Motivated by patterns with defects in natural and laboratory systems, we develop two quantitative measures of order for imperfect Bravais lattices in the plane. A tool from topological data analysis called persistent homology combined with the sliced Wasserstein distance, a metric on point distributions, are the key components for defining these measures. The measures generalize previous measures of order using persistent homology that were applicable only to imperfect hexagonal lattices in two dimensions. We illustrate the sensitivities of these measures to the degree of perturbation of perfect hexagonal, square, and rhombic Bravais lattices. We also study imperfect hexagonal, square, and rhombic lattices produced by numerical simulations of pattern-forming partial differential equations. These numerical experiments serve to compare the measures of lattice order and reveal differences in the evolution of the patterns in various partial differential equations.

Haros graphs have been recently introduced as a set of graphs bijectively related to real numbers in the unit interval. Here we consider the iterated dynamics of a graph operator $\mathcal{R}$ over the set of Haros graphs. This operator was previously defined in the realm of graph-theoretical characterization of low-dimensional nonlinear dynamics and has a renormalization group (RG) structure. We find that the dynamics of $\mathcal{R}$ over Haros graphs is complex and includes unstable periodic orbits of arbitrary period and nonmixing aperiodic orbits, overall portraiting a chaotic RG flow. We identify a single RG stable fixed point whose basin of attraction is associated with the set of rational numbers, and find periodic RG orbits that relate to (pure) quadratic irrationals and aperiodic RG orbits, related with (nonmixing) families of nonquadratic algebraic irrationals and transcendental numbers. Finally, we show that the graph entropy of Haros graphs is globally decreasing as the RG flows towards its stable fixed point, albeit in a strictly nonmonotonic way, and that such graph entropy remains constant inside the periodic RG orbit associated to a subset of irrationals, the so-called metallic ratios. We discuss the possible physical interpretation of such chaotic RG flow and put results regarding entropy gradients along RG flow in the context of $c$-theorems.

We demonstrate the existence of compactons matter waves in binary mixtures of Bose-Einstein condensates (BEC) trapped in deep optical lattices (OL) subjected to equal contributions of intraspecies Rashba and Dresselhaus spin-orbit coupling (SOC) under periodic time modulations of the intraspecies scattering length. We show that these modulations lead to a rescaling of the SOC parameters that involves the density imbalance of the two components. This gives rise to density dependent SOC parameters that strongly influence the existence and the stability of compacton matter waves. The stability of SOC-compactons is investigated both by linear stability analysis and by time integrations of the coupled Gross-Pitaevskii equations. We find that SOC restricts the parameter ranges for stable stationary SOC-compacton existence but, on the other side, it gives a more stringent signature of their occurrence. In particular, SOC-compactons should appear when the intraspecies interactions and the number of atoms in the two components are perfectly balanced (or close to being balanced for the metastable case). The possibility to use SOC-compactons as a tool for indirect measurements of the number of atoms and/or the intraspecies interactions is also suggested.

We consider a generic class of gene circuits affected by nonlinear extrinsic noise. To address this nonlinearity we introduce a general perturbative methodology based on assuming timescale separation between noise and gene dynamics, with fluctuations exhibiting a large but finite correlation time. We apply this methodology to the case of the toggle switch, and by considering biologically relevant log-normal fluctuations, we find that the system exhibits noise-induced transitions. The system becomes bimodal in regions of the parameter space where it would be deterministically monostable. We show that by including higher order corrections our methodology allows one to obtain correct predictions for the occurrence of transitions even for not so large correlation time of the fluctuations, thereby overcoming limitations of previous theoretical approaches. Interestingly we find that at intermediate noise intensities the noise-induced transition in the toggle switch affects one of the genes involved, but not the other one.

Clustering passive particles by active agents is a promising route for fabrication of colloidal structures. Here, we report the dynamic clustering of micrometric beads in a suspension of motile bacteria. We characterize the coarsening dynamics for various bead sizes, surface fractions, and bacterial concentrations. We show that the time scale $\tau$ for the onset of clustering is governed by the time of first encounter of diffusing beads. At large time ($t\gg \tau$), we observe a robust cluster growth as $t^{1/3}$, similar to the Ostwald ripening mechanism. From bead tracking measurements, we extract the short-range bacteria-induced attractive force at the origin of this clustering.

