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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.

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.

Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to analyze coupled oscillatory systems. Typically, the phase dynamics description is obtained in the weak coupling limit, i.e., in the first-order in the coupling strength. The extension beyond the first-order represents an unsolved problem and is an active area of research. In this paper, three partially synchronous states are investigated and presented in order of increasing complexity. First, the usage of the phase response curve for the description of macroscopic oscillators is analyzed. To achieve this, the response of the mean-field oscillations in a model of all-to-all coupled limit-cycle oscillators to pulse stimulation is measured. The next part treats a two-group Kuramoto model, where the interaction of one attractive and one repulsive group results in an interesting solitary state, situated between full synchrony and self-consistent partial synchrony. In the last part, the phase dynamics of a relatively simple system of three Stuart-Landau oscillators are extended beyond the weak coupling limit. The resulting model contains triplet terms in the high-order phase approximation, though the structural connections are only pairwise. Finally, the scaling of the new terms with the coupling is analyzed., Comment: 16 pages, 6 figures

By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient for identifying more specific behaviors. To improve this situation, we propose a topological approach that constructs the quantitative features describing the phase evolution of oscillators. Here, the phase data are mapped into a high-dimensional space at each time, and the topological features describing the shape of the data are subsequently extracted from the mapped points. These features are extended to time-variant topological features by adding the evolution time as an extra dimension in the topological feature space. The time-variant features provide crucial insights into the evolution of phase dynamics. Combining these features with the kernel method, we characterize the multi-clustered synchronized dynamics during the early evolution stages. Finally, we demonstrate that our method can qualitatively explain chimera states. The experimental results confirmed the superiority of our method over those based on order parameters, especially when the available data are limited to the early-stage dynamics., Comment: 13 pages, 8 figures

We investigate the physics of an adiabatic transition from a BCS superconductor to a Fermi liquid for an exponentially slow decreasing pairing interaction. In particular, we show that the metal keeps memory of the parent BCS state so it is possible to reverse the dynamics and go back to the original state similarly to a spin/photon echo experiment. Moreover, we study the evolution of the order parameter phase phi in transforming the BCS superconductor to a conventional metal. Since the global phase is the conjugate variable of the density we explicitly show how to use the dynamics of phi together with gauge invariance to build up the non-interacting chemical potential away from particle-hole symmetry. We further analyze the role of phi in restoring the gauge invariant current response when the non-interacting Fermi liquid is approached starting from a BCS superconductor in the presence of an external vector field., Comment: 13 pages, 12 figures

DNA supercoils are generated in genome regulation processes such as transcription and replication, and provide mechanical feedback to such processes. Under tension, DNA supercoil can present a coexistence state of plectonemic (P) and stretched (S) phases. Experiments have revealed the dynamic behaviors of plectoneme, e.g. diffusion, nucleation and hopping. To represent these dynamics with computational changes, we demonstrated first the fast dynamics on the DNA to reach torque equilibrium within the P and S phases, and then identified the two-phase boundaries as collective slow variables to describe the essential dynamics. According to the time scale separation demonstrated here, we accordingly developed a two-phase model on the dynamics of DNA supercoiling, which can capture physiologically relevant events across time scales of several orders of magnitudes. In this model, we systematically characterized the slow dynamics between the two phases, and compared the numerical results with that from the DNA polymer physics-based worm-like chain model. The supercoiling dynamics, including the nucleation, diffusion, and hopping of plectoneme, have been well represented and reproduced, using the two-phase dynamic model, at trivial computational costs. Our current developments, therefore, can be implemented to explore multi-scale physical mechanisms of the DNA supercoiling-dependent physiological processes.

Strongly correlated materials that exhibit an insulator-metal transition are key candidates in the search for new computing platforms. Understanding the pathways and timescales underlying the electrically-driven insulator-metal transition is crucial for uncovering the fundamental limits of device operation. Using stroboscopic electron diffraction, we perform synchronized time-resolved measurements of atomic motions and electronic transport in operating vanadium dioxide switches. We discover an electrically-triggered, isostructural state that forms transiently on microsecond timescales, stabilized by local heterogeneities and interfacial interactions between the equilibrium phases. This metastable phase bears striking similarity to that formed under photoexcitation within picoseconds, suggesting a universal transformation pathway across eight orders of magnitude of timescale. Our results establish a new route for uncovering non-equilibrium and metastable phases in correlated materials, and open avenues for engineering novel dynamical behavior in nanoelectronics.

It is well-established that Whitham's modulation equations approximate the dynamics of slowly varying periodic wave trains in dispersive systems. We are interested in its validity in dissipative systems with a conservation law. The prototype example for such a system is the generalized Ginzburg-Landau system that arises as a universal amplitude system for the description of a Turing-Hopf bifurcation in spatially extended pattern-forming systems with neutrally stable long modes. In this paper we prove rigorous error estimates between the approximation obtained through Whitham's modulation equations and true solutions to this Ginzburg-Landau system. Our proof relies on analytic smoothing, Cauchy-Kovalevskaya theory, energy estimates in Gevrey spaces, and a local decomposition in Fourier space, which separates center from stable modes and uncovers a (semi)derivative in front of the relevant nonlinear terms., Comment: 24 pages, 1 figure

The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of \emph{genuine nonlinearity}, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham Modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost., Comment: 38 pages