For brittle behavior, we achieve closed-form expressions for the temperature-dependent fracture stress and strain. This represents a generalized Griffith criterion, thus representing fracture as a genuine phase transition. The brittle-to-ductile transition reveals a complex critical state, where a threshold temperature dictates the shift between brittle and ductile fracture behavior, with a minimum and maximum yield strength, and a critical temperature indicative of overall failure. To validate the predictive power of the proposed models for thermal fracture behavior at the nanoscale, we successfully compared our theoretical results to molecular dynamics simulations of Si and GaN nanowires.

Step-like jumps are frequently observed in the magnetic hysteresis curve of a Dy-Fe-Ga-based ferrimagnetic alloy at a temperature of 2 Kelvin. The observed jumps exhibit a stochastic character concerning their magnitude and field position, uncorrelated with the duration of the field. The scale-independent nature of jumps is indicated by the power law variation in their size distribution. A two-dimensional random bond Ising-type spin system, a straightforward one, was used to model the dynamics. The jumps, along with their scale-invariant nature, are faithfully replicated by our computational model. The observed jumps in the hysteresis loop are also explained by the flipping of antiferromagnetically coupled Dy and Fe clusters. Employing the concept of self-organized criticality, these features are elucidated.

A generalized random walk (RW) is examined, built upon a deformed unitary step derived from the q-algebra, a mathematical structure foundational to nonextensive statistical mechanics. selleckchem A deformed random walk (DRW), characterized by a deformed Pascal triangle and inhomogeneous diffusion, is implied by a deformed step random walk (RW). The paths of RW particles in warped spacetime are divergent, whereas those of DRW particles converge to a fixed point. For q1, the standard random walk is observed, while a suppression of randomness is evident in the DRW when q is between -1 and 1, inclusive, and q equals 1 minus q. The continuum form of the DRW's master equation, given mobility and temperature proportional to 1 + qx, resulted in a van Kampen inhomogeneous diffusion equation. This equation, exhibiting exponential hyperdiffusion, localizes the particle to x = -1/q, aligning with the DRW's fixed point. The presented analysis is complemented by a comparative examination of the Plastino-Plastino Fokker-Planck equation. The 2D case is also investigated by developing a deformed 2D random walk and its accompanying deformed 2D Fokker-Planck equation. These calculations demonstrate convergence of 2D paths for the condition -1 < q1, q2 < 1 and diffusion with inhomogeneities under the influence of the deformation parameters q1 and q2 in the x and y coordinate directions. In the one-dimensional and two-dimensional scenarios, the transformation q-q signifies a reversal of the random walk path's boundary values, a consequence of the deformation applied.

Our investigation focused on the electrical conductance properties of two-dimensional (2D) random percolating networks of zero-width metallic nanowires, showcasing a mix of rings and sticks. In our assessment, the resistance of the nanowires per unit length was accounted for, as well as the resistance occurring at the junctions (nanowire-nanowire contacts). Based on a mean-field approximation (MFA), we formulated the total electrical conductance of these nanowire-based networks, showing its dependence on both geometrical and physical parameters. In our Monte Carlo (MC) numerical simulations, the MFA predictions were found to be accurate. The MC simulations were designed around the condition that the circumferences of the rings and the lengths of the wires were equal. The electrical conductance of the network was practically uninfluenced by the relative ratios of rings to sticks, as long as the resistance values in the wires and at the junctions remained equal. Jammed screw A linear correlation between network electrical conductance and the proportions of rings and sticks manifested when junction resistance surpassed wire resistance.

We examine the spectral characteristics of phase diffusion and quantum fluctuations within a one-dimensional Bose-Josephson junction (BJJ) which is nonlinearly coupled to a bosonic heat bath. Random fluctuations in BJJ modes lead to phase diffusion, resulting in a loss of initial coherence between ground and excited states. A linear (in bath operators) yet nonlinear (in system operators) interaction term in the system-reservoir Hamiltonian describes frequency modulation. We scrutinize the influence of on-site interactions and temperature on the phase diffusion coefficient in the zero- and -phase modes, revealing a phase transition-like behavior between the Josephson oscillation and the macroscopic quantum self-trapping (MQST) regimes specifically in the -phase mode. The thermal canonical Wigner distribution, the equilibrium solution of the related quantum Langevin equation for phase, enables calculation of the coherence factor for studying phase diffusion in the zero- and -phase modes. Analyzing quantum fluctuations of the relative phase and population imbalance in terms of fluctuation spectra, we find an intriguing shift in the Josephson frequency attributed to frequency fluctuations stemming from nonlinear system-reservoir coupling, along with the on-site interaction-induced splitting, within the weakly dissipative framework.