We use numerical simulations to systematically investigate the vesicle dynamics in two-dimensional (2D) Taylor-Green vortex flow in the absence of inertial forces. Vesicles are highly deformable membranes encapsulating an incompressible fluid and they serve as numerical and experimental proxies for biological cells such as red blood cells. Vesicle dynamics has been studied in free-space or bounded shear, Poiseuille, and Taylor-Couette flows in 2D and 3D. Taylor-Green vortex are characterized with even more complicated properties than those flows such as nonuniform flow line curvature, shear gradient. We study the effects of two parameters on the vesicle dynamics: the ratio of the interior fluid viscosity to that of the exterior one and the ratio of the shear forces on the vesicle to the membrane stiffness (characterized by the capillary number). Vesicle deformability nonlinearly depends on these parameters. Although the study is in 2D, our findings contribute to the wide spectrum of intriguing vesicle dynamics: Vesicles migrate inwards and eventually rotate at the vortex center if they are sufficiently deformable. If not, then they migrate away from the vortex center and travel across the periodic arrays of vortices. The outward migration of a vesicle is a new phenomenon in Taylor-Green vortex flow and has not been observed in any other flows so far. Such cross-streamline migration of deformable particles can be utilized in several applications such as microfluidics for cell separation.

The method of stress function in elasticity theory is a powerful analytical tool with applications to a wide range of physical systems, including defective crystals, fluctuating membranes, and more. A complex coordinates formulation of stress function, known as the Kolosov-Muskhelishvili formalism, enabled the analysis of elastic problems with singular domains, particularly cracks, forming the basis for fracture mechanics. A shortcoming of this method is its limitation to linear elasticity, which assumes Hookean energy and linear strain measure. Under finite loads, the linearized strain fails to describe the deformation field adequately, reflecting the onset of geometric nonlinearity. The latter is common in materials experiencing large rotations, such as regions close to the crack tip or elastic metamaterials. While a nonlinear stress function formalism exists, the Kolosov-Muskhelishvili complex representation had not been generalized and remained limited to linear elasticity. This paper develops a Kolosov-Muskhelishvili formalism for the nonlinear stress function. Our formalism allows us to port methods from complex analysis to nonlinear elasticity and to solve nonlinear problems in singular domains. Upon implementing the method to the crack problem, we discover that nonlinear solutions strongly depend on the applied remote loads, excluding a universal form of the solution close to the crack tip and questioning the validity of previous studies of nonlinear crack analysis.

The propagation of a dissipative soliton was experimentally studied in a two-dimensional binary complex plasma. The crystallization was suppressed in the center of the particle suspension where two types of particles were mixed. The motions of individual particles were recorded using video microscopy, and the macroscopic properties of the solitons were measured in the amorphous binary mixture in the center and in the plasma crystal in the periphery. Although the overall shape and parameters of solitons propagating in amorphous and crystalline regions were quite similar, their velocity structures at small scales as well as the velocity distributions were profoundly distinct. Moreover, the local structure rearranged drastically in and behind the soliton, which was not observed in the plasma crystal. Langevin dynamics simulations were performed, and the results agreed with the experimental observations.

Enantiomers are chiral molecules that exist in right-handed and left-handed conformations. Optical techniques of enantiomers' detection are widely employed to discriminate between left- and right-handed molecules. However, identical spectra of enantiomers make enantiomer detection a very challenging task. Here, we investigate the possibility of exploiting thermodynamic processes for enantiomer detection. In particular, we employ a quantum Otto cycle in which a chiral molecule described by a three-level system with cyclic optical transitions is considered a working medium. Each energy transition of the three-level system is coupled with an external laser drive. We find that the left- and right-handed enantiomers operate as a quantum heat engine and a thermal accelerator, respectively, when the overall phase is the control parameter. In addition, both enantiomers act as heat engines by keeping the overall phase constant and using the laser drives' detuning as the control parameter during the cycle. However, the molecules can still be distinguished because both cases' extracted work and efficiency are quantitatively very different. Accordingly, the left- and right-handed molecules can be distinguished by evaluating the work distribution in the Otto cycle.

Real-world networks are rarely static. Recently, there has been increasing interest in both network growth and network densification, in which the number of edges scales superlinearly with the number of nodes. Less studied but equally important, however, are scaling laws of higher-order cliques, which can drive clustering and network redundancy. In this paper, we study how cliques grow with network size, by analyzing several empirical networks from emails to Wikipedia interactions. Our results show superlinear scaling laws whose exponents increase with clique size, in contrast to predictions from a previous model. We then show that these results are in qualitative agreement with a model that we propose, the local preferential attachment model, where an incoming node links not only to a target node, but also to its higher-degree neighbors. Our results provide insights into how networks grow and where network redundancy occurs.

