Strong-field phenomena in solids exhibit extreme high-order nonlinear optical effects, which have triggered many theoretical and experimental investigations. However, there is still a lack of highly efficient numerical tools to simulate the relevant phenomena. In this paper, a versatile multiscale numerical tool set is developed for studying high-order nonlinear optical effects in solids, generated by ultrafast strong laser pulses. This tool is based on the tight-binding model approximation of the crystal structure, the related parameters of which are obtained from the density functional theory calculations. And the nonlinear effects are explored by solving the Maxwell equations coupled with the semiconductor Bloch equations. Our numerical tool can provide not only basic electronic structures and optical responses of the crystal, but also the real-time evolution of the macroscopic electromagnetic fields and the current density. The high-performance parallel computing and the interpolation method in our tool make it possible to study the strong-field nonlinear responses and propagation effects on a large spatial and temporal scale. Finally, three theoretical or experimental results published recently are satisfactorily reproduced, showing a good performance of the current toolbox.

Recent advances in experimental control of colloidal systems have spurred a revolution in the production of mesoscale thermodynamic devices. Functional “textbook” engines, such as the Stirling and Carnot cycles, have been produced in colloidal systems where they operate far from equilibrium. Simultaneously, significant theoretical advances have been made in the design and analysis of such devices. Here, we use methods from thermodynamic geometry to characterize the optimal finite-time nonequilibrium cyclic operation of the parametric harmonic oscillator in contact with a time-varying heat bath with particular focus on the Brownian Carnot cycle. We derive the optimally parametrized Carnot cycle, along with two other new cycles and compare their dissipated energy, efficiency, and steady-state power production against each other and a previously tested experimental protocol for the Carnot cycle. We demonstrate a 20% improvement in dissipated energy over previous experimentally tested protocols and a $\sim 50\%$ improvement under other conditions for one of our engines, whereas our final engine is more efficient and powerful than the others we considered. Our results provide the means for experimentally realizing optimal mesoscale heat engines.

Dependency between a response variable and the explanatory variables is a relationship of universal concern in various real-world problems. Multivariate linear regression (MLR) is a well-known method to focus on this issue. However, it is limited to dealing with stationary variables. In this work, we develop a MLR framework based on detrending moving average (DMA) analysis to reveal the actual dependency among variables with nonstationary measures. The DMA-based MLR can generate multiscale regression coefficients, which characterize different dependent behavior at different timescales. Artificial tests show that the DMA-MLR model can successfully resist the impact of trends on the studied series and produce more accurate regression coefficients with multiscale. Furthermore, some scale-dependent statistics are developed to deduce some important relationships in three typical DMA-based MLR models, which help us to deeply understand the DMA-MLR models in theory. The application of the proposed DMA-MLR framework to Beijing's air quality index system demonstrates that fine particulate matter with diameter $\le 2.5\mu \text{m}$ $\left({\mathrm{PM}}_{2.5}\right)$ is the dominant pollutant affecting the air quality of Beijing in recent years.

We perform a systematic analysis of the quality of fit of the stochastic block model (SBM) for 275 empirical networks spanning a wide range of domains and orders of size magnitude. We employ posterior predictive model checking as a criterion to assess the quality of fit, which involves comparing networks generated by the inferred model with the empirical network, according to a set of network descriptors. We observe that the SBM is capable of providing an accurate description for the majority of networks considered, but falls short of saturating all modeling requirements. In particular, networks possessing a large diameter and slow-mixing random walks tend to be badly described by the SBM. However, contrary to what is often assumed, networks with a high abundance of triangles can be well described by the SBM in many cases. We demonstrate that simple network descriptors can be used to evaluate whether or not the SBM can provide a sufficiently accurate representation, potentially pointing to possible model extensions that can systematically improve the expressiveness of this class of models.

