Phase Space Research Articles

The structural, elastic, optoelectronic properties and hydrogen storage capability of lead-free hydrides XZrH3 (X: Mg/Ca/Sr/Ba) for hydrogen storage application: A DFT study

Perovskite hydrides are promising materials for hydrogen capacity application to achieve the US DOE on-board criteria. We have investigated novel perovskite hydrides XZrH3 (X: Mg/Ca/Sr/Ba) for H2 storage and transportation applications. In this study we investigates the physical properties of XZrH3 light materials for solid-state hydrogen storage application by incorporating the DFT framework with the CASTEP code. We have theoretically examined the structural, mechanical, electronic, optical, and hydrogen storage properties of these materials. The selected compounds were fully relaxed and optimized in the cubic phase space group Pm-3 m. Structural phase stability was confirmed through thermodynamic, and mechanical analyses. Mechanical properties, evaluated based on Poisson’s ratio, the Puagh’s ratio, and Cauchy pressure, indicate the ductile behavior with a preference for ionic bonding. The electronic structure analysis reveals the metallic behavior of these materials. Optical calculations were also performed to provide additional insights into the physical properties of H2 compounds. The gravimetric hydrogen storage capacities were calculated as 2.55, 2.25, 1.66, and 1.31 wt% for MgZrH3, CaZrH3, SrZrH3, And BaZrH3 hydrides respectively. The identified properties of XZrH3 suggest that these materials could significantly enhance hydrogen storage systems, with potential integration into existing energy technologies, offering a pathway toward more efficient and sustainable hydrogen-based solutions.

Ultra-relativistic electron flux enhancement under persistent high speed solar wind stream

The physical mechanisms usually applied to explain the relativistic electron enhancement have been delved into to elucidate non-adiabatic electron acceleration resulting in the ultra-relativistic electron population observed in the outer radiation belt. We considered multisatellite observations of the solar wind parameters, magnetospheric waves, and particle flux to report an unusual local acceleration of ultra-relativistic electrons under a prolonged high-speed solar wind stream (HSS). A corotating interaction region reaches the Earth’s bowshock on August 3, 2016, causing a minor geomagnetic storm. Following this, the magnetosphere was driven for 72 h by a long-term HSS propagating at 600 km/s. During this period, the magnetosphere sustained both ultra-low frequency (ULF) and very-low frequency (VLF) waves in the outer radiation belt region. Besides the waves, the relativistic and ultra-relativistic electron fluxes were enhanced with different time lags regarding the magnetic storm main phase. The efficiency of wave-particle interaction in enhancing ultrarelativistic electrons is evaluated by the diffusion coefficient rates, considering both ULF and VLF waves together with phase space density analyses. Results show that local acceleration by whistler mode chorus waves can occur in a time scale of 2–4 h, whereas ULF waves take around 10’s of hours and magnetosonic waves take a time scale of days. This result is confirmed by the phase space density analysis. Accordingly, it shows that peaks of local acceleration of 1 MeV electrons are consistent with the observation of the highest chorus wave amplitude at the same L-shell and MLT. Thus, we argue that whistler mode chorus waves interacting with relativistic electrons are the main physical mechanisms leading to ultra-relativistic electron enhancement, while ULF and fast magnetosonic waves are found as secondary physical processes. Lastly, our analysis contributes to understanding how whistler and ULF waves can contribute to ultra-relativistic electrons showing up in the inner magnetosphere under the HSS driver.

Toward a Correct Description of Initial Electronic Coherence in Nonadiabatic Dynamics Simulations.

The recent improvement in experimental capabilities for interrogating and controlling molecular systems with ultrafast coherent light sources calls for the development of theoretical approaches that can accurately and efficiently treat electronic coherence. However, the most popular and practical nonadiabatic molecular dynamics techniques, Tully's fewest-switches surface hopping and Ehrenfest mean-field dynamics, are unable to describe the dynamics proceeding from an initial electronic coherence. While such issues are not encountered with the analogous coupled-trajectory algorithms or numerically exact quantum dynamics methods, applying such techniques necessarily comes with a higher computational cost. Here we show that a correct description of initial electronic coherence can indeed be achieved using independent-trajectory methods derived from the semiclassical mapping formalism. The key is the introduction of an initial sampling over the electronic phase space and a means of incorporating phase interference between trajectories, both of which are naturally achieved when working within the semiclassical mapping framework.

Tutorial on Molecular Latent Space Simulators (LSSs): Spatially and Temporally Continuous Data-Driven Surrogate Dynamical Models of Molecular Systems.

