We study the ground-state stability of the trapped one-dimensional Bose-Einstein condensate under a density-dependent gauge field by variational and numerical methods. The competition of density-dependent gauge field and mean-field atomic interaction induces the instability of the ground state, which results in irregular dynamics. The threshold of the gauge field for exciting the instability is obtained analytically and confirmed numerically. When the gauge field is less than the threshold, the system is stable, and the gauge field induces chiral dynamics of the wave packet. When the gauge field is greater than the threshold, the system is unstable, and the ground-state wave packet will be deformed and fragmented. Interestingly, we find that as the gauge field approaches the threshold, strong dipolar and breathing dynamics take place, and strong modes mixing occurs, the instability of the system sets in. In addition, we show that the stability of the system can be well controlled by periodical modulation of the trapping potential. We provide theoretical evidence to understand and control the irregular dynamics associated with chiral superfluid induced by density-dependent gauge field.

The theory of finite-strain elasticity is applied to the phenomenon of cavitation observed in polymer gels following liquid-liquid phase separation of the solvent, which opens a fascinating window on the role of finite-strain elasticity theory in soft materials in general. We show that compressibility effects strongly enhance cavitation in simple materials that obey neo-Hookean elasticity. On the other hand, cavitation phenomena in gels of flexible polymers in a binary solvent that phase separates are surprisingly similar to those of incompressible materials. We find that, as a function of the interfacial energy between the two solvent components, there is a sharp transition between cavitation and classical nucleation and growth. Next, biopolymer gels are characterized by strain hardening and even very low levels of strain hardening turn out to suppress cavitation in polymer gels that obey Flory-Huggins theory in the absence of strain hardening. Our results indicate that cavitation is, in essence, not possible for polymer networks that show strain hardening.

The electrical signal associated with a biopolymer translocating through a nanoscale pore depends on the size, topology, and configuration of each molecule. Building upon recent interest in using solid-state nanopores for studying the topology of knotted and supercoiled DNA, we present experimental observations of topologically linked catenanes translocating through a solid-state nanopore. Using restriction enzymes, linked circular molecules were isolated from the mitochondrial DNA of Crithidia fasciculata, a structure known as a kinetoplast that comprises thousands of topologically interlocked minicircles. Digested kinetoplasts produce a spectrum of catenane topologies, which are identified from their nanopore translocation signals by spikes in the blockade current associated with the topological linkages. We attribute the different patterns of the measured electrical signals to 2-catenanes, linear and triangular 3-catenanes, and several types of 4- and 5-catenanes as well as more complex structures. Measurements of the translocation time of signals consistent with 2- and 3-catenanes suggest that topological friction between the linkages and the pore slows the translocation time of these structures, as predicted in recent simulations.

Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, nonlinear feedback control. Specifically, the particle is subject to a force derived from a repulsive Gaussian potential depending on the difference between its instantaneous position, $\mathbf{r}\left(t\right)$, and its earlier position $\mathbf{r}(t-\tau )$, where $\tau$ is the delay time. Considering first the deterministic case, we provide analytical results for both the case of small displacements and the dynamics at long times. In particular, at appropriate values of the feedback parameters, the particle approaches a steady state with a constant, nonzero velocity whose direction is constant as well. In the presence of noise, the direction of motion becomes randomized at long times, but the (numerically obtained) velocity autocorrelation still reveals some persistence of motion. Moreover, the mean-squared displacement (MSD) reveals a mixed regime at intermediate times with contributions of both ballistic motion and diffusive translational motion, allowing us to extract an estimate for the effective propulsion velocity in presence of noise. We then analyze the data in terms of exact, known results for the MSD of active Brownian particles. The comparison indeed indicates a strong similarity between the dynamics of the particle under repulsive delayed feedback and active motion. This relation carries over to the behavior of the long-time diffusion coefficient $D_{\mathrm{eff}}$ which, similarly to active motion, is strongly enhanced compared to the free case. Finally, we show that, for small delays, $D_{\mathrm{eff}}$ can be estimated analytically.

The free-ion concentration in a nematic liquid crystal (LC) is found to be significantly reduced when gold nano-urchins (AuNUs) of 50-nm diameter are dispersed in the LC in dilute concentrations. The nano-urchins on AuNUs trap a significant amount of mobile ions, reducing the free-ion concentration in the LC media. The reduction of free ions results in a decreased rotational viscosity and accelerated electro-optic response of the LC. The study is carried out with several AuNUs concentrations in the LC, and the experimental results consistently suggest that there exists an optimal concentration of AuNUs, above which they tend to aggregate. At the optimal concentration, the ion trapping is maximum, rotational viscosity is at its lowest, and the electro-optic response is the fastest. Above this optimal AuNUs concentration, the rotational viscosity is found to increase, and consequently, the LC no longer exhibits an accelerated electro-optic response.

