We consider a paradigmatic quantum harmonic Otto engine operating in finite time. We investigate its performance when shortcut-to-adiabaticity techniques are used to speed up its cycle. We compute efficiency and power by taking the energetic cost of the shortcut driving explicitly into account. We analyze in detail three different shortcut methods: counterdiabatic driving, local counterdiabatic driving, and inverse engineering. We demonstrate that all three lead to a simultaneous increase of efficiency and power for fast cycles, thus outperforming traditional heat engines.

Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, substantially reducing the undesirable effects of parametric inaccuracy and noise. The procedure proposed here uses time and/or space asymmetric perturbations to move multistable attractors independently in phase space. Applying this mechanism, we increase by around $230\%$ the stable domains in Hénon's map, roughly $85\%$ in the ratchet current described by the Langevin equation, and $60\%$ in Chua's electronic circuit. The proposal is expected to have wide applications in a generic nonlinear complex system presenting multistability, so that related experiments can increase robustness under parametric inaccuracy and noise.

We present an optimized version of the symbolic shadowing algorithm for coarse graining a continuous state dynamical system, originally due to Hirata and co-workers [Phys. Rev. E 70, 016215 (2004)]. We validate our algorithm by finding generating partitions presented previously in the literature. We show that, unlike the original, the optimized algorithm can approximate generating partitions for periodically driven continuous-time nonlinear oscillators. We recover known generating partitions for the driven Duffing oscillator and compute generating partitions for the driven van der Pol oscillator. We also examine the problem of how algorithms such as ours can be applied “objectively,” that is, by starting from arbitrary initial partition guesses. By applying our algorithm to large ensembles of initial random partitions, we show that symbolic shadowing leads to a multiplicity of candidate generating partitions that localize points in phase space to a high degree, thus making it difficult to select the best choice(s). We thus propose using the Lempel-Ziv complexity to identify partitions from this set of candidates that are, in a specific sense, “minimal,” i.e., those with contiguous cells, fewer cell boundaries, and a smaller number of cells compared to their rivals. We also show how our methods can be used to indicate the appropriate number of symbols needed to approximate a generating partition.

A gap soliton is a solitonic state existing inside the band gap of an infinite-periodic exciton-polariton condensate (EPC). The combination of surface states and gap solitons forms the so-called surface gap solitons (SGSs). We analyze the existence of SGSs near the interface between uniform and semi-infinite periodic EPCs. We find that SGSs exist only when the system is excited by a pump with a smaller width. As the width of the pump increases, SGSs become unstable.

We investigate by numerical simulation and finite-size analysis the impact of long-range shortcuts on a spatially embedded transportation network. Our networks are built from two-dimensional ($d=2$) square lattices to be improved by the addition of long-range shortcuts added with probability $P\left(r_{ij}\right)\sim r_{ij}^{-\alpha }$ [J. M. Kleinberg, Nature 406, 845 (2000)]. Considering those improved networks, we performed numerical simulation of multiple discrete package navigation and found a limit for the amount of packages flowing through the network. Such a limit is characterized by a critical probability of creating packages $p_c$, where above this value a transition to a congested state occurs. Moreover, $p_c$ is found to follow a power law, $p_c\sim L^{-\gamma }$, where $L$ is the network size. Our results indicate the presence of an optimal value of ${\alpha }_{\min }\approx 1.7$, where the parameter $\gamma$ reaches its minimum value and the networks are more resilient to congestion for larger system sizes. Interestingly, this value is close to the analytically found value of $\alpha$ for the optimal navigation of single packages in spatially embedded networks, where ${\alpha }_{\mathrm{opt}}=d$. Finally, we show that the power spectrum for the number of packages navigating the network at a given time step $t$, which is related to the divergence of the expected delivery time, follows a universal Lorentzian function, regardless of the topological details of the networks.

This study shows that characteristic modes, such as the figure-eight mode, can be created in the path of the wing tip, which is caused by the fluid-structure interaction, using a flapping model wing with two lumped flexibilities describing the elevation motion as well as the pitching motion. A direct numerical simulation based on the three-dimensional finite element method for fluid-structure interaction (FSI) analyzes the behaviors of the model wing, the surrounding air, and their interaction, where the dynamic similarity law for the FSI is used to incorporate actual insect data, and the parallel computation algorithm is used to perform the systematic parametric study. Characteristic modes, such as the figure-eight mode, are observed in the path of the wing tip from the elevation motion of the simulated wing. This motion is considered as the forced vibration caused by the interaction with the surrounding fluid excited by the flapping of the wing. Therefore, this motion can be modulated by the flexibility to change the natural frequency, which can be controlled by the muscles at the base of the wing in the actual insect. The present simulation shows that the selection between these modes in the path of the wing tip depends on the ratio between the natural frequency of the elevation motion and the flapping frequency. In the case of the figure eight, the upward elevation motion of the wing acts on the leading-edge vortex (LEV) so as to keep its momentum upon stroke reversal. Therefore, this LEV can remain in the wake of the wing after stroke reversal and enhance the next LEV. Because of this effect, the lift increases significantly as the mode of the wing tip path shifts to the figure-eight mode. This understanding will contribute to a developed field of bioinspired micro air vehicles; i.e., it will reduce the complexity of electromechanical devices that prescribe entire motions of their wings.