The inherently serial nature and requirement for short integration time steps in the numerical integration of molecular dynamics (MD) calculations place strong limitations on the accessible simulation time scales and statistical uncertainties in sampling slowly relaxing dynamical modes and rare events. Molecular latent space simulators (LSSs) are a data-driven approach to learning a surrogate dynamical model of the molecular system from modest MD training trajectories that can generate synthetic trajectories at a fraction of the computational cost. The training data may comprise single long trajectories or multiple short, discontinuous trajectories collected over, for example, distributed computing resources. Provided the training data provide sufficient sampling of the relevant thermodynamic states and dynamical transitions to robustly learn the underlying microscopic propagator, an LSS furnishes a global model of the dynamics capable of producing temporally and spatially continuous molecular trajectories. Trained LSS models have produced simulation trajectories at up to 6 orders of magnitude lower cost than standard MD to enable dense sampling of molecular phase space and large reduction of the statistical errors in structural, thermodynamic, and kinetic observables. The LSS employs three deep learning architectures to solve three independent learning problems over the training data: (i) an encoding of the high-dimensional MD into a low-dimensional slow latent space using state-free reversible VAMPnets (SRVs), (ii) a propagator of the microscopic dynamics within the low-dimensional latent space using mixture density networks (MDNs), and (iii) a generative decoding of the low-dimensional latent coordinates back to the original high-dimensional molecular configuration space using conditional Wasserstein generative adversarial networks (cWGANs) or denoising diffusion probability models (DDPMs). In this software tutorial, we introduce the mathematical and numerical background and theory of LSS and present example applications of a user-friendly Python package software implementation to alanine dipeptide and a 28-residue beta-beta-alpha (BBA) protein within simple Google Colab notebooks.

Dynamical system approach of interacting dark energy models in $f(R,T^{\phi})$ gravity

Abstract We have examined an isotropic and homogeneous cosmological model in $f(R,T^{\phi})$ gravity, where $R$ represents the Ricci scalar and $T^{\phi}$ exhibits the energy momentum tensor's trace. We examine the stability criteria by performing the dynamical system analysis for our model $f(R,T^{\phi})=R+2(aT^{\phi}+b)$, where $a$ $\&$ $b$ are the constants. We derive a set of autonomous equations and find their solutions by assuming a flat potential $V_{0}$. We assess the equilibrium points from these equations and find the eigenvalues. We analyze the physical interpretation of the phase space for this system. We obtain three stable equilibrium points. We also examine the interaction between scalar field and dark energy, represented by $Q=\psi H\rho_{de}$ and determine the equilibrium points for this interaction. We identify four stable equilibrium points for this interaction. We calculate the values of the physical parameters for both scenarios at each equilibrium point, indicating the Universe's accelerated expansion.

Abstract Su805: Early-Latency Evoked Brain Response Revealed using Novel Filtering Technique

Background: Cardiac arrest (CA) can cause coma in resuscitated patients. Accuracy of prognosis is limited. Presence of brain signals such as somatosensory evoked potential (SSEP) reveals integrity of the thalamocortical pathway, which is necessary for arousal but insufficient to predict positive outcome. The N10 is a SSEP component that diminishes in CA. The N7, which can be obscured by stimulus artifact or other components, is associated with subcortical structures. Phase space area (PSA) quantifies SSEP morphology and is associated with CA recovery. It has been measured at least 5ms after stimulus. Hypothesis: Early SSEP and PSA diminish under anesthesia and during CA but may recover afterwards. Aims: By removing stimulus artifact, we capture early SSEP (N7 and early PSA) to enable improved prognostication. Methods: Six rats received 1.2, 1.8, and 2.5% isoflurane anesthesia for 30min. Two underwent 5 or 7min CA and were observed over 2hr. SSEP was recorded every 2s. An adaptive filter removed the artifact. Peaks were measured near 7 (N7) and 15 (N10) ms post-stimulus. PSA, the area occupied by the phase space curve, was recorded over 0-9ms (“early”) and 0-30ms (“total”). Signal-to-noise ratio (SNR) is the ratio of N10 amplitude to standard deviation of the signal. T tests were used for comparisons between SNR values and between experimental conditions. Results: We identified 4153 N7 peaks with latency (mean±95% C.I.) 8.6±1.3ms in the filtered data, compared to 2464 with latency 8.5±1.4ms in the unfiltered data. SNR was greater in the filtered signal (2.3±1.5) than unfiltered (0.3±0.4). N7 amplitude decreased at the highest anesthesia level; N10 decreased for each level. N7 and N10 decreased during CA and recovered after, although N10 remained below baseline during 2hr recovery. Early PSA was lower under the higher anesthesia levels, while total PSA decreased for each level. PSA decreased during CA and recovered after 5min CA; total PSA recovered to baseline and early PSA exceeded it after 2hr.Early PSA did not recover from 7min CA, while total PSA recovered but remained below baseline. Conclusion: We demonstrate a novel technique to discover an elusive early-latency response, adding detail to a neural pathway involved in arousal. We reduce noise, capture N7 consistently, and measure PSA beginning at 0ms, providing additional diagnostic dimensions responsive to anesthesia and CA. Future study will investigate outcomes in resuscitated patients.

