A heavy reliance on Hamiltonian formalism is generally needed to model particle dynamics in chaotic regimes and, consequently, predict key stochastic heating features, including particle distribution and chaos thresholds. Herein, we traverse a new, more intuitive path to condense the equations of motion for particles into models of known, accessible physical systems like the Kapitza pendulum and the gravitational pendulum. Employing these basic systems, we first outline a technique for determining chaos thresholds, by constructing a model of the pendulum bob's stretching and folding within the phase space. DiR chemical manufacturer This first model serves as the basis for a subsequent random walk model of particle dynamics above the chaos threshold. This model predicts major features of stochastic heating for any EM polarization or viewing angle.

We examine the frequency distribution of power within a signal comprising non-overlapping rectangular pulses. A general formula for calculating the power spectral density is developed for a signal constructed from a succession of distinct, non-overlapping pulses. Finally, we embark on a careful analysis of the rectangular pulse manifestation. Pure 1/f noise is discernible at extremely low frequencies, provided the duration of the characteristic pulse (or gap) is substantially longer than the characteristic gap (or pulse) duration, and these durations follow a power law. The determined outcomes are consistent across both ergodic and weakly non-ergodic processes.

We explore a stochastic version of the Wilson-Cowan model, where the response characteristics of neurons exhibit faster-than-linear growth above their firing threshold. A section of the model's parameter space exhibits the dual attractive fixed points of the dynamic system at the same time. One fixed point is distinguished by its lower activity and scale-free critical behavior; conversely, the second fixed point displays higher (supercritical) persistent activity, with small oscillations around a central value. In cases where the neuron count is not overly large, the network's parameters determine the probability of shifting between these two alternative states. Alongside state variations, the model showcases a bimodal distribution in activity avalanches, with power-law behavior linked to the critical state, and a concentration of large avalanches arising from the supercritical, high-activity state. The bistable nature of the system stems from a first-order (discontinuous) phase transition in its phase diagram; the observed critical behavior is directly related to the spinodal line, the point at which the low-activity state becomes unstable.

Biological flow networks, subjected to external stimuli originating from different locations in their surroundings, adjust their network morphology to enhance flow optimization. Adaptive flow networks' morphology preserves the memory of the stimulus's position. Nevertheless, the constraints on this memory, and the quantity of stimuli it can retain, are presently unknown. Herein, we investigate a numerical model for adaptive flow networks, utilizing the application of multiple stimuli, sequentially. Stimuli imprinted firmly and for extended durations in young networks are associated with significant memory signals. Due to this, networks hold significant storage capacity for stimuli lasting for intermediate periods, creating a harmonious relationship between the processes of imprinting and the effects of aging.

A two-dimensional monolayer of flexible planar trimer particles is observed for its self-organizing characteristics. The molecules are designed from two mesogenic units that are joined by a spacer, all of which are conceptualized as hard needles of equal length. Molecules exist in two dynamic configurations: a non-chiral bent (cis) shape and a chiral zigzag (trans) shape. Using Onsager-type density functional theory (DFT) in conjunction with constant-pressure Monte Carlo simulations, we ascertain that the system comprising these molecules displays a wide range of liquid crystalline phases. A noteworthy observation is the discovery of stable smectic splay-bend (S SB) and chiral smectic-A (S A^*) phases. The S SB phase maintains its stability even when restricted to exclusively cis-conformers. Within the substantial area of the phase diagram, the second phase is S A^* characterized by chiral layers, where adjacent layers exhibit opposing chirality. bio-functional foods Observations of the mean fractions of trans and cis conformers within different phases indicate a uniform distribution of all conformers in the isotropic phase, whereas the S A^* phase is substantially populated with chiral zigzag conformers, in contrast to the smectic splay-bend phase where achiral conformers prevail. DFT calculations are undertaken to determine the free energies of the nematic splay-bend (N SB) and S SB phases for cis- conformers, at densities showing stable S SB phases in simulations, to evaluate the possibility of stabilizing the N SB phase in trimers. nursing medical service The N SB phase, away from the nematic phase transition, proves unstable, its free energy consistently exceeding that of S SB, all the way down to the nematic transition, although the difference in free energies shrinks significantly as the transition is approached.

