High temporal resolution x-ray streak camera studies of micropinch formation in Cu hybrid $x$ pinches reveal key plasma conditions. Analysis of Ne-like Cu lines indicate an average electron temperature of about 200 eV and $4.5\times {10}^{28}{\text{m}}^{-3}$ electron density. The spectra suggest that the electron temperature jumps to about 1 keV, inferred from the continuum and the postcontinuum line emission that includes Li-like Cu lines. There is no sign of a rapid temperature change or a substantial surge in radiation emission during the 200 ps precontinuum x-ray burst, suggesting that the radiative collapse process does not play a major role in micropinch formation. Two-dimensional extended Magnetohydrodynamic (MHD) simulations, coupled to a collisional-radiative spectral analysis code, suggest the significance of the rapid radial implosion of high-temperature, low-density plasma, the axial outflow, and the dynamic plasma pressure in micropinch formation.

We investigate irreversible aggregation processes driven by a source of small mass clusters. In the spatially homogeneous situation, a well-mixed system consists of clusters of various masses whose concentrations evolve according to an infinite system of nonlinear ordinary differential equations. We focus on the cluster mass distribution in the long-time limit. An input-driven aggregation with rates proportional to the product of merging partners undergoes a percolation transition. We examine this process analytically and numerically. There are two theoretical schemes and two natural ways of numerical integration on the level of a truncated system with a finite number of equations. After the percolation transition, the behavior depends on the adopted approach: The giant component quickly engulfs the entire system (Flory approach), or a nontrivial stationary mass distribution emerges (Stockmayer approach). We also outline a generalization to ternary aggregation.

We propose a simple model of an interacting, fully spin-polarized Fermi gas in dimensions $d=2$ and $d=3$, and derive the approximate expression for the energy spectrum and the corresponding formula for the Helmholtz free energy. We analyze the thermodynamics of the system and find the lines of first-order phase transitions between the low- and high-density phases terminating at critical points. The properties of the corresponding phase diagrams are qualitatively different for $d=2$ and 3, and sensitively depend on the interparticle attraction, which marks a departure from the standard van der Waals theory. The differences originate from the Pauli exclusion principle and are embedded in the fermionic nature of the system under study.

The bosonic Josephson junction, one of the maximally simple models for periodic-driven many-body systems, has been intensively studied in the past two decades. Here, we revisit this problem with five different methods, all of which have solid theoretical reasoning. We find that to the order of ${\omega }^{-2}$ ($\omega$ is the modulating frequency), these approaches will yield slightly different effective Hamiltonians. In particular, the parameters in the effective Hamiltonians may be unchanged, increased, or decreased, depending on the approximations used. Especially, some of the methods generate new interactions, which still preserve the total number of particles, and the others do not. The validity of these five effective models is verified using dynamics of population imbalance and self-trapping phase transition, and we find that the method based on the rotating frame by a unitary transformation has the highest accuracy. The difference between these methods will become significant when the driving amplitude or interaction strengths are comparable with the driving frequency. These differences can also be manifested from their long-time dynamics. We demonstrate this physics using a Bose-Josephson junction, and it is to be hoped that the validity of these methods and their tiny differences put forward in this paper can be verified in realistic experiments in the future using quantum simulating platforms, including but not limited to ultracold atoms.

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation. We identify two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyze these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and traveling waves, and also lurching waves. We show that many of these solutions satisfy self-consistency equations which can be used to follow them as parameters are varied. We perform numerical bifurcation analysis of the neural field model, concentrating on the effects of varying gap junction coupling strength. Our methods are generally applicable to a wide variety of networks of quadratic integrate-and-fire neurons.

