The prediction of key stochastic heating features, including particle distribution and chaos thresholds, typically necessitates a substantial Hamiltonian formalism, which is crucial for modeling particle dynamics within chaotic environments. In this study, we investigate a more intuitive and alternative methodology, facilitating the simplification of particle motion equations to well-understood physical systems, including the Kapitza pendulum and the gravity pendulum. These basic systems allow us to first introduce a technique for estimating chaos thresholds, by developing a model that captures the stretching and folding motions of the pendulum bob within its phase space. dWIZ-2 From this initial model, a random walk model for particle dynamics above the chaos threshold is developed. This model allows for the prediction of major features of stochastic heating, considering all electromagnetic polarizations and observational angles.

Analyzing the power spectral density of a signal made up of non-overlapping rectangular impulses is our approach. A general formula for a signal's power spectral density, originating from an arrangement of non-overlapping pulses, is our starting point. After that, a detailed examination of the rectangular pulse situation will be carried out. Under the condition that the characteristic pulse (or gap) duration is longer than the characteristic gap (or pulse) duration, and both durations follow power-law distributions, we demonstrate pure 1/f noise can be observed at extremely low frequencies. Ergodic and weakly non-ergodic processes are both encompassed by the derived results.

A stochastic rendition of the Wilson-Cowan neural model is examined, demonstrating a neuron response function that increases faster than linearly beyond the activation threshold. The model's parameters indicate a region where two attractive fixed points, stemming from the dynamics, are present concurrently. One fixed point is defined by a lower activity level and scale-free critical behavior, contrasting with a second fixed point that exhibits a higher (supercritical) sustained activity, with subtle fluctuations around its mean value. If the neuron count is not extensive, the network can fluctuate between these two conditions with probability dependent on the network's parameters. The model demonstrates a bimodal distribution of activity avalanches, alongside state transitions. A power-law relationship characterizes the critical state's avalanches, while a distinct cluster of sizable avalanches arises from the supercritical, high-activity state. The bistability, a consequence of a first-order (discontinuous) transition within the phase diagram, is further characterized by the observed critical behavior, associated with the spinodal line, the dividing line between stability and instability of the low-activity state.

In response to external stimuli from different locations in their surroundings, biological flow networks modify their network morphology, thus enhancing flow optimization. The adaptive flow networks' morphology serves as a repository for the location of the remembered stimulus. Nevertheless, the constraints on this memory, and the quantity of stimuli it can retain, are presently unknown. Using multiple stimuli applied sequentially, this work examines a numerical model of adaptive flow networks. In young networks, stimuli imprinted for an extensive time period are associated with strong memory signals. In consequence, networks can accommodate extensive storage of stimuli for durations intermediate in nature, ensuring a compromise between the imprint of experience and the gradual effects of time.

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. A molecule can assume two distinct conformations: a non-symmetric bent shape (cis) and a chiral zigzag form (trans). Constant-pressure Monte Carlo simulations, in combination with Onsager-type density functional theory (DFT), are used to show that the molecular system demonstrates a rich tapestry of liquid crystalline phases. The identification of stable smectic splay-bend (S SB) and chiral smectic-A (S A^*) phases stands out as the most compelling observation. The S SB phase retains its stability when restricted, in the limit, to only cis-conformers. The second phase, S A^*, with chiral layers displaying opposite chirality in neighboring layers, comprises a substantial area in the phase diagram. Taxus media Statistical analysis of the average proportions of trans and cis conformers across various phases reveals a uniform distribution in the isotropic phase, whereas the S A^* phase is largely comprised of chiral zigzag conformers, in contrast to the achiral conformer prevalence observed in the smectic splay-bend phase. For trimers, the free energy of the nematic splay-bend (N SB) phase, as well as the S SB phase, is calculated using DFT for cis- conformers under densities where simulations confirm the stability of the S SB phase, to better understand the possibility of stabilization of the N SB phase. Extra-hepatic portal vein obstruction The N SB phase's instability is apparent when removed from the transition to the nematic phase. Its free energy perpetually exceeds that of S SB all the way to the nematic transition, although the difference in free energies becomes practically negligible as the transition point is reached.