A significant hurdle in time-series analysis is often encountered when predicting the evolution of a dynamic system using only partial or scalar observations. Takens' theorem demonstrates, for data originating from a smooth, compact manifold, that a time-delayed embedding of the partial state is diffeomorphic to the attractor. However, learning these delay coordinate mappings remains a significant challenge for chaotic and highly nonlinear systems. Our use of deep artificial neural networks (ANNs) facilitates the learning of discrete time maps and continuous time flows of the partial state. Using the training data of the complete state, we develop a reconstruction map as well. Time series forecasting is feasible by leveraging the current condition and prior observations, with embedding parameters derived from a comprehensive investigation of the time series's characteristics. The state space's dimension under time evolution exhibits a similar magnitude to reduced-order manifold models. These represent superiorities over recurrent neural network models, which necessitate a high-dimensional internal state, or the addition of memory terms and fine-tuning of their associated hyperparameters. We employ deep artificial neural networks to predict the chaotic nature of the Lorenz system, a three-dimensional manifold, from a single scalar measurement. Multivariate observations of the Kuramoto-Sivashinsky equation are included in our study; the dimensionality of observations needed to accurately reproduce the dynamics grows with the manifold dimension, increasing with the spatial breadth of the system.

Using statistical mechanics, we analyze the collective characteristics and limitations found in the combination of individual cooling units. Zones, modeled as thermostatically controlled loads (TCLs), are represented by these units in a large commercial or residential building. The air handling unit (AHU), a centralized control point, manages and directs the energy input for all TCLs, ensuring a unified cool-air delivery system. We sought to identify the salient qualitative aspects of the AHU-TCL coupling, achieving this by creating a basic yet realistic model, then investigating its operation under two different conditions: constant supply temperature (CST) and constant power input (CPI). In each case, our analysis revolves around the relaxation dynamics of individual TCL temperatures, which eventually attain a statistical steady state. Although the CST regime showcases relatively fast dynamics that keep all TCLs near the control point, the CPI regime introduces a bimodal probability distribution and two, potentially greatly disparate, time scales. In the CPI regime, the two modes are attributable to all TCLs uniformly operating in either low or high airflow states, with transitions between them occurring collectively, akin to Kramer's phenomenon in statistical mechanics. Our current knowledge indicates that this phenomenon has been neglected within the realm of building energy systems, despite its immediate and demonstrable influence on the systems' operation. The discussion points to a trade-off between occupational well-being—influenced by temperature variations in designated areas—and the energy resources required to regulate the environment.

Meter-scale dirt cones, composed of ice cones overlaid with a thin layer of ash, sand, or gravel, are naturally formed glacial surface features, originating from an initial debris patch. Our findings concerning cone formation in the French Alps encompass field observations, laboratory-based experiments, and the application of 2D discrete-element-method-finite-element-method simulations, which incorporate both grain mechanics and thermal parameters. We demonstrate that the granular layer's insulating properties result in cone formation, reducing ice melt beneath it compared to exposed ice. Differential ablation deforms the ice surface and initiates a quasistatic grain flow, leading to the formation of a cone, as the thermal length becomes comparatively smaller than the structure. Through continued growth, the cone achieves a stable state where the insulation provided by the dirt layer effectively balances the heat flux radiating from the enlarged external structure. These results provided insight into the essential physical mechanisms involved, allowing for the creation of a model capable of quantitatively replicating the numerous field observations and laboratory findings.

CB7CB [1,7-bis(4-cyanobiphenyl-4'-yl)heptane], mixed with a trace amount of a long-chain amphiphile, is analyzed for the structural features of twist-bend nematic (NTB) droplets acting as colloidal inclusions within the isotropic and nematic phases. During the isotropic phase, the radial (splay) geometry of the nucleating drops leads to the development of escaped, off-centered radial structures, incorporating both splay and bend distortions.