The critical frequencies associated with the vortex-lattice transition within an adiabatic rotation ramp are determined by conventional s-wave scattering lengths and are inversely proportional to the strength of nonlinear rotation, C, wherein the critical frequency decreases as C increases from negative values to positive ones. The critical ellipticity (cr) for vortex nucleation, during adiabatic trap ellipticity introduction, is contingent upon the characteristics of nonlinear rotation, alongside trap rotation frequency. Altering the strength of the Magnus force on the vortices, nonlinear rotation additionally affects their interactions with other vortices and their movement within the condensate. Fumed silica The nonlinear effects, in combination, produce non-Abrikosov vortex lattices and ring vortex arrangements within density-dependent Bose-Einstein condensates.

The boundaries of specific quantum spin chains host strong zero modes (SZMs), which are conserved operators, leading to the prolonged coherence times of the edge spins. We examine and delineate analogous operators within the framework of one-dimensional classical stochastic systems. In order to clarify our analysis, we concentrate on chains having just one particle per site, with transitions happening only between the nearest neighbors; notably, the examples we consider involve particle hopping and the creation and destruction of pairs. Integrable parameter selections yield the precise expressions for SZM operators. The dynamical ramifications of stochastic SZMs, given their non-diagonal representation in the classical basis, are markedly distinct from those of their quantum counterparts. The appearance of a stochastic SZM is signified by a specific set of exact correlations in time-correlation functions, a phenomenon absent in the same system when periodic boundaries are applied.

Calculating the thermophoretic drift of a single, charged colloidal particle with a hydrodynamically slipping surface, immersed in an electrolyte solution, is influenced by a modest temperature gradient. For the fluid dynamics and electrolyte ion transport, we utilize a linearized hydrodynamic method, while maintaining the complete nonlinearity of the unperturbed Poisson-Boltzmann equation to account for substantial surface charge buildup. Linear response methodology transforms the partial differential equations into a system of interlinked ordinary differential equations. Parameter regimes encompassing both small and large Debye shielding, along with diverse hydrodynamic boundary conditions represented by variable slip lengths, are explored through numerical solutions. The experimental observations of DNA thermophoresis are successfully mirrored by our results, which concur strongly with predictions from contemporary theoretical studies. We also analyze our calculated values in the context of the experimental data for polystyrene beads.

A heat engine cycle, the Carnot cycle, demonstrates how to extract the most mechanical energy possible from heat flux between two thermal reservoirs with a maximum efficiency given by the Carnot efficiency, C. This maximal efficiency stems from thermodynamical equilibrium processes that happen over infinite time, ultimately leading to no power-energy output. The pursuit of powerful energy leads us to ponder: is there a fundamental maximum efficiency for finite-time heat engines operating at a given power? In an experimental setup involving a finite-time Carnot cycle, sealed dry air acted as the working material, and a trade-off between power and efficiency was observed. At an efficiency of (05240034) C, the engine achieves maximum power, in agreement with the theoretical expectation of C/2. Fungal bioaerosols For studying finite-time thermodynamics, characterized by non-equilibrium processes, our experimental setup provides a platform.

We focus our attention on a generic family of gene circuits that are impacted by non-linear extrinsic noise. We introduce a general perturbative methodology to tackle this nonlinearity, based on the assumption of timescale separation between noise and gene dynamics, where fluctuations have a large yet finite correlation time. Through the application of this methodology, incorporating biologically relevant log-normal fluctuations, the toggle switch's system reveals noise-induced transitions. A transition from monostable determinism to bimodality in the system arises in the parameter space. We demonstrate that our approach, augmented by higher-order corrections, accurately predicts transitions, even with less substantial fluctuation correlation times, thereby overcoming shortcomings of earlier theoretical methods. Intriguingly, intermediate noise levels reveal a selective noise-induced toggle switch transition impacting only one of the target genes.