We study the energy structure and the transfer of an extra electron or hole along periodic polymers made of $N$ monomers, with a repetition unit made of $P$ monomers, using a tight-binding wire model, where a site is a monomer (e.g., in DNA, a base pair), for $P$ even, and deal with two categories of such polymers: made of the same monomer (GC…, GGCC…, etc.) and made of different monomers (GA…, GGAA…, etc.). We calculate the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenspectra, density of states, and HOMO-LUMO gap and find some limiting properties these categories possess, as $P$ increases. We further examine the properties of the mean over time probability to find the carrier at each monomer. We introduce the weighted mean frequency of each monomer and the total weighted mean frequency of the whole polymer, as a measure of the overall transfer frequency content. We study the pure mean transfer rates. These rates can be increased by many orders of magnitude with appropriate sequence choice. Generally, homopolymers display the most efficient charge transfer. Finally, we compare the pure mean transfer rates with experimental transfer rates obtained by time-resolved spectroscopy.

The free energy landscape responsible for crystallization can be complex even for relatively simple systems like hard sphere and charged stabilized colloids. In this work, using the hard-core repulsive Yukawa model, which is known to show complex phase behavior consisting of fluid, FCC, and BCC phases, we studied the interplay between the free energy landscape and polymorph selection during crystallization. When the stability of the BCC phase with respect to the fluid phase is gradually increased by changing the temperature and pressure at a fixed fluid-FCC stability, the final phase formed by crystallization is found to undergo a switch from the FCC to the BCC phase, even though FCC remains thermodynamically the most stable phase. We further show that the nature of local bond-orientational order parameter fluctuations in the metastable fluid phase as well as the composition of the critical cluster depend delicately on the free energy landscape and play a decisive role in the polymorph selection during crystallization.

There is considerable recent interest in intruders impacting into granular materials. Many studies focus on a collisional model where the drag force acting on an intruder varies as the square of the intruder speed. However, it is unclear how intruder friction affects granular impact dynamics. Here, we experimentally study impacts into quasi-two-dimensional beds of photoelastic granular beds of three circular intruders of similar size and mass, but with varying friction coefficients associated with the intruder edges (smooth, “sandy,” and gear). We compare typical measures of the dynamics for the three intruders, including impact depth and speed vs time. We show that the smooth and sandy intruders share similar impact dynamics, while the gear intruder displays smaller impact depth, speed, and impact time. We attribute the differences between the gear intruder's dynamics and those of the other two to differences in the collision-generated force networks associated with the grain-scale roughness of the gear intruder. For the smooth and sandy intruders, the force networks align close to the normal direction of the intruder boundaries. For the gear intruder, the grain-scale geometric roughness leads to force chains that are closer to vertical, rather than in the coarse-grained normal direction to the intruder edge. This leads to a stronger drag force for the gear intruder. Hence, in the range that we have explored, the granular impact dynamics are highly sensitive to grain-scale roughness of the intruder and relatively insensitive to microscale roughness that is associated with the conventional friction coefficient.

We consider freely decaying two-dimensional homogeneous and isotropic turbulent motion in a self-similar limit that is achieved at large Reynolds numbers based on time and the mean kinetic energy of the flow provided that initial average enstrophy tends to infinity as fluid viscosity tens to zero. In this case, the enstrophy dissipation rate has a nonzero finite limit. The vorticity correlation function and the spectral enstrophy density are investigated in an inertial range of distances and wave numbers where these functions are free from the influence of viscosity and large-scale flow parameters. It turns out that in freely decaying two-dimensional self-similar turbulence, the inertial range exists in real space but is absent in the space of wave numbers. This means that turbulent eddies of the appropriate size do not contribute to the spectral density and the known $k^{-1}$ law does not hold. The spectral enstrophy density at large wave numbers behaves nonmonotonically: it first decreases faster than in accordance with the $k^{-1}$ law and then, in the dissipation region, has a growth portion and a second maximum. The enstrophy spectral flux at the boundary of the dissipation region is only a fraction of the enstrophy dissipation rate.

