Description Of Dynamics Research Articles

Dynamic Description of soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms

Abstract The article presents an analytical solution for the higher-order nonlinear Schrödinger equation (NLSE), which describes the propagation of short light pulses in monomode optical fibers. Various traveling wave solutions are obtained using the generalized exponential rational function method, a technique with substantial applications in physics and mathematics. Additionally, the parameters leading to the occurrence of optical bright and multipeak solitons in this medium are provided along with their formation conditions. The derived solutions are graphically displayed to enhance the understanding of the model’s physical phenomena. This approach is credible, potent, and successful in solving a wide variety of different models of this kind that arise in the applied sciences. Its robustness, strength, and efficiency make it suitable for addressing various higher-order nonlinear problems in current research fields, extending beyond the models encountered in the applied sciences.

Pattern‐moving‐based dynamic description and optimal control for non‐Newtonian mechanical systems with generalized cell mapping

AbstractThis article focuses on the problem of modelling and control for a non‐Newtonian mechanical system that may be subject to the statistical law instead of the traditional Newtonian principles mechanics. A discrete method, synthesizing the generalized cell mapping (GCM) together with dynamic programming (DP), with inverse search strategy, using pattern moving theory (PMT) framework, was proposed. The basic idea is to describe and control the system's dynamic peculiarity utilizing pattern class variable in ‘pattern moving space’. First, a few prior concepts were reviewed, including PMT, cell mapping, and optimal control for this kind system. Then, we articulated a cross‐mapping method to analyze the system dynamic behaviour, which takes into account the computational and statistical properties of pattern class variable simultaneously. For system optimal control, the improved GCM and cost function were performed to determine the discrete optimal control table (DOCT) in accordance with dynamic programming and inverse search. Finally, simulation results of two cases demonstrate the efficiency and practicality of the proposed approach. The study has resulted in a solution of describing and controlling based on pattern class variable for non‐Newtonian mechanical systems, and its main objective was to give a different perspective in term of research into non mechanistic principles modelling and application of nonlinear systems.

Online commercial sexual exploitation of children in a national victim survey.

To describe the characteristics and consequences of online commercial sexual exploitation of children using a nationally representative sample. The online survey sample comprised 2,639 respondents aged 18-28 from the KnowledgePanel maintained by the survey research firm Ipsos. Fifty-eight respondents or a weighted 1.7% of the sample described childhood experiences in which they used technology to exchange sexual talks, sexual images, or other sexual activities for money, drugs, or other valuable items. The episodes were very diverse. Sixty-three percent were girls, 30% boys, 7% gender fluid, and 42% sexual minorities. Half were ages 16 or 17, and half were younger at the time of the activity. Many (44%) were involved in offline sexual activity. The purchasers were not exclusively anonymous internet contacts; 19% were current or former intimate partners and another 10% friends or acquaintances. Most of the exchanges (92%) were self-negotiated, and only 8% involved a facilitator. Nonetheless, most reported negative reactions involving embarrassment, anxiety, and feeling afraid. Sexual minority youth reported more exchanging sexual talk, having a facilitator involved, feeling afraid and falling behind in school or work than heterosexual youth. This national survey reveals a high frequency of childhood commercial sex that diverges from descriptions of dynamics based on police and social agency data. Such dynamics suggest the need for alternative approaches to prevention. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Renormalization in Lorenz maps - completely invariant sets and periodic orbits

The paper deals with dynamics of expanding Lorenz maps, which appear in a natural way as Poincarè maps in geometric models of well-known Lorenz attractor. Using both analytical and symbolic approaches, we study connections between periodic points, completely invariant sets and renormalizations. We show that some renormalizations may be connected with completely invariant sets while some others don't. We provide an algorithm to detect the renormalizations that can be recovered from completely invariant sets. Furthermore, we discuss the importance of distinguish one-side and double-side preimage. This way we provide a better insight into the structure of renormalizations in Lorenz maps. These relations remained unnoticed in the literature, therefore we are correcting some gaps existing in the literature, improving and completing to some extent the description of possible dynamics in this important field of study.

