The nonlinear evolution of bubble and spike fronts growing through the generalized Rayleigh-Taylor instability are studied by numerical simulations and by solving an extension of Alon's [Phys. Rev. E 48, 1008 (1993)] statistical model based on the asymptotic velocity of a single-mode bubble and the merging bubble process. In this work, the generalized Rayleigh-Taylor instability includes a frictional force due to collision with a secondary fluid. Depending on its strength the behavior during the nonlinear stage leads to two different regimes: the first is the classical inertial case where the bubble front is known to grow as $h\propto t^2$ and evolves towards large structures, and the second is the collisional case where the front grows as $h\propto t$ and maintains structures of relatively constant size. In this new regime, the importance of adding the bifurcation process, the opposite process of merging, is highlighted.

Proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both “fluence-based” techniques and high-fidelity “mesh-based” methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.

Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a growth process in which an interface formed by the local phase field gradually roughens and eventually saturates. Such a process is here shown to display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang universality class, including a Tracy-Widom probability distribution for phase fluctuations around their mean. This is revealed by numerical explorations of a variety of oscillator systems: rings of generic phase oscillators and rings of paradigmatic limit-cycle oscillators, like Stuart-Landau and van der Pol. It also agrees with analytical expectations derived under conditions of strong mutual coupling. The nonequilibrium critical behavior that we find is robust and transcends the details of the oscillators considered. Hence, it may well be accessible to experimental ensembles of oscillators in the presence of, e.g., thermal noise.

Topology in many-body physics usually emerges as a feature of equilibrium quantum states. We show that topological fingerprints can also appear in the relaxation rates of open quantum systems. To demonstrate this we consider one of the simplest models that has two topologically distinct phases in its ground state: the Kitaev chain model for the $p$-wave superconductor. After introducing dissipation to this model we estimate the Liouvillian gap in both strong and weak dissipative limits. Our results show that a nonzero superconducting pairing opens a Liouvillian gap that remains open in the limit of infinite system size. At strong dissipation this gap is essentially unaffected by the topology of the underlying Hamiltonian ground state. In contrast, when dissipation is weak, the topological phase of the Hamiltonian ground state plays a crucial role in determining the character of the Liouvillian gap. We find, for example, that in the topological phase this gap is completely immune to changes in the chemical potential. On the other hand, in the nontopological phase the Liouvillian gap is suppressed by a large chemical potential.

We study two prototypical models of self-organized criticality, namely sandpile automata with deterministic (Bak-Tang-Wiesenfeld) and probabilistic (Manna model) dynamical rules, focusing on the nature of stress fluctuations induced by driving—adding grains during avalanche propagation, and dissipation through avalanches that hit the system boundary. Our analysis of stress evolution time series reveals robust cyclical trends modulated by collective fluctuations with dissipative avalanches. These modulated cycles attain higher harmonics, characterized by multifractal measures within a broad range of timescales. The features of the associated singularity spectra capture the differences in the dynamic rules behind the self-organized critical states at adiabatic driving and their pertinent response to the increased driving rate, which alters the process of stochasticity and causes a loss of avalanche scaling. In sequences of outflow current carried by dissipative avalanches, the first return distributions follow the q-Gaussian law in the adiabatic limit. They appear to follow different laws at an intermediate scale with an increased driving rate, describing different pathways to the gradual loss of cooperative behavior in these two models. The robust appearance of cyclical trends and their multifractal modulation thus represents another remarkable feature of self-organized dynamics beyond the scaling of avalanches. It can also help identify the prominence of self-organizational phenomenology in an empirical time series when underlying interactions and driving modes remain hidden.

We study Ruelle-Pollicott resonances in translationally invariant quantum many-body lattice systems via spectra of a momentum-resolved operator propagator on infinite systems. Momentum dependence gives insight into the decay of correlation functions, showing that, depending on their symmetries, different correlation functions in general decay with different rates. Focusing on the kicked Ising model, the spectrum seems to be typically composed of an annular random matrix-like ring whose size we theoretically predict, and few isolated resonances. We identify several interesting regimes, including a mixing regime with a power-law decay of correlation functions. In that regime, we also observe a huge difference in timescales of different correlation functions due to an almost conserved operator. An exact expression for the singular values of the operator propagator is conjectured, showing that it becomes singular at a special point.

The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has received limited attention. Here, we adapt and enhance the mean-field approach originally proposed by Stiller and Radons [Phys. Rev. E 58, 1789 (1998)] to study the asynchronous state in the Kuramoto model with a finite number of oscillators and with disordered connectivity. By employing an iterative stochastic mean field approximation, the complex $N$-oscillator system can effectively be reduced to a one-dimensional dynamics, both for homogeneous and heterogeneous networks. This method allows us to investigate the power spectra of individual oscillators as well as of the multiplicative “network noise” in the Kuramoto model in the asynchronous regime. By taking into account the finite system size and disorder in the connectivity, our findings become relevant for the dynamics of coupled oscillators that appear in the context of biological or technical systems.

Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure, noisy data, missing observations in time, as well as an efficient incorporation of prior information to minimize the number of samples required for an accurate learning. Here, we introduce a universal learning method based on a scalable dynamic message-passing technique that addresses these challenges often encountered in real data. The algorithm leverages available prior knowledge on the model and on the data, and reconstructs both network structure and parameters of a spreading model. We show that a linear computational complexity of the method with the key model parameters makes the algorithm scalable to large network instances.

Mass transfer to the reactive wall of a curved cylindrical tube is analyzed in the combined entry region where both momentum and concentration boundary layers are developing. The velocity and concentration distributions developing from uniform inlet profiles are obtained using perturbation analysis, accounting for acceleration of the inviscid flow outside the boundary layer arising from channel curvature and flow displacement. The enhancement in the average flux of the reactive species at the tube wall downstream of the inlet is determined and compared to predictions of numerical simulations. A regression model is presented for the cross-sectional average of the Sherwood number, valid for distances up to ten tube diameters downstream of the tube inlet over a wide range of Reynolds and Schmidt numbers.

In this paper, we introduce a computational technique for modeling heterogeneous thermoresponsive hydrogels. The model resolves local fluid-solid interactions in hydrogel pores during the deswelling process. The model is a Lagrangian particle-based technique, which benefits from computational grids that represent polymer beads inside hydrogel scaffolds. The results show that the mechanical properties of hydrogels during deswelling, e.g., shrinkage ratio and elastic modulus, have a direct effect on the development of the front of expelled fluid. It is also observed that in certain parameter regimes the hydrogel may generate inertial fluid jets at the early stages of deswelling. Finally, simple heterogeneous designs are developed using Menger sponge-inspired shapes to investigate the effect of design heterogeneity on promoting directional release.

Dielectric elastomer actuators (DEAs) are an emerging type of soft actuators based on intelligent electroactive polymers. Compared with conventional rigid actuators, DEAs can adapt to extreme hydrostatic pressures without any bulky protective vessels and, therefore, have demonstrated great promises in high-hydrostatic pressure applications such as deep-sea explorations. However, the effects of the enormous hydrostatic compressions on the mechanical and electromechanical coupling properties and electrical breakdown strengths of DEAs remain unclear due to the restrictions in the existing theoretical models and limitations in the experimental techniques developed for DEAs. To bridge these gaps, this paper develops a hydrostatic pressure-coupled DEA model and introduces a series of experimental characterization techniques for accurately quantifying such effects introduced by the hydrostatic pressures. A wide range of hydrostatic pressures up to 105 MPa (close to the hydrostatic pressure in Mariana Trench) are investigated and its effects on the stiffening of the elastomer, reduction of the actuation strain, and increase of the breakdown electric field of the DEAs are reported in both experiments and models. The contributions of this paper can offer guidelines for characterizing the performances of DEAs under high-hydrostatic compressions and for designing the next-generation soft robotic systems for deep-sea applications.

We calculate the shear relaxation times in four important simple monatomic model fluids: Lennard-Jones, Yukawa, soft-sphere, and hard-sphere fluids. It is observed that in properly reduced units, the shear relaxation times exhibit quasiuniversal behavior when the density increases from the gaslike low values to the high-density regime near crystallization. They first decrease with density at low densities, reach minima at moderate densities, and then increase toward the freezing point. The reduced relaxation times at the minima and at the fluid-solid phase transition are all comparable for the various systems investigated, despite more than ten orders of magnitude difference in real systems. Important implications of these results are discussed.

Nearly half of the bee species can perform a fascinating stereotyped behavior to collect pollen grains by vibrating flowers, known as buzz pollination. During the floral visit, these bees mechanically transfer the vibrations produced by their thoracic indirect flight muscles to the flower anther, inducing the movement of the pollen grains and leading them to be released through a small pore or slit placed at the tip of the anther in poricidal flowers. In such flowers, pollen release is affected by the vibrational behavior of buzzing bees, primarily their duration and velocity amplitude. However, we know little about how poricidal anther morphology may influence it. In this work, we investigated through a theoretical and numerical point of view the buzz pollination process considering a typical poricidal anther of a tomato flower (Solanum lycopersicum), which in our work will be approached by a rectangular billiard, experiencing vibrations applied by a bumblebee (Bombus terrestris). Our primary goals in this paper are (i) to understand the mechanism behind the pollen release in this model, (ii) to observe some scale effects associated with morphological variations of the anther (as pore size and anther shape), and (iii) analyze how these results are related to natural buzz pollination systems.

We study dynamical localization in an ultracold atom confined in an optical lattice that is simultaneously shaken by two competing pulsatile modulations with different amplitudes, periods, and waveforms. The effects of finite-width time pulses, modulation waveforms, and commensurable and incommensurable driving periods are investigated. We describe a particularly complex scenario and conclude that dynamical localization can survive, or even increase, when a periodic modulation is replaced by a quasiperiodic one of equal amplitude. Our analytical and numerical results indicate that there exists a strong correlation between the strengths of chaos (stochastic layer width) and dynamical localization (difference between the classical and quantum momentum dispersions) over the entire parameter space, which is maintained regardless of the periodic or quasiperiodic nature of the modulation. This persistent correlation provides a useful guide to optimally control the strength of dynamical localization by tuning the modulation parameters in real-world systems subjected to pulses of finite width.