We study the phase separation kinetics of miktoarm star polymer (MSP) melts/blends with diverse architectures using dissipative particle dynamics simulation. Our study focuses on symmetric and asymmetric miktoarm star polymer (SMSP/AMSP) mixtures based on arm composition and number. For a fixed MSP chain size, the characteristic microphase-separated domains initially show diffusive growth with a growth exponent $\varphi \sim 1/3$ for both melts that gradually crossover to saturation at late times. The simulation results demonstrate that the evolution morphology of SMSP melt exhibits perfect dynamic scaling with varying arm numbers; the timescale follows a power-law decay with an exponent $\theta \simeq 1$ as the number of arms increases. The structural constraints on AMSP melts cause the domain growth rate to decrease as the number of one type of arms increases while their length remains fixed. This increase in the number of arms for AMSP corresponds to increased off-criticality. The saturation length in AMSP follows a power-law increase with an exponent $\lambda \simeq 2/3$ as off-criticality decreases. Additionally, macrophase separation kinetics in SMSP/AMSP blends show a transition from viscous ($\varphi \sim 1$) to inertial ($\varphi \sim 2/3$) hydrodynamic growth regimes at late times; this exhibits the same dynamical universality class as linear polymer blends, with slight deviations at early stages.

The electrical conductivity of a suspension of graphite and silicone oil in the presence of a small electric potential difference and vibration (40÷50Hz) is considered. The concentration of the suspension was selected near the percolation threshold. It has been found that such a nonequilibrium system evolves to increase its dissipation power, and low-energy vibrations accelerate, and high-energy ones hinder this process. Since the dissipation power of the considered system is proportional to entropy production, the results obtained are consistent with the so-called maximum entropy production principle (MEPP). This is the first experimental confirmation of MEPP in the case of a nonequilibrium process with continuous transformations under conditions for the emergence of alternative variants for the development. The possibility of choice among alternatives in a complex system is a fundamental point in the experimental discussion of MEPP, and it was previously underestimated.

The liquid state thermophysical properties and amorphous solidification kinetics of $\mathrm{F}{\mathrm{e}}_{50-x}\mathrm{C}{\mathrm{o}}_x\mathrm{C}{\mathrm{r}}_{14}\mathrm{M}{\mathrm{o}}_{14}{\mathrm{C}}_9{\mathrm{B}}_8\mathrm{T}{\mathrm{m}}_5$ ($x=10$, 15, 20, and 25) alloys were explored by electromagnetic and electrostatic levitation techniques. It was found that the surface tension of liquid alloys with Fe contents below 30 at. % had a strong temperature dependence. The high surface tension led to a sharp increase in the interfacial free-energy penalty. A high nucleation barrier was formed inside the melt, which greatly inhibited the nucleation rate. The liquid viscosity revealed the strong liquid feature of this alloy series, which became the dominant kinetic factor determining their solidification mechanisms. The high viscosity hindered atomic diffusion and delayed nucleation. The long crystallizing incubation time of $\mathrm{F}{\mathrm{e}}_{30}\mathrm{C}{\mathrm{o}}_{20}\mathrm{C}{\mathrm{r}}_{14}\mathrm{M}{\mathrm{o}}_{14}{\mathrm{C}}_9{\mathrm{B}}_8\mathrm{T}{\mathrm{m}}_5$ ensured a strong glass-forming ability and a low critical cooling rate of $2.11\times {10}^3\mathrm{K}{\mathrm{s}}^{-1}$. As a result, a bulk metallic glass rod with an 8-mm diameter was successfully prepared by a convenient casting procedure. This rod could remain in a glassy state at a higher temperature and over a wider temperature range due to its high glass-transition temperature and large undercooled liquid region. The apparent activation energy for nucleation was derived as 463.8 $\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ according to the nonisothermal crystallization kinetics, indicating that the bulk metallic glass had to absorb a large amount of energy to overcome the potential barriers before nucleation and thus exhibited excellent thermal stability.

We use Clifford's geometric algebra to extend the Stuart-Landau system to dimensions $D>2$ and give an exact solution of the oscillator equations in the general case. At the supercritical Hopf bifurcation marked by a transition from stable fixed-point dynamics to oscillatory motion, the Jacobian matrix evaluated at the fixed point has $N=\lfloor D/2\rfloor$ pairs of complex conjugate eigenvalues which cross the imaginary axis simultaneously. For odd $D$ there is an additional purely real eigenvalue that does the same. Oscillatory dynamics is asymptotically confined to a hypersphere ${\mathbb{S}}^{D-1}$ and is characterised by extreme multistability, namely the coexistence of an infinite number of limiting orbits, each of which has the geometry of a torus ${\mathbb{T}}^N$ on which the motion is either periodic or quasiperiodic. We also comment on similar Clifford extensions of other limit cycle oscillator systems and their generalizations.