Analytic solutions for equatorial, Kelvin, Rossby, and Yanai beams

Wind-driven equatorial Kelvin, Rossby, and Yanai waves are known to propagate vertically, as well as zonally, and packets of them can form “beams” that descend into the deep ocean along ray paths consistent with wave-group theory. Here, we obtain analytic solutions to a simplified ocean model that provide a more complete description of beam properties and dynamics than in previous studies.The model is a linear, continuously stratified (LCS) system, in which the bottom is ignored and the background Vaisala frequency Nb is constant. Solutions are forced by an oscillatory wind stress, τα=τoαXxexp−iσt, where: α is x or y; Xx is confined to the region −L<x<L and increases and decreases monotonically; and τα enters the ocean as a body force with the profile Zz=2/πh/z2+h2. Under these restrictions, solutions can be represented as cosine transforms in z that can be readily inverted.Beam solutions for all three wave types have similar mathematical forms, and hence share many properties. Among other things, the solutions show how the structure and amplitude of beams depend on the above model parameters. Potential impacts of processes neglected in the solutions are noted.

Quantitative Standardized Expansion Assay: An Artificial Intelligence-Powered Morphometric Description of Blastocyst Expansion and Zona Thinning Dynamics

Artificial intelligence applied to time-lapse microscopy may revolutionize embryo selection in IVF by automating data collection and standardizing the assessments. In this context, blastocyst expansion dynamics, although being associated with reproductive fitness, have been poorly studied. This retrospective study (N = 2184 blastocysts from 786 cycles) exploited both technologies to picture the association between embryo and inner-cell-mass (ICM) area in µm2, the ICM/Trophectoderm ratio, and the zona pellucida thickness in µm (zp-T) at sequential blastocyst expansion stages, with (i) euploidy and (ii) live-birth per transfer (N = 548 transfers). A quantitative-standardized-expansion-assay (qSEA) was also set-up; a novel approach involving automatic annotations of all expansion metrics every 30 min across 5 h following blastulation. Multivariate regressions and ROC curve analyses were conducted. Aneuploid blastocysts were slower, expanded less and showed thicker zp. The qSEA outlined faster and more consistent zp thinning processes among euploid blastocysts, being more or as effective as the embryologists in ranking euploid embryo as top-quality of their cohorts in 69% of the cases. The qSEA also outlined faster and more consistent blastocyst expansion and zp thinning dynamics among euploid implanted versus not implanted blastocysts, disagreeing with embryologists’ priority choice in about 50% of the cases. In conclusion, qSEA is a promising objective, quantitative, and user-friendly strategy to predict embryo competence that now deserves prospective validations.

Deformable bodies in two dimensions and the gauge aspect of bottle flip

Abstract The water-bottle flip demonstration, that has received quite a viewership on media, involves tossing a bottle filled (up&amp;#xD;to some fraction of its volume) with water up in the air while giving it a transverse spin in such a way that it lands&amp;#xD;perfectly upright on its base. A mathematical description of the actual dynamics of the bottle flip is bound to be very&amp;#xD;complicated due to the highly non-linear motion of the fluid. A model that is amenable to an analytical treatment has&amp;#xD;been proposed in the literature. Conservation of angular momentum in the center of mass frame allows the angular&amp;#xD;velocity of the bottle to change, and in particular it becomes very low right before the landing. This is thought to&amp;#xD;be the essential feature needed for an upright landing of the bottle. In this paper we study a mathematical formalism&amp;#xD;that would be useful to improve upon the analysis of this model. We point out that the proper mathematical setting to&amp;#xD;analyze such systems is to model the content of the bottle as a deformable body. This brings out the gauge dependence&amp;#xD;of the angular velocity and shows that it can even go to zero without violating the conservation of angular momentum.&amp;#xD;The mechanism is well studied in literature under the heading of the falling cat problem. Indeed, from our point of&amp;#xD;view the bottle-flip system is a two dimensional analog of the falling cat problem (modulo the self-control of the cat)

SMASH as an event generator for heavy-ion collisions

In this article we present an overview of the SMASH hadronic transport approach that is applied for non-equilibrium dynamics of hadrons in heavy-ion collisions. We will give an overview about the ingredients of the approach and the applications for the dynamical description of heavy-ion collisions and for calculations of fundamental properties of the hadron gas. The main emphasis of the article will be the infrastructure for sustainable software development that we have developed over the last 10 years including extensive unit tests and continuous integration. We will also provide one section about the performance of the code and how it can be analyzed and improved in the future.