The solutions of multi-phase-field models exhibit boundary layer behavior not only along the binary interfaces but also at the common contacts of three or more phases, i.e., junctions. Hence, to completely determine the asymptotic behavior of a multi-phase-field model, the inner analysis of both types of layers has to be carried out, whereas, traditionally, the junctions part is ignored. This is remedied in the current work for a phase-field model of simple grain growth in two spatial dimensions. Since the junction neighbourhoods are fundamentally different from those of the binary interfaces, pertinent matching conditions had to be derived from scratch, which is also accomplished in a detailed manner. The leading-order matching analysis of the junctions exposed the restrictions present on the interfacial arrangement at the common meeting point, while the next-to-the-leading one uncovered the law governing the instantaneous motion of the latter. In particular, it is predicted for the considered model that the Young's law is always satisfied at a triple point, whether or not it is at rest. Surprisingly, the mobilities and the curvatures of the involving interfaces as well as the driving forces on the them do not affect this result. However, they do play a significant role in determining the instantaneous velocity of the junction point. The study has opened up many new directions for future research.

The technique of atomic force microscopy (AFM) bending tests of a suspended nano-object (scroll, tube, rod) makes it possible to calculate the Young's modulus of the material it is made of based on experimental data. However, the calculation results involve a large error due to uncertain conditions (console or bridge) of fixing the test object. One of the ways to reduce this error is based on the theoretical consideration of consoles or bridges as beams with one or two ends resting on Winkler elastic foundations. The beam bending problems have been solved in both cases using Krylov's functions. This has allowed for developing an approach to the analytical identification of fixing conditions and including them in the calculations. The application of the approach is illustrated by AFM measurements of the Young's modulus of ${\mathrm{MgNi}}_2{\mathrm{Si}}_2{\mathrm{O}}_5{\left(\mathrm{OH}\right)}_4$ nanoscrolls.

A charged body moving in a plasma can excite a variety of linear and nonlinear waves in the form of trailing wakes, fore-wake shocks, and precursor solitons. These structures can further interact with the background plasma to create secondary effects that can serve as signatures of the passage of the charged body. Using particle-in-cell simulations, we carry out a basic investigation of the dynamics of a plasma system that is being traversed by an energetic charged body. Using two different shapes of this charged source, namely, an idealized infinite length planar source and a two-dimensional thin rectangular source, we examine the differences in the nature of the excited wave structures and their consequent impact on the background plasma. Our simulations reveal interesting features such as the dependence of the precursor speeds on the total charge on the driving source, local particle trapping, and energization of the trapped particles in various regions along the traversal path leading to the formation of energetic charged beamlets. Our basic findings could find practical applications such as in analyzing the trajectories of charged objects like space debris orbiting in the ionosphere.

The aim of this work is to generalize the method of Hubbard fields in fermion quantum Monte Carlo simulations to the case of link fields. The introduced Hubbard link fields play the role of the interaction fields responsible for the attraction and repulsion of electronic excitations at the nodes. Such improvements lead to a number of advantages concerning thermalization time, autocorrelations, metastable states, and probability distributions of the quantities. It is demonstrated that computations using five fields are more stable and reliable in the case of energy observables.

When a stationary bubble and a stationary droplet immersed in a liquid pool are brought into contact, they form a bubble-droplet aggregate. Its equilibrium morphology and stability largely depend on the combination of different components' surface tensions, known as the “spreading factor.” In this study, we look at the interaction between a rising bubble and a stationary droplet to better understand the dynamics of coalescence and rising and morphological changes for the bubble-droplet aggregate. A systematic study is conducted on the interaction processes with various bubble sizes and spreading factors in two dimensions. The current simulation framework consists of the ternary conservative phase-field lattice Boltzmann method (LBM) for interface tracking and the velocity-pressure LBM for hydrodynamics, which is validated by benchmark cases such as the liquid lens and parasitic currents around a static droplet with several popular surface tension formulations. We further test our LBM for the morphology changes of two droplets initially in contact with various spreading factors and depict the final morphologies in a phase diagram. The separated, partially engulfed, and completely engulfed morphologies can be replicated by systematically altering the sign of the spreading factors. The rising bubble and stationary droplet interaction are simulated based on the final morphologies obtained under stationary conditions by imposing an imaginary buoyancy force on the rising bubble. The results indicate that the bubble-droplet aggregate with double emulsion morphology can minimize the distortion of the bubble-droplet aggregate and achieve a greater terminal velocity than the aggregate with partially engulfed morphology.

