A smeared dislocation's location, along a line segment oblique to a reflectional symmetry axis, is a seam. The DSHE, contrasting with the dispersive Kuramoto-Sivashinsky equation, possesses a narrow band of unstable wavelengths that are closely situated to the instability threshold. This enables the development of analytical insights. Our analysis reveals that the amplitude equation describing the DSHE at the threshold is a special case of the anisotropic complex Ginzburg-Landau equation (ACGLE), and that the characteristic seams of the DSHE correspond to spiral waves in the ACGLE. Chains of spiral waves are often the result of seam defects, and we can calculate formulas for the speed of the central spiral wave cores and the gap between them. A perturbative analysis, applied in the context of significant dispersion, provides a relationship between the wavelength, amplitude, and velocity of propagation of a stripe pattern. Numerical integration of the ACGLE and DSHE equations provides further evidence for these analytical outcomes.

Analyzing measured time series data from complex systems to infer the direction of coupling presents a significant obstacle. From cross-distance vectors within a state-space framework, we derive a causality measure quantifying the potency of interaction. The noise-robust, parameter-sparse model-free method is utilized. This approach, demonstrating resilience to artifacts and missing values, can be applied to bivariate time series data. DDR1-IN-1 DDR inhibitor The analysis delivers two coupling indices, which provide a more accurate measure of coupling strength in every direction, representing an improvement on the already established state-space methods. A comprehensive analysis of numerical stability accompanies the testing of the proposed approach on different dynamic systems. Ultimately, a method for choosing the best parameters is devised, thereby avoiding the difficulty of deciding on the best embedding parameters. We demonstrate its resilience to noise and dependable performance in brief time series. Besides this, our study demonstrates its potential to identify cardiorespiratory associations in the monitored data. https://repo.ijs.si/e2pub/cd-vec houses a numerically efficient implementation.

Optical lattices confining ultracold atoms offer a platform for simulating phenomena otherwise challenging to observe in condensed matter and chemical systems. A prominent area of investigation is the process through which isolated condensed matter systems reach thermalization. Thermalization in quantum systems is demonstrably linked to a shift towards chaos in their corresponding classical systems. The honeycomb optical lattice's compromised spatial symmetries are shown to precipitate a transition to chaos in the motion of individual particles. This, in turn, leads to a blending of the energy bands within the quantum honeycomb lattice. Within single-particle chaotic systems, soft interatomic interactions are responsible for achieving thermalization, taking the form of a Fermi-Dirac distribution for fermions and a Bose-Einstein distribution for bosons respectively.

Numerical analysis examines the parametric instability of a viscous, incompressible, Boussinesq fluid layer sandwiched between two parallel planes. A supposition exists concerning the layer's inclined position relative to the horizontal. Periodic heating cycles are applied to the planes which encompass the layer. Exceeding a predetermined temperature threshold, the temperature difference across the layer destabilizes an initially stable or parallel flow, conditional on the inclination angle. A Floquet analysis of the underlying system indicates that, when modulated, instability arises in a convective-roll pattern exhibiting harmonic or subharmonic temporal oscillations, contingent upon the modulation, the angle of inclination, and the Prandtl number of the fluid. The spatial manifestation of instability onset, when modulation is present, can either be longitudinal or transverse. It has been determined that the angle of inclination at the codimension-2 point is in fact a function of the frequency and the amplitude of the modulating signal. Moreover, the temporal reaction is harmonious, or subharmonic, or bicritical, contingent upon the modulation. In inclined layer convection, temperature modulation leads to a favorable influence on the time-varying characteristics of heat and mass transfer.

The characteristics of real-world networks are rarely constant and often transform. A recent surge in interest surrounds network expansion and the burgeoning density of networks, characterized by an edge count that escalates faster than the node count. Scaling laws of higher-order cliques, while less studied, are equally important to understanding network clustering and redundancy. This paper investigates clique expansion as network size increases, examining empirical data ranging from email exchanges to Wikipedia interactions. Superlinear scaling laws, whose exponents escalate with clique size, are indicated by our findings, standing in opposition to the projections of a preceding model. Ascending infection We subsequently corroborate these findings with the local preferential attachment model, which we posit, demonstrating connections from an incoming node not just to the target, but also to its neighbors having greater degrees. By examining our results, we gain comprehension of network development and the presence of redundant network infrastructure.

