commonly studied phase approximations. As the coupling strength increases, however, predicting the location and criticality of transition, whether continuous or discontinuous, from the phase dynamics may depend on the order of the phase approximation -- or a phase description of the network dynamics that neglects amplitudes may become impossible altogether. Here we analyze synchronization transitions and their criticality systematically for varying coupling strength in theory and experiments with coupled electrochemical oscillators. First, we analyze bifurcations analysis of synchrony and splay states in an abstract phase model and discuss conditions under which synchronization transitions with different criticalities are possible. Second, we illustrate that transitions with different criticality indeed occur in experimental systems. Third, we highlight that the amplitude dynamics observed in the experiments can be captured in a numerical bifurcation analysis of delay-coupled oscillators. Our results showcase that reduced order phase models may miss important features that one would expect in the dynamics of the full system., Comment: 10 pages, 6 figures

In the absence of vortices or phase slips, the phase dynamics of exciton-polariton condensates was shown to map onto the Kardar-Parisi-Zhang (KPZ) equation, which describes the stochastic growth of a classical interface. This implies that the coherence of such non-equilibrium quasi-condensates decays in space and time following stretched exponentials, characterized by KPZ universal critical exponents. In this work, we focus on the time evolution of the average phase of a one-dimensional exciton-polariton condensate in the KPZ regime and determine the frequency of its evolution, which is given by the blueshift, i.e. the non-equilibrium analog of the chemical potential. We determine the stochastic corrections to the blueshift within Bogoliubov linearized theory and find that while this correction physically originates from short scale effects, and depends both on density and phase fluctuations, it can still be related to the effective large-scale KPZ parameters. Using numerical simulations of the full dynamics, we investigate the dependence of these blueshift corrections on both noise and interaction strength, and compare the results to the Bogoliubov prediction. Our finding contributes both to the close comparison between equilibrium and non-equilibrium condensates, and to the theoretical understanding of the KPZ mapping.

We experimentally investigate the electronic transport properties of a three-terminal graphene Josephson junction. We find that self-heating effects strongly influence the behaviour of this multiterminal Josephson junction (MTJJ) system. We show that existing simulation methods based on resistively and capacitively shunted Josephson junction networks can be significantly improved by taking into account these heating effects. We also investigate the phase dynamics in our MTJJ by measuring its switching current distribution and find correlated switching events in different junctions. We show that the switching dynamics is governed by phase diffusion at low temperatures. Furthermore, we find that self-heating introduces additional damping which results in overdamped I-V characteristics when normal and supercurrents coexist in the device.