Coarsening entails the disappearance of small-scale structures, resulting in the dominance of large-scale structures. Model A is studied here for spectral energy transfers, where the order parameter undergoes evolution based on non-conserved dynamics. Nonlinear interactions are shown to dissipate fluctuations, promoting energy exchange amongst Fourier modes. This process culminates in the (k=0) mode, with k being the wave number, alone approaching an asymptotic value of either +1 or -1. We examine the coarsening evolution, starting with the initial condition (x,t=0) = 0, and compare it to the coarsening under uniformly positive or negative (x,t=0) initial conditions.

An investigation into the theoretical implications of weak anchoring phenomena within a static, two-dimensional, pinned nematic liquid crystal ridge, thin and situated on a flat solid substrate, is conducted while considering a passive gas atmosphere. A reduced case of the governing equations recently published by Cousins et al. [Proc. constitutes our subject matter. screening biomarkers R. Soc., this item, is to be returned. Publication 20210849 (2022)101098/rspa.20210849, published in 2021, features study 478. Under the one-constant approximation of the Frank-Oseen bulk elastic energy, the shape of a symmetric, thin ridge and the director's behavior within it can be determined by considering pinned contact lines. Numerical studies, covering a broad range of parameter settings, suggest five different types of solution, each energetically preferred and distinguished by their respective values of the Jenkins-Barratt-Barbero-Barberi critical thickness. According to the theoretical model, anchoring failure is localized close to the contact points. A nematic ridge of 4'-pentyl-4-biphenylcarbonitrile (5CB) exhibits the agreement between theoretical predictions and the findings from physical experiments. These experiments reveal that the homeotropic anchoring condition at the gas-nematic interface becomes less effective near the contact lines in the presence of the more powerful rubbed planar anchoring at the nematic-substrate interface. A comparison of the ridge's experimentally determined effective refractive index with the corresponding theoretical predictions enables a preliminary calculation of the anchoring strength for an air-5CB interface at 2215°C, resulting in (980112)×10⁻⁶ Nm⁻¹.

Solution-state nuclear magnetic resonance (NMR) sensitivity was recently enhanced via J-driven dynamic nuclear polarization (JDNP), an innovative approach that bypasses the limitations of standard Overhauser DNP at the magnetic fields crucial for analytical investigations. Both Overhauser DNP and JDNP share the application of high-frequency microwaves to saturate electronic polarization, a process known to exhibit poor penetration and associated heating effects in the majority of liquids. Seeking to augment the sensitivity of solution NMR, the microwave-free JDNP (MF-JDNP) methodology suggests shuttling the sample between high-field and low-field magnetic environments, ensuring one field resonates with the electron Larmor frequency dictated by the interelectron exchange coupling, J ex. Should spins traverse this purported JDNP condition at a sufficiently rapid rate, we anticipate the formation of a substantial nuclear polarization absent microwave excitation. The MF-JDNP proposal mandates radicals exhibiting singlet-triplet self-relaxation rates primarily determined by dipolar hyperfine relaxation, and shuttling times capable of matching these electron relaxation processes in speed. This paper investigates the MF-JDNP theory, along with suggested radicals and enabling conditions for improved NMR sensitivity.

In a quantum framework, distinct energy eigenstates exhibit unique characteristics, enabling the development of a classifier for their categorization into disparate groups. The energy eigenstate proportions within an energy shell, bounded by E ± E/2, remain consistent regardless of shell width E or Planck's constant alterations, provided the shell contains a sufficiently large number of eigenstates. Our analysis indicates that self-similarity in energy eigenstates is a common property of all quantum systems, as corroborated numerically by considering diverse quantum models like the circular billiard, the double top model, the kicked rotor, and the Heisenberg XXZ model.

The crossing of charged particles through the interference zone created by two colliding electromagnetic waves is known to produce chaotic behavior, leading to a stochastic heating of the particle distribution. A deep comprehension of the stochastic heating process is essential for optimizing many physical applications demanding high EM energy deposition into these charged particles.