We investigate a geometric Brownian information engine (GBIE) in the presence of an error-free feedback controller that transforms the information gathered on the state of Brownian particles entrapped in monolobal geometric confinement into extractable work. Outcomes of the information engine depend on the reference measurement distance $x_m$, the feedback site $x_f$, and the transverse force $G$. We determine the benchmarks for utilizing the available information in an output work and the optimum operating requisites for best achievable work. Transverse bias force $\left(G\right)$ tunes the entropic contribution in the effective potential and hence the standard deviation $\left(\sigma \right)$ of the equilibrium marginal probability distribution. We recognize that the amount of extractable work reaches a global maximum when $x_f=2x_m$ with $x_m\sim 0.6\sigma$, irrespective of the extent of the entropic limitation. Because of the higher loss of information during the relaxation process, the best achievable work of a GBIE is lower in an entropic system. The feedback regulation also bears the unidirectional passage of particles. The average displacement increases with growing entropic control and is maximum when $x_m\sim 0.81\sigma$. Finally, we explore the efficacy of the information engine, a quantity that regulates the efficiency in utilizing the information acquired. With $x_f=2x_m$, the maximum efficacy reduces with increasing entropic control and shows a crossover from 2 to $11/9$. We discover that the condition for the best efficacy depends only on the confinement lengthscale along the feedback direction. The broader marginal probability distribution accredits the increased average displacement in a cycle and the lower efficacy in an entropy-dominated system.

In this paper, a $(u+1)\times v$ horn torus resistor network with a special boundary is researched. According to Kirchhoff's law and the recursion-transform method, a model of the resistor network is established by the voltage $V$ and a perturbed tridiagonal Toeplitz matrix. We obtain the exact potential formula of a horn torus resistor network. First, the orthogonal matrix transformation is constructed to obtain the eigenvalues and eigenvectors of this perturbed tridiagonal Toeplitz matrix; second, the solution of the node voltage is given by using the famous fifth kind of discrete sine transform (DST-V). We introduce Chebyshev polynomials to represent the exact potential formula. In addition, the equivalent resistance formulae in special cases are given and displayed by a three-dimensional dynamic view. Finally, a fast algorithm of computing potential is proposed by using the mathematical model, famous DST-V, and fast matrix-vector multiplication. The exact potential formula and the proposed fast algorithm realize large-scale fast and efficient operation for a $(u+1)\times v$ horn torus resistor network, respectively.

We are exploring two archetypal noise-induced escape scenarios: Escape from a finite interval and from the positive half-line under the action of the mixture of Lévy and Gaussian white noises in the overdamped regime, for the random acceleration process and higher-order processes. In the case of escape from finite intervals, the mixture of noises can result in the change of value of the mean first passage time in comparison to the action of each noise separately. At the same time, for the random acceleration process on the (positive) half-line, over the wide range of parameters, the exponent characterizing the power-law decay of the survival probability is equal to the one characterizing the decay of the survival probability under action of the (pure) Lévy noise. There is a transient region, the width of which increases with stability index $\alpha$, when the exponent decreases from the one for Lévy noise to the one corresponding to the Gaussian white noise driving.

The alignment of biological sequences such as DNA, RNA, and proteins, is one of the basic tools that allow to detect evolutionary patterns, as well as functional or structural characterizations between homologous sequences in different organisms. Typically, state-of-the-art bioinformatics tools are based on profile models that assume the statistical independence of the different sites of the sequences. Over the last years, it has become increasingly clear that homologous sequences show complex patterns of long-range correlations over the primary sequence as a consequence of the natural evolution process that selects genetic variants under the constraint of preserving the functional or structural determinants of the sequence. Here, we present an alignment algorithm based on message passing techniques that overcomes the limitations of profile models. Our method is based on a perturbative small-coupling expansion of the free energy of the model that assumes a linear chain approximation as the zeroth-order of the expansion. We test the potentiality of the algorithm against standard competing strategies on several biological sequences.

We consider a disk-shaped cold atom Bose-Einstein condensate with repulsive atom-atom interactions within a circular trap, described by a two-dimensional time-dependent Gross-Pitaevskii equation with cubic nonlinearity and a circular box potential. In this setup, we discuss the existence of a type of stationary nonlinear waves with propagation-invariant density profiles, consisting of vortices located at the vertices of a regular polygon with or without an antivortex at its center. These polygons rotate around the center of the system and we provide approximate expressions for their angular velocity. For any size of the trap, we find a unique regular polygon solution that is static and is seemingly stable for long evolutions. It consists of a triangle of vortices with unit charge placed around a singly charged antivortex, with the size of the triangle fixed by the cancellation of competing effects on its rotation. There exist other geometries with discrete rotational symmetry that yield static solutions, even if they turn out to be unstable. By numerically integrating in real time the Gross-Pitaevskii equation, we compute the evolution of the vortex structures and discuss their stability and the fate of the instabilities that can unravel the regular polygon configurations. Such instabilities can be driven by the instability of the vortices themselves, by vortex-antivortex annihilation or by the eventual breaking of the symmetry due to the motion of the vortices.