We investigate how to count the number of solutions in the Boolean satisfiability (SAT) problem, a fundamental problem in theoretical computer science that has applications in various domains. We convert the problem to a spin-glass problem in statistical physics and approximately compute the entropy of the problem, which corresponds to the logarithm of the number of solutions. We propose a new method for the entropy computing problem based on a combination of the tensor network method and the message-passing algorithm. The significance of the proposed method is its ability to consider the effects of both long loops and short loops present in the factor graph of the SAT problem. We validate the efficacy of our approach using 3-SAT problems defined on the random graphs and structured graphs, and show that the proposed method gives more accurate results on the number of solutions than the standard belief propagation algorithms. We also discuss the applications of our method across a wide range of combinatorial optimization problems.

The kinetic theory description of a low-density gas of hard spheres or disks, confined between two parallel plates separated at a distance smaller than twice the diameter of the particles, is addressed starting from the Liouville equation of the system. The associated Bogoliubov, Born, Green, Kirkwood, and Yvon hierarchy of equations for the reduced distribution functions is expanded in powers of a parameter measuring the density of the system in the appropriate dimensionless units. The Boltzmann level of description is obtained by keeping only the two lowest orders in the parameter. In particular, the one-particle distribution function obeys a couple of equations. Contrary to what happens with a Boltzmann-like kinetic equation that has been proposed for the same system on a heuristic basis, the kinetic theory formulated here admits stationary solutions that are consistent with equilibrium statistical mechanics, in both the absence and presence of external fields. In the latter case, the density profile is rather complex due to the coupling between the inhomogeneities generated by the confinement and by the external fields. The general theory formulated provides a solid basis for the study of the properties of strongly confined dilute gases.

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models. Subsequently, we demonstrate the existence of vibrational resonance (VR) and nonlinear resonance phenomena at the combination tones of the driving frequencies in a simple bistable potential without self-sustained oscillations. We find that periodic forcing by the obliquity and frequencies similar to those of the precession cycle can generate output dominated by 100-kyr cycles, thereby offering a mechanism for explaining the observations in geological data. While previous studies of VR have assumed one periodic driver to have a frequency much higher than the other, we show that for a range of amplitudes, both phenomena can occur at the orbital cycle frequencies. We find that the nonlinear resonance phenomenon is more robust to noise than VR between eccentricity and obliquity and emerges within a much larger range of amplitudes of forcing. Finally, we conclude that it is conceivable that nonlinear resonance between obliquity and precession might explain the spectral frequencies observed in the late Pleistocene.

Nonequilibrium cluster-cluster aggregation of particles diffusing in or at the cell membrane has been hypothesized to lead to domains of finite size in different biological contexts, such as lipid rafts, cell adhesion complexes, or postsynaptic domains in neurons. In this scenario, the desorption of particles balances a continuous flux to the membrane, imposing a cutoff on possible aggregate sizes and giving rise to a stationary size distribution. Here, we investigate the case of nonequilibrium cluster-cluster aggregation in two dimensions where diffusing particles and/or clusters remain fixed in space at specific anchoring sites, which should be particularly relevant for synapses but may also be present in other biological or physical systems. Using an effective mean-field description of the concentration field around anchored clusters, we derive an expression for their average size as a function of parameters such as the anchoring site density. We furthermore propose and solve appropriate rate equations that allow us to predict the size distributions of both diffusing and fixed clusters. We confirm our results with particle-based simulations and discuss potential implications for biological and physical systems.