The mechanism underlying the spatiotemporal chromosome organization in Escherichia coli cells remains an open question, though experiments have been able to visually see the evolving chromosome organization in fast- and slow-growing cells. We had proposed [D. Mitra et al., Soft Matter 18, 5615 (2022)] that the DNA ring polymer adopts a specific polymer topology as it goes through its cell cycle, which in turn self-organizes the chromosome by entropic forces during slow growth. The fast-growing E. coli cells have four (or more) copies of the replicating DNA, with overlapping rounds of replication going on simultaneously. This makes the spatial segregation and the subsequent organization of the multiple generations of DNA a complex task. Here, we establish that the same simple principles of entropic repulsion between polymer segments which provided an understanding of self-organization of DNA in slow-growth conditions also explains the organization of chromosomes in the much more complex scenario of fast-growth conditions. Repulsion between DNA-polymer segments through entropic mechanisms is harnessed by modifying polymer topology. The ring-polymer topology is modified by introducing crosslinks (emulating the effects of linker proteins) between specific segments. Our simulation reproduces the emergent evolution of the organization of chromosomes as seen in vivo in fluorescent in situ hybridization experiments. Furthermore, we reconcile the mechanism of longitudinal organization of the chromosomes arms in fast-growth conditions by a suitable adaptation of the model. Thus, polymer physics principles, previously used to understand chromosome organization in slow-growing E. coli cells also resolve DNA organization in more complex scenarios with multiple rounds of replication occurring in parallel.

We derive several versions of the cell theory for a crystal phase of hard equilateral triangles. To that purpose we analytically calculated the free area of a frozen oriented or freely rotating particle inside the cavity formed by its neighbors in a chiral configuration of their orientations. From the most successful versions of the theory we predict an equation of state which, despite being derived from a crystal configuration of particles, describes very reasonably the equation of state of the 6-atic liquid-crystal phase at packing fractions not very close from the isotropic-6-atic bifurcation. Also, the same equation of state performs well when compared to that from MC simulations for the stable crystal phase. The agreement can even be improved by selecting adequate values for the angle of chirality. Despite the success of two versions of the theory, we show that the free energy is an increasing function of the angle of chirality, implying that the most stable phase is the achiral phase. Furthermore, we show that possible clustering effects, such as the formation of perfect chiral hexagonal clusters, which in turn crystallize into an hexagonal lattice, cannot explain the presence of the chirality observed in simulations.

Moment methods are often used to solve transport problems involving the Boltzmann-BGK equation. Because the moment equations are underdetermined, these methods require an additional "closure equation" that relates higher to lower-order moments. Here, we examine the closure equation and higher-order moment relations implicit in the lattice Boltzmann method (LBM) that use Gauss-Hermite quadrature for their discrete velocity sets. It is shown that the discrete-velocity-set itself defines the closure equation and higher-order moment relations, the precise forms of which are yet to be reported. The general formula we present facilitates the efficient computational evaluation of higher-order moments and provides insight into the operation of LBM that is anticipated to be useful in theoretical analyses of its performance. Derived formulas for two different velocity sets are validated against numerical implementations of the LBM for steady Couette flow.

We investigate the interaction between two flat-top solitons within the cubic-quintic nonlinear Schrödinger equation framework. Our study results point towards a significant departure of flat-top solitons' collisional characteristics from the conventional behaviors exhibited in the scattering dynamics of two bright solitons. Our investigation outlines specific regimes corresponding to the dual flat-top solitons' elastic and inelastic collisions. We determine regimes in the parameter space where exchange in the widths of the interacting flat-top solitons is possible, even within the elastic collision domain. We find a periodic occurrence of completely elastic scattering of flat-top solitons in terms of the solitons' parameters. Investigating the internal energy transfers between the solitons and the emitted radiation reveals the origin of inelasticity in flat-top soliton collisions. We perform a variational calculation that accounts for the amount of radiation produced by the collision and hence provides further insight into the physics underlying the loss of elasticity of collisions.

The fractional differentiation method's broad possibilities are demonstrated with rather simple but important examples of the anomalous diffusion trapping problems. In particular we evaluate the reaction rate coefficients for the subdiffusion-controlled reactions and for reactions describing by a diffusion equation with a half-order time derivative as a damping term. The distinctive feature of this aproach is that the reaction rate coefficient may be obtained by means of some factorization procedure immediately, without a preliminary solution to the corresponding initial boundary value diffusion problem. The explanations given in the paper are detailed enough to provide the mathematical background for the fractional differentiation method needed to apply it to a wide range of reaction-diffusion problems with time-fractional derivatives in the Riemann-Liouville sense.