As a newly introduced collection, Haros graphs are bijectively associated with real numbers falling within the unit interval. conservation biocontrol The iterated dynamics of a graph operator R are explored for Haros graphs. The operator's renormalization group (RG) structure is evident in its prior graph-theoretical characterization within the realm of low-dimensional nonlinear dynamics. A chaotic RG flow is demonstrated by R's dynamics on Haros graphs, which include unstable periodic orbits of arbitrary periods and non-mixing aperiodic orbits. A single, stable RG fixed point is identified, its basin encompassing the rational numbers, and periodic RG orbits are found, connected to pure quadratic irrationals. Aperiodic RG orbits are also detected, correlated with non-mixing families of non-quadratic algebraic irrationals and transcendental numbers. In the end, we ascertain that the graph entropy of Haros graphs exhibits a general decline as the RG transformation approaches its stable fixed point, albeit in a non-monotonic fashion. This entropy parameter persists as a constant within the periodic RG orbits linked to metallic ratios, a specific subset of irrational numbers. Considering the chaotic renormalization group flow, we analyze possible physical interpretations and place results concerning entropy gradients along the flow within the context of c-theorems.

Employing a Becker-Döring-style model incorporating cluster formation, we investigate the potential for transforming stable crystals into metastable crystals within a solution via cyclic temperature fluctuations. At low temperatures, both stable and metastable crystals are predicted to expand through the joining of monomers and their associated small clusters. At elevated temperatures, a substantial number of minuscule clusters, a consequence of crystal dissolution, impede the process of crystal dissolution, leading to a disproportionate increase in the quantity of crystals. Employing this cyclic thermal process, the oscillation of temperatures can accomplish the changeover from stable crystals to metastable crystals.

This paper builds upon the earlier investigation [Mehri et al., Phys.] into the isotropic and nematic phases of the Gay-Berne liquid-crystal model. The presence of the smectic-B phase, as reported in Rev. E 105, 064703 (2022)2470-0045101103/PhysRevE.105064703, is linked to high density and low temperatures. In this phase, there is a substantial correlation between the thermal fluctuations of virial and potential energy, mirroring hidden scale invariance and implying the presence of isomorphic structures. Confirmed by simulations of the standard and orientational radial distribution functions, mean-square displacement versus time, and force, torque, velocity, angular velocity, and orientational time-autocorrelation functions, the predicted approximate isomorph invariance of physics holds true. The isomorph theory enables a complete simplification of the liquid-crystal experiment-relevant regions within the Gay-Berne model.

Water and salts, such as sodium, potassium, and magnesium, form the solvent environment in which DNA naturally exists. A critical aspect in defining DNA's form and conductance is the interaction of the DNA sequence with the solvent's properties. In the course of the last two decades, researchers have systematically assessed DNA conductivity under conditions ranging from hydrated to nearly dry (dehydrated). Although meticulous environmental control is essential, experimental constraints make it extraordinarily challenging to dissect the conductance results into their individual environmental contributions. As a result, modeling efforts can supply us with a valuable appreciation of the varied factors that shape charge transport behaviours. Providing both the structural integrity and the links between base pairs, the DNA backbone's phosphate groups are naturally negatively charged, thereby underpinning the double helix. The negative charges in the backbone are neutralized by positively charged ions, such as sodium ions (Na+), a frequently utilized counterion. A computational model examines the impact of counterions on charge movement through DNA, considering both solvent-containing and solvent-free scenarios. Experiments using computational methods on dry DNA indicate that the presence of counterions alters electron movement at the lowest unoccupied molecular orbital energies. Despite this, the counterions, while present in the solution, contribute very little to the transmission. The transmission rate at both the highest occupied and lowest unoccupied molecular orbital energies is markedly higher in a water environment than in a dry one, as predicted by polarizable continuum model calculations.