In thermodynamic theory, the liquid-vapor fluids can be described by a single multiphase equation of state and the surface wettability is usually characterized by the surface free-energy density. In this work, we propose an equation-of-state-dependent surface free-energy density for the wettability of the liquid-vapor fluids on a solid surface, which can lead to a simple closed-form analytical expression for the contact angle. Meanwhile, the thermodynamically derived equilibrium condition is equivalent to the geometric formulation of the contact angle. To numerically validate the present surface free-energy density, the mesoscopic multiphase lattice Boltzmann model with self-tuning equation of state, which is strictly consistent with thermodynamic theory, is employed, and the two-dimensional wetting condition treatment is extended to the three-dimensional situation with flat and curved surfaces. Two- and three-dimensional lattice Boltzmann simulations of static droplets on flat and curved surfaces are first performed, and the obtained contact angles agree well with the closed-form analytical expression. Then, the three-dimensional lattice Boltzmann simulation of a moving droplet on an inclined wall, which is vertically and sinusoidally oscillated, is carried out. The dynamic contact angles well satisfy the Cox-Voinov law. The droplet movement regimes are consistent with previous experiments and two-dimensional simulations. The dependence of the droplet overall velocity with respect to the dimensionless oscillation strength is also discussed in detail.

In most papers, ${\phi }^4$-field theory with the vector ($d$-component) field ${\phi }_{\alpha }$ is considered as a particular case of the $n$-component field model for $n=d$ and $O\left(n\right)$ symmetry. However, in such a model the symmetry $O\left(d\right)$ admits an addition to the action of a term proportional to the squared divergence of the field $\sim h{\left({\partial }_{\alpha }{\phi }_{\alpha }\right)}^2$. From the point of view of renormalization group analysis, it requires a separate consideration, because it may well change the nature of the critical behavior of the system. Therefore, this frequently neglected term in the action requires a detailed and accurate study on the issue of the existence of new fixed points and their stability. It is known that within the lower order of perturbation theory the only infrared stable fixed point with $h=0$ exists but the corresponding positive value of stability exponent ${\omega }_h$ is tiny. This led us to analyze this constant in higher orders of perturbation theory by calculating the four-loop renormalization group contributions for ${\omega }_h$ in $d=4-2\varepsilon$ within the minimal subtraction scheme, which should be enough to infer positivity or negativity of this exponent. The value turned out to be undoubtedly positive, although still small even in higher loops: 0.0156(3). These results cause the corresponding term to be neglected in the action when analyzing the critical behavior of the $O\left(n\right)$-symmetric model. At the same time, the small value of ${\omega }_h$ shows that the corresponding corrections to the critical scaling are significant in a wide range.

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs and also simplify the task of making the computation as a whole thermodynamically reversible. The inherent reversibility of mechanical logic gates would make them good candidates for the design of practical logically reversible computing systems if not for the relatively large size and mass of such systems. In this paper we outline the design and simulation of reversible molecular mechanical logic gates that come close to the limits of thermodynamic reversibility even under the effects of thermal noise, and outline associated circuit components from which arbitrary combinatorial reversible circuits can be constructed and simulated. We demonstrate that isolated components can be operated in a thermodynamically reversible manner, and explore the complexities of combining components to implement more complex computations. Finally, we demonstrate a method to construct arbitrarily large reversible combinatorial circuits using multiple external controls and signal boosters with a working half-adder circuit.

We study a population of swarmalators (swarming/mobile oscillators) which run on a ring and are subject to random pinning. The pinning represents the tendency of particles to stick to defects in the underlying medium which competes with the tendency to sync and swarm. The result is rich collective behavior. A highlight is low dimensional chaos which in systems of ordinary, Kuramoto-type oscillators is uncommon. Some of the states (the phase wave and split phase wave) resemble those seen in systems of Janus matchsticks or Japanese tree frogs. The others (such as the sync and unsteady states) may be observable in systems of vinegar eels, electrorotated Quincke rollers, or other swarmalators moving in disordered environments.