The fluctuation relation, a hallmark of modern thermodynamics, requires the existence and measurability of a set of fundamental currents for its establishment. We show that systems incorporating hidden transitions still adhere to this principle when observations are tied to the frequency of observable transitions, stopping the experiment after a defined number of these transitions instead of using an external timer. Thermodynamic symmetries, when considered in terms of transitions, display enhanced resilience to the loss of information.

The complex dynamics inherent in anisotropic colloidal particles are of paramount importance for their function, movement, and phase properties. This correspondence investigates the two-dimensional diffusion of smoothly curved colloidal rods, also referred to as colloidal bananas, in accordance with their opening angle. Particle translational and rotational diffusion coefficients are ascertained with opening angles spanning the range of 0 degrees (straight rods) up to almost 360 degrees (closed rings). Our findings indicate a non-monotonic variation in particle anisotropic diffusion, contingent upon the particles' opening angle, and a shift in the fastest diffusion axis, transitioning from the long axis to the short one, at angles exceeding 180 degrees. A noteworthy observation is that the rotational diffusion coefficient is approximately ten times higher for nearly closed rings compared to straight rods of equal length. Our experimental results, presented lastly, are in accord with slender body theory, which suggests that the particles' dynamical actions stem principally from their local drag anisotropy. These results bring to light the correlation between curvature and the Brownian motion of elongated colloidal particles, emphasizing the need to account for this relationship when investigating curved colloidal particle behavior.

Recognizing a temporal network's trajectory as a latent graph dynamic system, we introduce the notion of dynamic instability and develop a measure to determine a temporal network's maximum Lyapunov exponent (nMLE). By extending conventional algorithmic approaches from nonlinear time-series analysis to network systems, we demonstrate how to measure sensitive dependence on initial conditions and directly calculate the nMLE from a single network trajectory. We validate our methodology using synthetic generative network models displaying both low- and high-dimensional chaotic characteristics, and we then turn to discussing potential applications.

The coupling of a Brownian oscillator to its environment is investigated with respect to its possible role in creating a localized normal mode. With smaller values of the oscillator's natural frequency 'c', the localized mode is not present; the unperturbed oscillator then reaches thermal equilibrium. In cases where the value of c is substantial and a localized mode emerges, the unperturbed oscillator does not achieve thermal equilibrium, but rather transitions to a non-equilibrium cyclostationary state. We investigate how an external, periodic force impacts the oscillator's behavior. Even with environmental coupling, the oscillator manifests unbounded resonance (with a linearly escalating response over time) when the external force's frequency is identical to the localized mode's frequency. read more The oscillator exhibits a peculiar resonance, a quasiresonance, at the critical natural frequency 'c', which marks the boundary between thermalizing (ergodic) and nonthermalizing (nonergodic) states. Over time, the resonance response exhibits a sublinear growth, indicative of a resonant coupling between the applied external force and the nascent localized mode.

We refine the encounter-based model for imperfect diffusion-controlled reactions, where encounter frequencies are applied to represent surface reactions. Our approach is applied more broadly to situations where the reactive zone is surrounded by a reflecting border and an exit zone. We obtain a spectral decomposition of the complete propagator and examine the characteristics and probabilistic significances of the resultant probability current density. Our analysis yields the combined probability density for the escape time and the number of reactive region encounters before escape, and the probability density function for the first passage time given a particular number of encounters. We examine the generalized Poissonian surface reaction mechanism, conventionally described by Robin boundary conditions, along with its potential applications in chemistry and biophysics.

Past a critical coupling intensity, the Kuramoto model explains how coupled oscillators synchronize their phases. A recent extension to the model involved a re-conceptualization of oscillators as particles moving along the surface of unit spheres situated within a D-dimensional space. Particles are each described using a D-dimensional unit vector; for D equalling two, the particles' movement is confined to the unit circle, and their vectors are characterized by a single phase value, replicating the original Kuramoto model. The multi-dimensional description can be extended further by promoting the coupling constant between particles to a matrix K that acts on the fundamental unit vectors. Variances in the coupling matrix, impacting the vector's trajectory, are akin to a generalized frustration, hindering synchronized behavior.