An optimal transformation method for inferring ocean tracer sources and sinks

Abstract. The geography of changes in the fluxes of heat, carbon, freshwater and other tracers at the sea surface is highly uncertain and is critical to our understanding of climate change and its impacts. We present a state estimation framework wherein prior estimates of boundary fluxes can be adjusted to make them consistent with the evolving ocean state. In this framework, we define a discrete set of ocean water masses distinguished by their geographical, thermodynamic and chemical properties for specific time periods. Ocean circulation then moves these water masses in geographic space. In phase space, geographically adjacent water masses are able to mix together, representing a convergence, and air–sea property fluxes move the water masses over time. We define an optimisation problem whose solution is constrained by the physically permissible bounds of changes in ocean circulation, air–sea fluxes and mixing. As a proof-of-concept implementation, we use data from a historical numerical climate model simulation with a closed heat and salinity budget. An inverse model solution is found for the evolution of temperature and salinity that is consistent with “true” air–sea heat and freshwater fluxes which are introduced as model priors. When biases are introduced into the prior fluxes, the inverse model finds a solution closer to the true fluxes. This framework, which we call the optimal transformation method, represents a modular, relatively computationally cost-effective, open-source and transparent state estimation tool that complements existing approaches.

Shock compression of crystalline TeO2 to the high-pressure fluid regime: Insights from ab initio molecular dynamics simulations

The shock response of fully-dense and porous crystalline tellurium dioxide (TeO2) to the high-pressure and high-temperature fluid regime was investigated within the framework of density functional theory with Mermin’s generalization to finite temperatures. The principal and porous shock Hugoniot curves were predicted from canonical ab initio molecular dynamics (AIMD) simulations, with the phase space sampled along isotherms up to 80 000 K, for densities ranging from ρ=3 to 17 g/cm3. The polymorphs investigated are α-TeO2 paratellurite (P41212), TeO2 cotunnite (Pnma), and TeO2 post-cotunnite (P21/m). Based on the discontinuity found in the calculated Us−up slope of TeO2 post-cotunnite at a shock velocity of Us≃8.35 km/s and a particle velocity of up≃3.64 km/s, the shock melting temperature and pressure are predicted to be ≃6500 K and ≃170 GPa. Results from the AIMD simulations are in line with the static compression data of TeO2 paratellurite and cotunnite, and with the recent shock Hugoniot data for single-crystal α-TeO2 for pressures up to 85 GPa, obtained using the inclined-mirror method and the velocity interferometer system for any reflector combined with powder gun and two-stage light-gas gun.

Dark matter limits from the tip of the red giant branch of globular clusters

Capture and annihilation of weakly interacting massive particle (WIMP)-like dark matter in red giant stars can lead to faster-than-expected ignition of the helium core, and thus a lower tip of the red giant branch (TRGB) luminosity. We use data to place constraints on the dark matter-nucleon cross section using 22 globular clusters with measured TRGB luminosities, and place projections on the sensitivity resulting from 161 clusters with full phase space distributions observed by . Although limits remain weaker than those from Earth-based direct detection experiments, they represent a constraint that is fully independent of dark matter properties in the solar neighborhood, probing its properties across the entire Milky Way galaxy. Based on our findings, it is likely that the use of the TRGB as a standard candle in H0 measurements is very robust against the effects of dark matter. Published by the American Physical Society 2024

Nonlinear time series analysis of state-wise COVID-19 in Malaysia using wavelet and persistent homology.