Tenth-order compact difference code Miranda is used to perform large-eddy simulation (LES) of a hydrogen gas–plastic mixing layer in a spherical geometry. Once the mixing layer has achieved self-similar growth, it is heated to 1 keV, and the second-order arbitrary Lagrangian-Eulerian (ALE) code Ares is used to simulate mixing layer evolution as it undergoes thermonuclear (TN) burn. Both premixed (in which deuterium and tritium are initially present in the gas) and nonpremixed (in which deuterium is initially present only in the plastic) variants are considered at Atwood numbers 0.05 and 0.50. The impact of turbulent mixing on mean TN reaction rate is examined, and a four-equation $k\text{−}L\text{−}a\text{−}V$ Reynolds-averaged Navier-Stokes (RANS) model is presented. The $k\text{−}L\text{−}a\text{−}V$ model, which represents an extension of the $k\text{−}L\text{−}a$ model [Morgan and Wickett, Phys. Rev. E 91, 043002 (2015)] by the addition of a transport equation for the scalar mass fraction variance, is then applied in one-dimensional simulations of the reacting mixing layer under consideration. Excellent agreement is obtained between LES and RANS in total TN neutron production when fluctuations in reaction cross-section can be neglected.

Fast electron transport has been studied in cold solid density CH, cold CH foam ($200\mathrm{mg}/{\mathrm{cm}}^3$), and CH plasma (40 eV $30\mathrm{mg}/{\mathrm{cm}}^3$) targets—the latter created by shocking the CH foam with a 1.2 kJ long pulse laser and allowing it to expand. The fast electrons were produced using the OMEGA EP laser pulse (800 J, 8 ps) incident on a Au flat target. With the CH plasma, the fluence of fast electrons reaching a Cu foil at the far side of the transport was reduced significantly ($25\times$ weaker peak $K\alpha$ emission). Particle-in-cell simulations using the osiris code modeled fast electron transport in the unshocked foam and plasma cases assuming fixed ionization and including source generation, transport in Au and CH layers, Coulomb collisions, and refluxing. Simulations indicate two main mechanisms which alter electron energy transport through the target between the foam and plasma cases, both due to the magnetic field: a collimating field in the CH region, caused by the resistivity of the return current and more prevalent in the foam; and an insulating field at the Au-CH interface, present only with the plasma.

Pore-scale simulation is an essential tool to understand complex physical process in many environmental problems. However, structural heterogeneity and data scarcity render the porous medium, and in turn its macroscopic properties, uncertain. Meanwhile, direct numerical simulation of the medium at the fine scale often incurs high computational cost, which further limits efforts to quantify the parametric uncertainty over those macroscopic properties. To address this challenge, we propose a framework to compute the probabilistic density function (PDF) of the macroscopic property based on the generalized polynomial chaos expansion method and the Minkowski functionals. To illustrate the effectiveness of our approach, we conduct numerical experiments for one macroscopic property, namely the permeability, and we compare its PDF with that obtained from Monte Carlo simulations. Both two- and three-dimensional cases show that our framework requires much fewer realizations while maintaining the desired accuracy.

Classical molecular dynamics simulations of hydrogen plasmas have been performed with an emphasis on the analysis of the equilibration process. The theoretical basis of the simulation model as well as numerically relevant aspects, such as the proper choice and definition of simulation units, are discussed in detail, thus proving a thorough implementation of the computer simulation technique. Because of the lack of experimental data, molecular dynamics simulations are often considered as idealized computational experiments for benchmarking of theoretical models. However, these simulations are certainly challenging and consequently a validation procedure is also demanded. In this work we develop an analytical statistical equilibrium model for computational validity assessment of plasma particle dynamics simulations. Remarkable agreement between model and molecular dynamics results including a classical treatment of the ionization-recombination mechanism is obtained for a wide range of plasma coupling parameter values. Furthermore, the analytical model provides guidance to securely terminate simulation runs once the equilibrium stage has been reached, which in turn gives confidence in the statistics that potentially may be extracted from time histories of simulated physical quantities.

We demonstrate the possibility to reproduce the experimental evolution of an interface, here a flame front, through the trajectory of a few poles whose position in the complex plane expresses the interface shape. These poles are analytical solutions of the Sivashinsky equation and they evolve according to an ordinary differential equation. The direct comparison with experimental flame fronts propagating in a quasi-two-dimensional configuration is made at the nonlinear but deterministic stages of the front dynamics, reproducing a cell creation and fusion process. At later times, when the front is sensitive to noise as in the Kardar-Parisi-Zhang equation, we demonstrate that the cell size distribution is still ruled by the pole attractive nature.

The thermodynamic uncertainty relation sets the minimal bound of the cost-precision tradeoff relation for dissipative processes. Examining the dynamics of an internally coupled system that is driven by a constant thermodynamic force, we, however, find that the tradeoff relation of a subsystem is not constrained by the minimal bound of conventional uncertainty relation. We made our point explicit by using an exactly solvable model of interacting oscillators. As the number ($N$) of interacting oscillators increases, the uncertainty bound of individual oscillators is reduced to $2k_{B}T/N$ upon full synchronization under strong coupling. The cost-precision tradeoff for interacting subsystems is particularly relevant for subcellular processes where interactions among multiple energy-expending components lead to emergence of collective dynamics.