Gradient dynamics approach to reactive thin-film hydrodynamics

Wetting and dewetting dynamics of simple and complex liquids is described by kinetic equations in gradient dynamics form that incorporates the various coupled dissipative processes in a fully thermodynamically consistent manner. After briefly reviewing this, we also review how chemical reactions can be captured by a related gradient dynamics description, assuming detailed balanced mass action type kinetics. Then, we bring both aspects together and discuss mesoscopic reactive thin-film hydrodynamics illustrated by two examples, namely, models for reactive wetting and reactive surfactants. These models can describe the approach to equilibrium but may also be employed to study out-of-equilibrium chemo-mechanical dynamics. In the latter case, one breaks the gradient dynamics form by chemostatting to obtain active systems. In this way, for reactive wetting we recover running drops that are driven by chemically sustained wettability gradients and for drops covered by autocatalytic reactive surfactants we find complex forms of self-propulsion and self-excited oscillations.

Dynamics of finite width Kernel and prediction fluctuations in mean field neural networks*

Abstract We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O ( 1 / width ) fluctuations of the dynamical mean field theory order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. We find that once the mean field/µP parameterization is adopted, the leading finite size effect on the dynamics is to introduce initialization variance in the predictions and feature kernels of the networks. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently. In two layer networks, we show how feature learning can dynamically reduce the variance of the final tangent kernel and final network predictions. We also show how initialization variance can slow down online learning in wide but finite networks. In deeper networks, kernel variance can dramatically accumulate through subsequent layers at large feature learning strengths, but feature learning continues to improve the signal-to-noise ratio of the feature kernels. In discrete time, we demonstrate that large learning rate phenomena such as edge of stability effects can be well captured by infinite width dynamics and that initialization variance can decrease dynamically. For convolutional neural networks trained on CIFAR-10, we empirically find significant corrections to both the bias and variance of network dynamics due to finite width.

Dynamic Random Intersection Graph: Dynamic Local Convergence and Giant Structure

ABSTRACTRandom intersection graphs containing an underlying community structure are a popular choice for modeling real‐world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when they share at least one group. We extend this approach and make the communities dynamic by letting them alternate between an active and inactive phase. We analyse the new model, delivering results on degree distribution, local convergence, largest connected component, and maximum group size, paying particular attention to the dynamic description of these properties. We also describe the connection between our model and the bipartite configuration model, which is of independent interest.

An efficient device model for ferroelectric thin-film transistors

Ferroelectric thin-film transistors (Fe-TFTs) have promising potential for flexible electronics, memory, and neuromorphic computing applications. Here, we report on a physics-based efficient device model for Fe-TFTs that effectively describes memory switching and device I–V characteristics. This model combines a stochastic multi-domain description of FE switching dynamics with a virtual source treatment of TFT device characteristics. It demonstrates that the memory window of Fe-TFTs depends on the amplitude and duration of the applied voltage pulses, thus suggesting quantitative means of programming and control. Additionally, we introduce a machine-learning-enabled method to automatically generate optimal voltage pulses for accurately programming multiple intermediate FE states, which is crucial for multi-bit memory and neuromorphic computing applications. To showcase the model’s applications, we simulate a 4×4 crossbar array circuit based on Fe-TFTs, highlighting its utility in performing multiply-accumulate computing operations. This small array can achieve a high speed of ∼1.28 tera operations per second (OPS) and a power efficiency of ∼0.43 W/PetaOPS. The model developed here is valuable for exploring the capabilities of Fe-TFTs in future flexible memory and computing technologies.