The nonlinear progression of COVID-19 positive cases, their fluctuations, the correlations in amplitudes and phases across different regions, along with seasonality or periodicity, pose challenges to thoroughly examining the data for revealing similarities or detecting anomalous trajectories. To address this, we conducted a nonlinear time series analysis combining wavelet and persistent homology to detect the qualitative properties underlying COVID-19 daily infection numbers at the state level from the pandemic's onset to June 2024 in Malaysia. The first phase involved investigating the evolution of daily confirmed cases by state in the time-frequency domain using wavelets. Subsequently, a topological feature-based time series clustering is performed by reconstructing a higher-dimensional phase space through a delay embedding method. Our findings reveal a prominent 7-day periodicity in case numbers from mid-2021 to the end of 2022. The state-wise daily cases are moderately correlated in both amplitudes and phases during the Delta and Omicron waves. Biweekly averaged data significantly enhances the detection of topological loops associated with these waves. Selangor demonstrates unique case trajectories, while Pahang shows the highest similarity with other states. This methodological framework provides a more detailed understanding of epidemiological time series data, offering valuable insights for preparing for future public health crises.

Divergence and Similarity Characteristics for Two Fuzzy Measures Based on Associated Probabilities

Abstract: The article deals with the definitions of the distance, divergence, and similarity characteristics between two finite fuzzy measures, which are generalizations of the same definitions between two finite probability distributions. As is known, a fuzzy measure can be uniquely represented by the so-called its associated probability class (APC). The idea of generalization is that new definitions of distance, divergence, and similarity between fuzzy measures are reduced to the definitions of distance, divergence, and similarity between the APCs of fuzzy measures. These definitions are based on the concept of distance generator. The proof of the correctness of generalizations is provided. Constructed distance, similarity, and divergence relations can be used in such applied problems as: determining the difference between Dempster-Shafer belief structures; Constructions of collaborative filtering similarity relations; non-additive and interactive parameters of machine learning in phase space metrics definition, object clustering, classification and other tasks. In this work, a new concept is used in the fuzzy measure identification problem for a certain multi-attribute decision-making (MADM) environment. For this, a conditional optimization problem with one objective function representing the distance, divergence or similarity index is formulated. Numerical examples are discussed and a comparative analysis of the obtained results is presented.

Quantum instability and Ehrenfest time for an inverted harmonic oscillator

We use out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for an inverted harmonic oscillator (IHO). For initial states located in the stable manifolds of the IHO we find that the corresponding OTOC exhibits identical evolutionary characteristics to the saddle point before the Ehrenfest time. For initial states located in the unstable manifolds, the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during exponential growth of the OTOCs. Our results show that quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the photon number of the initial system but also on the central positions of the initial states in phase space.

On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining

Abstract This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining procedure that leads to convergence. We prove that the time evolution of phase space distributions is an isometry for a broad class of statistical distance metrics, implying that ensembles do not get any closer to (or farther from) equilibrium, according to these metrics. This extends the known result that strong convergence of phase space distributions to the microcanonical distribution does not occur. However, it has long been known that weak convergence can occur, such that coarse-grained distributions---defined by partitioning phase space into a finite number of cells---converge pointwise to the microcanonical distribution. We define a generalization of coarse-graining that removes the need for partitioning phase space into cells. We prove that our generalized coarse-grained distribution converges pointwise to the microcanonical distribution if the dynamics are strong mixing. As an example, we study an ensemble of triangular billiard systems.

π+π− Coulomb interaction study and its use in data processing

In this work, the Coulomb effects (Coulomb correlations) in π+π− pairs produced in p+Ni collisions at 24 GeV/c, are studied using experimental π+π− pair distributions in Q, the relative momentum in the pair center-of-mass system (c.m.s.), and its projections QL (longitudinal component) and Qt (transverse component) relative to the pair direction in the laboratory system (LS). The major part of the pion pairs (“Coulomb pairs”) is produced in the decay of ρ, ω and Δ resonances and other short-lived sources. In these pairs, the significant Coulomb interaction occurs at small Q, dominating the π+π− interaction in the final state. The minor part of the pairs (“non-Coulomb pairs”) is produced if one or both pions arose from long-lived sources like η,η′ or from different interactions. In this case, the final state interaction is practically absent. The Q, QL, and Qt distributions of the Coulomb pairs in the c.m.s. have been simulated assuming they are described by the phase space modified by the known point-like Coulomb correlation function AC(Q), corrected for small effects due to the nonpointlike pair production and the strong two-pion interaction. The same distributions of non-Coulomb pairs have been simulated according to the phase space, but without AC(Q). In all Qt intervals, the experimental QL spectrum shows a peak around QL=0 caused by the Coulomb final state interaction. The full width at half maximum increases with Qt from 3 MeV/c for 0<Qt<0.25 MeV/c to 11 MeV/c for 4.0<Qt<5.0 MeV/c. The experimental QL distributions have been fitted with two free parameters: the fraction of Coulomb pairs and the normalization constant. The precision of the description of these distributions is better than 2% in Qt intervals 2–3, 3–4, and 4–5 MeV/c and better than 0.5% in the total Qt interval 0–5 MeV/c. It is shown that the number of Coulomb pairs in all Qt intervals, including the small Qt (small opening angles θ in the LS) is calculated with theoretical precision better than 2%. The comparison of the simulated and experimental numbers of Coulomb pairs at small Qt allows us to check and correct the detection efficiency for the pairs with small θ (0.06 mrad and smaller). It is shown that Coulomb pairs can be used as a new physical tool to check and correct the quality of the simulated events. The special property of the Coulomb pairs is the possibility of checking and correcting the detection efficiency, especially for the pairs with small opening angles. Published by the American Physical Society 2024

Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems

Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems

Dynamical system analysis in modified Galileon cosmology

Abstract In this paper, we have investigated the phase space analysis in modified Galileon cosmology, where the Galileon term is considered a coupled scalar field, F ( ϕ ) . We focus on the exponential type function of F ( ϕ ) and the three well-motivated potential functions V ( ϕ ) . We obtain the critical points of the autonomous system, along with their stability conditions and cosmological properties. The critical points of the autonomous system describe different phases of the Universe. The scaling solution for critical points was found in our analysis to determine the matter-dark energy and radiation-dark energy-dominated eras of the Universe. In these scaling solutions, dark energy is typically introduced alongside another component, such as radiation or matter, and helps explain the transition between cosmological eras. The dark energy dominated critical points show stable behavior and indicate the late-time cosmic acceleration phase of the Universe. Further, the results are examined with the Hubble rate H(z) and the Supernovae Ia cosmological data sets.

Advances and Challenges in Milestoning Simulations for Drug-Target Kinetics.

Molecular dynamics simulations have become indispensable for exploring complex biological processes, yet their limitations in capturing rare events hinder our understanding of drug-target kinetics. In this Perspective, we investigate the domain of milestoning simulations to understand this challenge. The milestoning approach divides the phase space of the drug-target complex into discrete cells, offering extended time scale insights. This Perspective traces the history, applications, and future potential of milestoning simulations in the context of drug-target kinetics. It explores the fundamental principles of milestoning, highlighting the importance of probabilistic transitions and transition time independence. Markovian milestoning with Voronoi tessellations is revisited to address the traditional milestoning challenges. While observing the advancements in this field, this Perspective also addresses impending challenges in estimating drug-target unbinding rate constants through milestoning simulations, paving the way for more effective drug design strategies.

Infinitely rugged intra-cage potential energy landscape in metallic glasses caused by many-body interaction

The absence of translational symmetry in glassy materials poses a significant challenge in establishing effective structure-property relationships in real space. Consequently, the potential energy landscape (PEL) in phase space is widely utilized to comprehend the complex phenomena in glasses. The classical PEL features a two-scale profile comprising mega-basins and sub-basins, corresponding to α-relaxations (e.g. glass transition) and β-relaxations (e.g. local cage-breaking atomic rearrangements), respectively. Recent studies, however, reveal that sub-basins are not smooth and contain finer structures, the origins of which remain elusive. Here we probe the smoothness of sub-basin bottoms in glasses' PEL by introducing small intra-cage cyclic loading and then measuring the net changes in atomic-level stresses. Compared to glasses with pair interaction, glasses with many-body interaction exhibit orders-of-magnitude larger and loading-dependent stress changes even before the first cage-breaking event takes place, which reflect much more feature-rich sub-basins. We further demonstrate this stark contrast stems from the spatial distribution of individual atom's constraining force field. Specifically, at vanishing perturbations, many-body interactions disrupt the positive-definite synchrony in energy variations of the perturbed atom and the whole system, causing inherently less confined atomic responses and infinitely rugged sub-basins. The implications of these findings for the selective addition or removal of fine structures in the PEL and the subsequent tuning of glassy materials' responses to external stimuli are also explored.

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

A New Filter Based on Sliding Mode Method with Discrete‐Time Implementation for Noise Attenuation and Differentiation

AbstractThis paper presents a novel filter based on the sliding mode method for filtering noise and extracting reliable signals from noisy signals by enhancing Levant's sliding mode filter. Specifically, the proposed sliding mode filter takes advantage of the generalized signum function to adjust the gain in different regions of phase space, thereby decreasing the overshoot during the response phase. Additionally, the discrete‐time implementation of the proposed sliding mode filter is achieved by utilizing the implicit‐Euler algorithm, which effectively eliminates chattering in the output. The effectiveness of the presented sliding mode filter is substantiated via numerical simulation cases.