In this work we employ molecular dynamics simulations to investigate the first-order-reversal-curve distribution and switching-field distribution of magnetic elastomers. We model magnetic elastomers in a bead-spring approximation with permanently magnetized spherical particles of two different sizes. We find that a different fractional composition of particles affects the magnetic properties of elastomers obtained as a result. We prove that the hysteresis of the elastomer can be attributed to the broad energy landscape with multiple shallow minima and caused by dipolar interactions.

We report in this paper the study towards revealing the energy distribution of lost high-energy runaway electrons based on their bremsstrahlung emission. The high-energy hard x-rays are originated from the bremsstrahlung emission of lost runaway electrons in the experimental advanced superconducting tokamak (EAST) tokamak, and the energy spectra are measured using a gamma spectrometer. The energy distribution of the runaway electrons is reconstructed from this hard x-ray energy spectrum using a deconvolution algorithm. The results indicate that the energy distribution of the lost high-energy runaway electrons can be obtained with the deconvolution approach. In the specific case in this paper, the runaway electron energy was peaked around 8 MeV, covering from 6 MeV to 14 MeV.

Electrowetting has become a widely used tool for manipulating tiny amounts of liquids on surfaces. This paper proposes an electrowetting lattice Boltzmann method for manipulating micro-nano droplets. The hydrodynamics with the nonideal effect is modeled by the chemical-potential multiphase model, in which the phase transition and equilibrium are directly driven by chemical potential. For electrostatics, droplets in the micro-nano scale cannot be considered as equipotential as macroscopic droplets due to the Debye screening effect. Therefore, we linearly discretize the continuous Poisson-Boltzmann equation in a Cartesian coordinate system, and the electric potential distribution is stabilized by iterative computations. The electric potential distribution of droplets at different scales suggests that the electric field can still penetrate micro-nano droplets even with the screening effect. The accuracy of the numerical method is verified by simulating the static equilibrium of the droplet under the applied voltage, and the results show the apparent contact angles agree very well with the Lippmann–Young equation. The microscopic contact angles present some obvious deviations due to the sharp decrease of electric field strength near the three-phase contact point. These are consistent with previously reported experimental and theoretical analyses. Then, the droplet migrations on different electrode structures are simulated, and the results show that droplet speed can be stabilized more quickly due to the more uniform force on the droplet in the closed symmetric electrode structure. Finally, the electrowetting multiphase model is applied to study the lateral rebound of droplets impacting on the electrically heterogeneous surface. The electrostatic force prevents the droplets from contracting on the side which is applied voltage, resulting in the lateral rebound and transport toward the side.

Stochastic dynamics of a nonlinear thermal circuit is studied. Due to the existence of negative differential thermal resistance, there exist two stable steady states that satisfy both the continuity and stability conditions. The dynamics of such a system is governed by a stochastic equation which describes originally an overdamped Brownian particle that undergoes a double-well potential. Correspondingly, the finite time temperature distribution takes a double-peak profile and each peak is approximately Gaussian. Owing to the thermal fluctuation, the system is able to jump occasionally from one stable steady state to the other. The probability density distribution of the lifetime $\tau$ for each stable steady state follows a power-law decay ${\tau }^{-3/2}$ in the short-$\tau$ regime and an exponential decay $e^{-\tau /{\tau }_0}$ in the long-$\tau$ regime. All these observations can be well explained analytically.

Precisely controlling heat transfer in a quantum mechanical system is particularly significant for designing quantum thermodynamical devices. With the technology of experiment advances, circuit quantum electrodynamics (circuit QED) has become a promising system due to controllable light-matter interactions as well as flexible coupling strengths. In this paper, we design a thermal diode in terms of the two-photon Rabi model of the circuit QED system. We find that the thermal diode can not only be realized in the resonant coupling but also achieve better performance, especially for the detuned qubit-photon ultrastrong coupling. We also study the photonic detection rates and their nonreciprocity, which indicate similar behaviors with the nonreciprocal heat transport. This provides the potential to understand thermal diode behavior from the quantum optical perspective and could shed new insight into the relevant research on thermodynamical devices.