We derive universal entanglement entropy and Schmidt eigenvalue behaviors for the eigenstates of two quantum chaotic systems coupled with a weak interaction. The progression from a lack of entanglement in the noninteracting limit to the entanglement expected of fully randomized states in the opposite limit is governed by the single scaling transition parameter $\mathrm{\Lambda }$. The behaviors apply equally well to few- and many-body systems, e.g., interacting particles in quantum dots, spin chains, coupled quantum maps, and Floquet systems, as long as their subsystems are quantum chaotic and not localized in some manner. To calculate the generalized moments of the Schmidt eigenvalues in the perturbative regime, a regularized theory is applied, whose leading-order behaviors depend on $\sqrt{\mathrm{\Lambda }}$. The marginal case of the $1/2$ moment, which is related to the distance to the closest maximally entangled state, is an exception having a $\sqrt{\mathrm{\Lambda }}ln\mathrm{\Lambda }$ leading order and a logarithmic dependence on subsystem size. A recursive embedding of the regularized perturbation theory gives a simple exponential behavior for the von Neumann entropy and the Havrda-Charvát-Tsallis entropies for increasing interaction strength, demonstrating a universal transition to nearly maximal entanglement. Moreover, the full probability densities of the Schmidt eigenvalues, i.e., the entanglement spectrum, show a transition from power laws and Lévy distribution in the weakly interacting regime to random matrix results for the strongly interacting regime. The predicted behaviors are tested on a pair of weakly interacting kicked rotors, which follow the universal behaviors extremely well.

Graphs of the most probable transitions for a transition probability matrix, $e^{\tau K}$, i.e., the time evolution matrix of the transition rate matrix $K$ over a finite time interval $\tau$, are considered. We study how the graph structures of the most probable transitions change as functions of $\tau$, thereby elucidating that a kinetic threshold ${\tau }_g$ for the graph structures exists. Namely, for $\tau <{\tau }_g$, the number of connected graph components is constant. In contrast, for $\tau \ge {\tau }_g$, recombinations of most probable transitions over the connected graph components occur multiple times, which introduce drastic changes into the graph structures. Using an illustrative multifunnel model, we show that the recombination patterns indicate the existence of the eigenvalues and eigenvectors of the slowest relaxation modes quite precisely. We also devise an evaluation formula that enables us to correct the values of eigenvalues with high accuracy from the data of merging processes. We show that the graph-based method is valid for a wide range of kinetic systems with degenerate, as well as nondegenerate, relaxation rates.

Synchronization in time-varying complex dynamical systems has been explored in a variety of different coupling topologies during the last two decades. In most of the previous cases, the basic time-varying coupling topologies were considered to be a single interaction between the nodes or in a monolayer configuration, although in many real situations the types of interactions are more than one or in the form of multilayer. In this work, we study the synchronization in multiplex neuronal network, which evolves with time, and each layer consists of more than one interaction function. Specifically, we consider a neuronal hypernetwork at each layer in which neurons are communicated with each other via electrical and chemical synapses simultaneously and independently. The network corresponding to the electrical gap junctional coupling form a small-world network while the connection associated with the chemical synaptic interaction forms a unidirectional random network. Then intralayer connections are allowed to switch stochastically over time with a characteristic rewiring frequency, whereas interlayer connections via electrical synapses are time invariant. We explore the intralayer and interlayer neuronal synchrony in such network and analytically derive the necessary stability conditions for synchrony using master stability function approach, and excellently match with our numerical findings. Interestingly, we find that the higher frequency of switching links in the intralayer enhances both intralayer and interlayer synchrony and conferring larger windows of synchrony. We also analyze the robustness of these synchronization states with respect to initial conditions using the basin stability framework. Furthermore we find that rapidly changing networks take much less time to reach synchronization state. Lastly, we inspect the dynamical robustness of interlayer synchronization against stochastic demultiplexing of each replica, with analytical justification.

The dynamics of electron injection in the direct laser acceleration (DLA) regime is investigated using three-dimensional particle-in-cell simulations and theoretical analyses. It is shown that, as an ultraintense laser pulse propagates into a near-critical density or relativistically transparent plasma, the longitudinal charge-separation electric field excites ion density spikes, which modulate the local electric field. The corresponding electric field acts as a series of potential wells to guide the electrons on the edge of the plasma channel into its center where the DLA can take place. On the other hand, an azimuthal magnetic field is self-generated, and it can deflect the injected electrons from the intense laser-field region. Understanding these physical processes paves the way for further optimizing the properties of direct-laser accelerated electron beams and the associated x- and $\gamma$-ray sources.