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

We perform a bifurcation analysis of the steady states of Rayleigh-Bénard convection with no-slip boundary conditions in two dimensions using a numerical method called deflated continuation. By combining this method with an initialization strategy based on the eigenmodes of the conducting state, we are able to discover multiple solutions to this nonlinear problem, including disconnected branches of the bifurcation diagram, without the need for any prior knowledge of the solutions. One of the disconnected branches we find contains an $\mathsf{S}$-shaped curve with hysteresis, which is the origin of a flow pattern that may be related to the dynamics of flow reversals in the turbulent regime. Linear stability analysis is also performed to analyze the steady and unsteady regimes of the solutions in the parameter space and to characterise the type of instabilities.

We analyze the performance of slowly driven meso- and microscale refrigerators and heat engines that operate between two thermal baths with a small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasistatic limit if the driving protocols are suitably optimized and the temperature difference between the baths goes to zero with the driving frequency. These results hold under generic conditions for any thermodynamically consistent dynamics admitting a well-defined adiabatic-response regime and a generalized Onsager symmetry. For illustration, we work out models of a qubit-refrigerator and a coherent charge pump operating as a cooling device.

Semiclassical methods are extremely important in the subjects of wave-packet and coherent-state dynamics. Unfortunately, these essentially saddle-point approximations are considered nearly impossible to carry out in detail for systems with multiple degrees of freedom due to the difficulties of solving the resulting two-point boundary-value problems. However, recent developments have extended the applicability to a broader range of systems and circumstances. The most important advances are first to generate a set of real reference trajectories using appropriately reduced dimensional spaces of initial conditions, and second to feed that set into a Newton-Raphson search scheme to locate the exposed complex saddle trajectories. The arguments for this approach were based mostly on intuition and numerical verification. In this paper, the methods are put on a firmer theoretical foundation and then extended to incorporate saddles hidden from Newton-Raphson searches initiated with real trajectories. This hidden class of saddles is relevant to tunneling-type processes, but a hidden saddle can sometimes contribute just as much as or more than an exposed one. The distinctions between hidden and exposed saddles clarifies the interpretation of what constitutes tunneling for wave packets and coherent states in the time domain.

Saddle-point approximations, extremely important in a wide variety of physical contexts, require the analytical continuation of canonically conjugate quantities to complex variables in quantum mechanics. An important component of this approximation's implementation is arriving at the phase correction attributable to caustics, which involves determinantal prefactors. The common prescription of using the inverse of half a certain determinant's total accumulated phase sometimes leads to sign errors. The root of this problem is traced to the zeros of the determinants at complex times crossing the real time axis. Deformed complex time contours around the zeros can repair the sign errors that sometimes occur, but a much more practical way is given that links saddles back to associated real trajectories and avoids the necessity of locating the complex time zeros of the determinants.

We study a dimer in a periodic potential well, which is a conservative but nonintegrable system. This seemingly simple system exhibits a surprisingly rich dynamics. Using a systematic asymptotic analysis, we demonstrate that the translation mode of the dimer (center of mass motion) may induce a parametric resonance of the oscillatory mode. No external forcing occurs, thus this system belongs to the class of autoparametric systems. When the dimer energy is such that both particles are trapped in neighboring potential wells, we derive the relevant amplitude equations for the eigenmodes (center of mass motion and relative motion) and show that they are integrable. In the opposite limit, when the dimer slides along the external potential so that the center of mass motion is basically a translation, we also exhibit autoparametric amplification of the relative motion. In both cases our calculations provide reliable estimates of the relevant parameters for the autoparametric resonance to appear. Moreover, the comparison between the numerical integration of the actual system and the asymptotic analysis evidences an excellent quantitative agreement.