Nonhomogeneous hidden semi-Markov models for toroidal data

Abstract A nonhomogeneous hidden semi-Markov model is proposed to segment bivariate time series of wind and wave directions according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process’ survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates. It includes nonhomogeneous hidden Markov models and hidden semi-Markov models as special cases. Parameter estimates are obtained using an Expectation-Maximization algorithm that relies on an efficient augmentation of the latent process. Fitted on a time series of wind and wave directions recorded in the Adriatic Sea, the model offers a clear-cut description of sea state dynamics in terms of latent regimes and captures the influence of time-varying weather conditions on the duration of such regimes.

Quantum Molecular Charge-Transfer Model for Multistep Auger-Meitner Decay Cascade Dynamics.

The fragmentation of molecular cations following inner-shell decay processes in molecules containing heavy elements underpins the X-ray damage effects observed in X-ray scattering measurements of biological and chemical materials, as well as in medical applications involving Auger electron-emitting radionuclides. Traditionally, these processes are modeled using simulations that describe the electronic structure at an atomic level, thereby omitting molecular bonding effects. This work addresses the gap by introducing a novel approach that couples Auger-Meitner decay to nuclear dynamics across multiple decay steps, by developing a decay spawning dynamics algorithm and applying it to potential energy surfaces characterized with ab initio molecular dynamics simulations. We showcase the approach on a model decay cascade following K-shell ionization of IBr and subsequent Kβ fluorescence decay. We examine two competing channels that undergo two decay steps, resulting in ion pairs with a total 3+ charge state. This approach provides a continuous description of the electron transfer dynamics occurring during the multistep decay cascade and molecular fragmentation, revealing the combined inner-shell decay and charge transfer time scale to be approximately 75 fs. Our computed kinetic energies of ion fragments show good agreement with experimental data.

A Microscopic On-Ramp Model Based on Macroscopic Network Flows

While macroscopic traffic flow models adopt a fluid dynamic description of traffic, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena accurately remains a challenge for microscopic models, especially in complex road sections. Based on a macroscopic network flow model calibrated to real traffic data and new rules for the acceleration and merging behavior on the on-ramp, we propose a microscopic model for on-ramps. To evaluate the performance of the new flow-based model, we conduct traffic simulations assessing speeds, accelerations, lane change positions, and risky behavior. Our results show that, although the proposed model exhibits some limitations, its performance is superior to the Intelligent Driver Model in the evaluated aspects. While the Intelligent Driver Model simulations are almost free of conflicts, the proposed model evokes a realistic amount and severity of conflicts and therefore can be considered for safety analysis.

Subdiffusion of heavy quarks in hot QCD matter by the fractional Langevin equation

The subdiffusion phenomena are studied for heavy quarks dynamics in the hot QCD matter. Our approach aims to provide a more realistic description of heavy quark dynamics through detailed theoretical analyses and numerical simulations, utilizing the fractional Langevin equation framework with the Caputo fractional derivative. I present numerical schemes for the fractional Langevin equation for subdiffusion and calculate the time evolution mean squared displacement and mean squared momentum of the heavy quarks. My results indicate that the mean squared displacements of the heavy quarks for the subdiffusion process deviate from a linear relationship with time. Further, I calculate the normalized momentum correlation function, kinetic energy, and momentum spread. Finally, I show the effect of subdiffusion on experimental observables, the nuclear modification factor. Published by the American Physical Society 2024

Flux qubit based detector of microwave photons

A theory of detection of microwave photons with a flux qubit based detector is presented. We consider a semiclassical approximation with the electromagnetic field being in a coherent state. The flux qubit is considered as a multilevel quantum system (qudit). By solving the Lindblad equation, we describe the time evolution of occupations of the qudit's levels for readout and reset stages of detection. When considering the reset stage, the time evolution is described by multiple avoided-level crossings, thus providing a multilevel Landau-Zener-Stückelberg-Majorana (LZSM) problem. In addition to numerical calculations, we present an approximate solution for the description of the reset stage dynamics based on the adiabatic-impulse approximation and rate equation approach. Our theory may be useful for the theoretical description of driven-dissipative dynamics of qudits, including applications such as single-photon detection. Published by the American Physical Society 2024