The task of predicting the intricate workings of a time-series based on only scalar or partial information about the underlying dynamic system represents a frequent problem. Takens' theorem shows a diffeomorphic relationship between the attractor and a time-delayed embedding of the partial state for data on a smooth, compact manifold, although the learning of delay coordinate mappings remains challenging in chaotic and highly nonlinear systems. To acquire knowledge of discrete time maps and continuous time flows of the partial state, we resort to the use of deep artificial neural networks (ANNs). The training data for the full state enables the learning of a reconstruction map. Predictions for a time series are enabled by using the current state and previous data points, with parameters for embedding determined through the examination of the time series. The state space's dimension during time evolution is similar in scale to the dimensionality of reduced-order manifold models. Compared to recurrent neural network models, these advantages stem from the avoidance of a complex, high-dimensional internal state or supplementary memory terms, and 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. In examining the Kuramoto-Sivashinsky equation, multivariate observations are also considered. Here, the observation dimension needed for accurate dynamic reproduction rises in proportion to the manifold dimension, determined by the system's spatial coverage.

Employing statistical mechanics principles, we investigate the phenomena and restrictions arising from the combination of individual cooling units. Inside a large commercial or residential building, these units are characterized by being modeled as thermostatically controlled loads (TCLs) to represent zones. A coordinated energy input, controlled by the air handling unit (AHU), delivers cool air to each TCL, forming a cohesive system. By developing a basic, yet comprehensive model of the AHU-to-TCL linkage, we aimed to identify the key qualitative attributes. This model was subsequently analyzed within two distinct operating conditions: constant supply temperature (CST) and constant power input (CPI). Our analysis in both scenarios focuses on how individual TCL temperatures reach a consistent statistical state through relaxation dynamics. The CST regime shows relatively quick dynamics causing all TCLs to revolve around the control set point. Conversely, the CPI regime displays a bimodal probability distribution and two time scales that may be largely separated. Analysis reveals that the CPI regime's two modes are linked to all TCLs being in identical low or high airflow states, interspersed with collective transitions reminiscent of Kramer's phenomenon in statistical physics. 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 sentence underscores a trade-off between the comfort of the work environment, contingent on varying temperatures in different zones, and the expense of energy consumption.

Ice cones, concealed by a thin layer of ash, sand, or gravel, form meter-scale dirt cones on glacial surfaces, structures naturally arising from a foundational patch of debris. In the French Alps, field observations of cone formation are detailed, alongside controlled laboratory experiments replicating these structures, and supported by 2D discrete-element-method-finite-element-method numerical simulations integrating both grain mechanics and thermal effects. Cones develop due to the insulating qualities of the granular layer, which mitigates ice melt underneath, as opposed to the melt rate of exposed ice. The deformation of the ice surface, caused by differential ablation, prompts a quasistatic grain flow, ultimately manifesting as a conic shape, given the thermal length's reduction relative to structural size. The dirt layer's insulation, within the cone, gradually builds until the heat flux from the expanding outer structure is perfectly counteracted. These results led to the identification of the central physical mechanisms active in this system, and to the development of a model that could quantitatively reproduce the diverse data gathered from field studies and experiments.

Within the mesogen CB7CB [1,7-bis(4-cyanobiphenyl-4'-yl)heptane], blended with a small quantity of a long-chain amphiphile, the structural attributes of twist-bend nematic (NTB) droplets, acting as colloidal inclusions in isotropic and nematic phases, are studied. The isotropic phase witnesses the development of drops, originally nucleated in a radial (splay) geometry, into escaped, off-centered radial structures that are characterized by both splay and bend distortions.