Accurate modeling of particle dynamics in chaotic regimes requires a substantial Hamiltonian formalism for predicting key stochastic heating features, such as particle distribution and chaos thresholds. Through an alternative, more intuitively grasped method, the complex equations of motion for particles are reduced to familiar physical frameworks, exemplified by the Kapitza pendulum and gravitational pendulum. Building upon these fundamental systems, we initially provide a method for calculating chaos thresholds, derived from a model which describes the stretching and folding patterns of the pendulum bob's trajectory through phase space. genetic rewiring Following this initial model, we subsequently develop a random walk model for particle dynamics exceeding the chaos threshold, capable of predicting key aspects of stochastic heating regardless of electromagnetic polarization or observation angle.

Our investigation into the power spectral density centers on a signal formed by independent, rectangular pulses. A general formula for a signal's power spectral density, originating from an arrangement of non-overlapping pulses, is our starting point. We proceed to conduct a meticulous analysis of the rectangular pulse case. We present evidence that pure 1/f noise manifests down to extremely low frequencies when the characteristic pulse duration or gap duration is prolonged in comparison to the characteristic gap or pulse duration, and the durations follow a power law distribution. The results obtained are applicable to ergodic and weakly non-ergodic processes in their entirety.

Our study focuses on a probabilistic variant of the Wilson-Cowan model, with neuron response functions increasing at a rate exceeding linearity above the threshold level. The dynamic system's attractive fixed points, according to the model, can exist simultaneously within a specific region of parameter space. Characterized by lower activity and scale-free critical behavior, a specific fixed point stands in contrast to another fixed point that demonstrates higher (supercritical) persistent activity, exhibiting minute fluctuations around a mean. Provided the number of neurons isn't excessive, the system's ability to transition between the two states is probabilistically tied to the network's configuration. State transitions within the model are accompanied by a bimodal distribution of activity avalanches, which exhibit a power-law relation in the critical state. A concentration of exceptionally large avalanches is further observed in the high-activity supercritical state. Bistability arises from a first-order (discontinuous) phase transition, with the observed critical behavior correlating to the spinodal line, the demarcation of instability for the low-activity state.

Biological flow networks, in response to environmental stimuli from varying spatial locations, modify their network structure for optimal flow. Adaptive flow networks' structural memory is linked to the location of the stimulus. Nevertheless, the constraints on this memory, and the quantity of stimuli it can retain, are presently unknown. By sequentially applying multiple stimuli, we study a numerical model of adaptive flow networks in this paper. We observe pronounced memory signals in young networks exposed to stimuli retained over prolonged periods. 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.

Self-organization within a monolayer of flexible planar trimer particles (a two-dimensional system) is investigated. Molecules are composed of two mesogenic units, separated by a spacer, which are all represented by rigid needles of the same length. Each molecule can switch between a non-chiral bent (cis) conformation and a chiral zigzag (trans) configuration. Monte Carlo simulations under constant pressure, in conjunction with Onsager-type density functional theory (DFT), unveil a variety of liquid crystalline phases within this molecular system. The most important observation made was the identification of stable smectic splay-bend (S SB) and chiral smectic-A (S A^*) phases. The S SB phase retains its stability when restricted, in the limit, to only 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. anticipated pain medication needs A comparative analysis of the average fractions of trans and cis conformers across various phases shows that the isotropic phase equally populates all conformers, but the S A^* phase exhibits a significant preponderance of chiral zigzag conformers, whereas the smectic splay-bend phase is predominantly composed of achiral conformers. The free energies of the nematic splay-bend (N SB) and S SB phases, for trimers, are calculated using Density Functional Theory (DFT) for cis- conformations at densities where simulations indicate a stable S SB phase, to clarify the potential for stabilizing the N SB phase. selleck inhibitor Away from the nematic phase transition, the N SB phase demonstrates instability, its free energy always greater than S SB, persisting right down to the transition, the difference in free energies, however, becoming remarkably small as the transition is approached.

Dynamic systems analysis frequently faces the challenge of predicting behaviour based on either incomplete or scalar observations of the underlying system. Takens' theorem asserts a diffeomorphic correspondence between the attractor and a time-delayed embedding of the partial state for data arising from a smooth and compact manifold. Learning these delay coordinate mappings, however, remains problematic in the context of chaotic and highly nonlinear systems. Deep artificial neural networks (ANNs) are instrumental in our approach to learning discrete time maps and continuous time flows of the partial state. In conjunction with the complete state's training data, we also learn a reconstruction mapping. Hence, estimations regarding a time series's future trajectory are possible, by incorporating the present state and prior observations, with embedded parameters resulting from time-series analysis. Reduced order manifold models share a comparable dimensional characteristic to the state space undergoing time evolution. These advantages over recurrent neural network models derive from their avoidance of a complex high-dimensional internal state and additional memory terms; thus, their dependence on hyperparameters is lower. Deep artificial neural networks, as demonstrated through the Lorenz system, are shown to predict the chaotic dynamics on a three-dimensional manifold, based on a single scalar input. We also take into account multivariate observations of the Kuramoto-Sivashinsky equation, where the required observation dimensionality for precise reproduction of dynamics grows with the manifold's dimension, scaling proportionally with the system's spatial expanse.

The statistical mechanics perspective is applied to understanding the collective patterns and constraints observed in the aggregation of individual cooling units. Representing zones, these units are modeled as thermostatically controlled loads (TCLs) in a large commercial or residential building. Cool air is distributed to all TCLs by the centralized air handling unit (AHU), which controls the energy input, interlinking them. With the objective of determining the significant qualitative attributes of the AHU-to-TCL coupling, we formulated a simple but realistic model, and then evaluated its behavior under two operational regimes: 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 displays relatively fast dynamics, resulting in all TCLs converging around the control point; in contrast, the CPI regime manifests a bimodal probability distribution and two, possibly significantly separated, timescales. 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. According to our understanding, this phenomenon has been neglected within the context of building energy systems, despite its clear effect on actual operation. A key point is the balance between employee comfort in different temperature zones and the energy costs involved.

Dirt cones, structures of meter scale, observed on glacial surfaces, originate naturally from an initial debris patch. These formations consist of ice cones covered by a thin layer of ash, sand, or gravel. We present in this article field observations of cone formation in the French Alps, which are substantiated by corresponding laboratory experiments reproducing these formations under controlled circumstances, with further investigation via 2D discrete-element-method-finite-element-method numerical simulations considering both grain mechanics and thermal effects. Cone formation is attributed to the insulating effect of the granular layer, which impedes ice melt in the underlying areas relative to bare ice. A conical shape arises from the quasistatic grain flow induced by the differential ablation-induced deformation of the ice surface, as thermal length becomes smaller than structural size. As the cone expands, its insulation layer composed of dirt steadily adjusts to precisely balance the heat flux emerging from the growing external surface area. 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.

To determine the structural characteristics of twist-bend nematic (NTB) drops, serving as colloidal inclusions in both isotropic and nematic environments, the mesogen CB7CB [1,7-bis(4-cyanobiphenyl-4'-yl)heptane] is combined with a small amount of a long-chain amphiphile. 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.