The problem of ion transport in porous media is fundamental to many practical applications such as capacitive deionization, where ions are electrostatically attracted to a porous electrode and stored in the electric double layer, leaving a partially desalinated solution. These electrodes are functionalized to achieve maximum efficiency: it is intended that for each depleted electron one ion is removed. For this purpose, the surface is coated with a polyelectrolyte layer of the same sign as the electronic charge. In this work, the movement of ions from the solution to the soft or polyelectrolyte-coated electrodes is studied. For this purpose, a one-dimensional model is used to study the electric and diffusive fluxes produced by the application of an electric field and the storage of these ions in the micropores. The partial differential equations governing the process are numerically solved using the explicit Euler method. The results of the model indicate that the number of ions removed using soft electrodes is approximately 15% greater than that achieved with bare electrodes. Ion adsorption kinetics show that coated electrodes provide slightly slower adsorption compared to bare electrodes. Regarding the charging time of the micropores, it can be seen that it is a faster process (characteristic time of 100 s) compared to the time in which the ion concentration reaches equilibrium: electromigration is faster than diffusion. Comparing the situations with and without polyelectrolyte coating, it is observed that saturation in the micropores is reached earlier when the electrodes are coated. Concerning the cell geometry, it has been found that the characteristic time is proportional to the length of the spacer and inversely proportional to the length of the electrodes. With regard to microporosity, the rate of the process is approximately constant, irrespective of the number of micropores. Moreover, the number of adsorbed ions strongly depends on their initial concentration. Finally, the analysis of the ionic diffusion coefficient is determinant in the kinetics of the process: Taking into account the tortuosity of the porous electrode, which directly affects the diffusion in the channel, is fundamental to obtain model predictions close to reality.

The intermittent damage evolution preceding the failure of heterogeneous brittle solids is well described by scaling laws. In deciphering its origins, failure is routinely interpreted as a critical transition. However at odds with expectations of universality, a large scatter in the value of the scaling exponents is reported during acoustic emission experiments. Here we numerically examine the precursory damage activity to reconcile the experimental observations with critical phenomena framework. Along with the strength of disorder, we consider an additional parameter that describes the progressive damageability of material elements at mesoscopic scale. This hardening behavior encapsulates the microfracturing processes taking place at lower length scales. We find that damage hardening can not only delay the final failure but also affect the preceding damage accumulation. When hardening is low, the precursory activity is strongly influenced by the strength of the disorder and is reminiscent of damage percolation. On the contrary, for large hardening, long-range elastic interactions prevail over disorder, ensuring a rather homogeneous evolution of the damage field in the material. The power-law statistics of the damage bursts is robust to the strength of the disorder and is reminiscent of the collective avalanche dynamics of elastic interfaces near the depinning transition. The existence of these two distinct universality classes also manifests as different values of the scaling exponent characterizing the divergence of the precursor size on approaching failure. Our finding sheds new light on the connection between the level of quasibrittleness of materials and the statistical features of the failure precursors. Finally, it also provides a more complete description of the acoustic precursors and thus paves the way for quantitative techniques of damage monitoring of structures-in-service.

We study the role of record statistics of damage avalanches in predicting the fracture of a heterogeneous material under tensile loading. The material is modeled using a two-dimensional random spring network where disorder is introduced through randomness in the breakage threshold strains of the springs. It is shown that the waiting strain interval between successive records of avalanches has a maximum for moderate disorder, thus showing an acceleration in occurrence of records when approaching final fracture. Such a signature is absent for low disorder when the fracture is nucleation-dominated, as well as for high disorder when the fracture is percolation type. We examine the correlation between the record with the maximum waiting strain interval and the crossover record at which the avalanche statistics change from off-critical to critical. Compared to the avalanche exponent crossover based prediction for failure, we show that the record statistics have the advantage of both being real-time as well as being a precursor significantly prior to final fracture. We also find that in the avalanche-dominated regime, the failure strain is at best weakly correlated with the strain at the maximum waiting strain interval. A stronger correlation is observed between the index of the largest record and the index of the record at the maximum waiting strain interval.

Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive particles confined on a disk under the Hamiltonian dynamics by the recently developed algorithm called the random batch method. This algorithm is specifically designed for reducing the computational complexity of long-range interacting particle systems. We highlight the revealed intrinsic statistical regularity of topological charges that is otherwise unattainable by the continuum analysis of particle density. We also identify distinct collective dynamics of the interacting particles under short- and long-range repulsive forces. This work shows the robustness and effectiveness of the concept of topological charge for characterizing the convoluted particle dynamics, and it demonstrates the promising potential of the random batch method for exploring fundamental scientific questions arising in a variety of long-range interacting particle systems in soft matter physics and other relevant fields.

It is shown that most of the existing versions of the Bhatnagar-Gross-Krook model—those whose coefficient are independent of the molecular velocity—do not satisfy the Onsager relations. This circumstance poses a problem when calibrating these models, making their transport properties match those of a specific fluid.