Excitation and manipulation of super cavity solitons in multi-stable passive Kerr resonators

We report on the theoretical analysis as well as the numerical simulations about the nonlinear dynamics of cavity solitons in a passive Kerr resonator operating in the multistable regime under the condition of a sufficiently strong pump. In this regime, the adjacent tilted cavity resonances might overlap, thus leading to the co-existence of combinatory states of temporal cavity solitons and the extended modulation instability patterns. The cavity in the regime of multistablity may sustain distinct families of cavity solitons, vividly termed as super cavity solitons with much higher intensity and broader spectra if compared with those in the conventional bi-stable regime. The description of such complex cavity dynamics in the multstable regime requires either the infinite-dimensional Ikeda map, or the derived mean-field coupled Lugiato-Lefever equations by involving multiple contributing cavity resonances. With the latter model, we revealed the existence of different orders of super cavity solitons, whose stationary solutions were obtained by using the Newton-Raphson algorithm. Along this line, with the continuation calculation, we have plotted the Hopf / saddle-node bifurcation curves, thus identifying the existing map of the stable and breathing (super) cavity solitons. With this defined parameter space, we have proposed an efficient method to excite and switch the super cavity solitons by adding an appropriate intensity (or phase) perturbation on the pump. Such deterministic cavity soliton manipulation technique is demonstrated to underpin the multi-level coding, which may enable the large capacity all-optical buffering based on the passive fiber ring cavities.

A global–land snow scheme (GLASS) v1.0 for the GFDL Earth System Model: formulation and evaluation at instrumented sites

Abstract. Snowpacks modulate water storage over extended land regions and at the same time play a central role in the surface albedo feedback, impacting the climate system energy balance. Despite the complexity of snow processes and their importance for both land hydrology and global climate, several state-of-the-art land surface models and Earth System Models still employ relatively simple descriptions of the snowpack dynamics. In this study we present a newly-developed snow scheme tailored to the Geophysical Fluid Dynamics Laboratory (GFDL) land model version 4.1. This new snowpack model, named GLASS (Global LAnd–Snow Scheme), includes a refined and dynamical vertical-layering snow structure that allows us to track the temporal evolution of snow grain properties in each snow layer, while at the same time limiting the model computational expense, as is necessary for a model suited to global-scale climate simulations. In GLASS, the evolution of snow grain size and shape is explicitly resolved, with implications for predicted bulk snow properties, as they directly impact snow depth, snow thermal conductivity, and optical properties. Here we describe the physical processes in GLASS and their implementation, as well as the interactions with other surface processes and the land–atmosphere coupling in the GFDL Earth System Model. The performance of GLASS is tested over 10 experimental sites, where in situ observations allow for a comprehensive model evaluation. We find that when compared to the current GFDL snow model, GLASS improves predictions of seasonal snow water equivalent, primarily as a consequence of improved snow albedo. The simulated soil temperature under the snowpack also improves by about 1.5 K on average across the sites, while a negative bias of about 1 K in snow surface temperature is observed.

Models of the Sea Surface Height Expression of the Internal-Wave Continuum

Abstract Several models are presented for the sea surface height (SSH) signature of the interior-ocean internal-wave continuum. Most are based on the Garrett–Munk internal-wave model. One is derived from the frequency spectrum of dynamic height from mooring observations. The different models are all plausibly consistent with accepted dynamical and semiempirical spectral descriptions of the climatological interval-wave field in the interior ocean, but they result in different proportionalities between interior and SSH spectral energy levels. The differences arise in part from differences in the treatment of near-surface stratification, and a major source of uncertainty for all the models comes from inadequately constrained assumptions about the energy in the low-vertical-mode internal-wave field. Most of these models suggest that the SSH signature of the internal-wave continuum will be visible in SSH measurements from the Surface Water and Ocean Topography (SWOT) wide-swath satellite altimeter. Temporal variability of internal-wave energy levels and the internal-wave directional spectrum are less well characterized but will also be consequential for the observability of internal-wave signals in SWOT data.