We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems; they are responsible for chaotic transients, fractal basin boundaries, and chaotic scattering, and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increases the transient times and we analyze the phenomenon of crisis induced intermittency.

Human contact behaviors involve both dormant and active processes. The dormant (active) process goes from the disappearance (creation) to the creation (disappearance) of an edge. The dormant (active) time is the elapsed time since the edge became dormant (active). Many empirical studies have revealed that dormant and active times in human contact behaviors tend to show a long-tailed distribution. Previous researches focused on the impact of the dormant process on spreading dynamics. However, the epidemic spreading happens on the active process. This raises the question of how the active process affects epidemic spreading in complex networks. Here, we propose a novel time-varying network model in which the distributions of both the dormant time and active time of edges are adjustable. We develop a pairwise approximation method to describe the spreading dynamical processes in the time-varying networks. Through extensive numerical simulations, we find that the epidemic threshold is proportional to the mean dormant time and inversely proportional to the mean active time. The attack rate decreases with the increase of mean dormant time and increases with the increase of mean active time. It is worth noting that the epidemic threshold and the attack rate (e.g., the infected density in the steady state) are independent of the heterogeneities of the dormant time distribution and the active time distribution. Increasing the heterogeneity of the dormant time distribution accelerates epidemic spreading while increasing the heterogeneity of the active time distribution slows it down.

In the analysis of complex ecosystems it is common to use random interaction coefficients, which are often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by imposing hierarchical interspecies interactions. These are incorporated into a generalized Lotka-Volterra dynamical system. In a hierarchical community species benefit more, on average, from interactions with species further below them in the hierarchy than from interactions with those above. Using dynamic mean-field theory, we demonstrate that a strong hierarchical structure is stabilizing, but that it reduces the number of species in the surviving community, as well as their abundances. Additionally, we show that increased heterogeneity in the variances of the interaction coefficients across positions in the hierarchy is destabilizing. We also comment on the structure of the surviving community and demonstrate that the abundance and probability of survival of a species are dependent on its position in the hierarchy.

In the study of network synchronization, an outstanding question of both theoretical and practical significance is how to allocate a given set of heterogeneous oscillators on a complex network in order to improve the synchronization performance. Whereas methods have been proposed to address this question in the literature, the methods are all based on accurate models describing the system dynamics, which, however, are normally unavailable in realistic situations. Here, we show that this question can be addressed by the model-free technique of a feed-forward neural network (FNN) in machine learning. Specifically, we measure the synchronization performance of a number of allocation schemes and use the measured data to train a machine. It is found that the trained machine is able to not only infer the synchronization performance of any new allocation scheme, but also find from a huge amount of candidates the optimal allocation scheme for synchronization.

Here we investigate phenotypic evolution from the perspective of the Ornstein-Uhlenbeck (OU) process. Evolutionarily speaking, the model assumes the existence of stabilizing selection toward a phenotypic optimum. The standard (OU) model is modified to include environmental variation by taking a moving phenotypic optimum and endowing organisms with phenotypic plasticity. These two processes lead to an effective fitness landscape, which deforms the original. We observe that the simultaneous occurrence of environmental variation and phenotypic plasticity leads to skewed phenotypic distributions. The skewness of the resulting phenotypic distributions strongly depends on the rate of environmental variation and strength of selection. When generalized to more than one trait, the phenotypic distributions are not only affected by the magnitude of the rate of environmental variation but also by its direction. A remarkable feature of our predictions is the existence of an upper bound for the critical rate of environmental variation to allow population persistence, even if there is no cost associated with phenotypic plasticity.

We present a numerical study of the advancing and receding apparent contact angles for a liquid meniscus in contact with random self-affine rough surfaces in Wenzel's wetting regime. Within the framework of the Wilhelmy plate geometry, we use the full capillary model to obtain these global angles for a wide range of local equilibrium contact angles and for different parameters that determine the self-affine solid surfaces: Hurst exponent, wave vector domain, and root-mean-square roughness. We find that the advancing and receding contact angles are single-valued functions that depend only on the roughness factor determined by the set of values of the parameters of the self-affine solid surface. Moreover, the cosines of these angles are found to depend linearly on the surface roughness factor. The relations between the advancing, the receding, and Wenzel's equilibrium contact angles are investigated. It is shown that for materials with self-affine surface structure, the hysteresis force is the same for different liquids and it depends only on the surface roughness factor. A comparison with existing numerical and experimental results is carried out.