An analytically tractable generalization of the $N$-person snowdrift (NSG) game that illustrates how cooperation can be enhanced is proposed and studied. The number of players competing within a NSG varies from one time step to another. Exact equations governing the frequency of cooperation $f_c\left(r\right)$ as a function of the cost-to-benefit ratio $r$ within an imitation strategy updating scheme are presented. For group sizes $g$ uniformly distributed within the range $g\in [1,g_m]$, an analytic formula for the critical value $r_c\left(g_m\right)$, below which the system evolves into a totally cooperative (AllC) state, is derived. In contrast, a fixed group size NSG does not support an AllC state. The result $r_c\left(g_m\right)$ requires the presence of sole-player groups and involves the inverse of the harmonic numbers and, more generally, the inverse first moment of the group size distribution. For $r>r_c\left(g_m\right)$, the equation that determines the dynamical mixed states $f_c\left(r\right)$ is given, with exact solutions existing for $g_m\le 5$. The exact treatment allows the study of the phase boundary between the AllC state and the mixed states. The analytic results are checked against simulation results and exact agreements are demonstrated. The analytic form of the critical $r_c\left(g_m\right)$ illustrates the necessity of having groups of a sole player in the evolutionary process. This result is supported by simulations with group sizes excluding the sole groups for which no AllC state emerges. A physically transparent picture of the importance of the sole players in inducing an AllC state is further presented based on the last surviving pattern before the AllC state is attained. The exact expression $r_c\left(g_m\right)$ turns out to remain valid for nonuniform group-size distributions. Our analytical tractable generalization, therefore, sheds light on how a competing environment with variable group sizes could enhance cooperation and induce an AllC state.

Percolation on networks is a common framework to model a wide range of processes, from cascading failures to epidemic spreading. Standard percolation assumes short-range interactions, implying that nodes can merge into clusters only if they are nearest neighbors. Cumulative merging percolation (CMP) is a percolation process that assumes long-range interactions such that nodes can merge into clusters even if they are topologically distant. Hence, in CMP clusters do not coincide with the topologically connected components of the network. Previous work has shown that a specific formulation of CMP features peculiar mechanisms for the formation of the giant cluster and allows one to model different network dynamics such as recurrent epidemic processes. Here we develop a more general formulation of CMP in terms of the functional form of the cluster interaction range, showing an even richer phase transition scenario with competition of different mechanisms resulting in crossover phenomena. Our analytic predictions are confirmed by numerical simulations.

Systems with multistability are characterized by exhibiting complex nonlinear waves between equilibria. Experimentally, near the smectic-$A$ to chiral nematic transition in a liquid crystal mixture cell with planar anchoring, we observe finger fronts emerge in the smectic-$A$ phase when applying an electric field, a reorientation transition. Finger fronts propagate in the direction orthogonal to the anchoring. Colorimetry characterization allows us to describe the molecular reorientation transition and front dynamics. We reveal that the reorientation transition is of the first-order type and determine their critical points. The front speed is determined as a function of the applied voltage. Theoretically, based on a prototype model of liquid crystal transitions, we qualitatively describe the experimental observations. We have analytically determined the bifurcation diagram and the propagation speeds of finger fronts, finding a fair agreement with the experimental observations.

In the field of liquid crystals, it is well known that rodlike molecules interacting via long-range attractive interactions or short-range repulsive potentials can exhibit orientational order. In this work, we are interested in what would happen to systems of rodlike particles interacting via a long-range repulsive potential. In our model, each particle consists of a number of point dipoles uniformly distributed along the particle length, with all dipoles pointing along the $z$ axis so that the rodlike particles repel each other when they lie in the $x\text{−}y$ plane. Dipoles from different particles interact via an $r^{-3}$ potential, where $r$ is the distance between the dipoles. We have considered two model systems, each with $N$ particles in a unit cell with periodic boundary conditions. In the first, particle centers are fixed on a square or triangular lattice but they are free to rotate. In the second, particles are free to translate as well as rotate in cells with variable shapes. Here they self-assemble to form configurations where the stress tensors are isotropic. Our numerical results show that, at low temperatures, the particles tend to form stripes with alternating orientations, resembling herringbone patterns or the anticlinic Sm-${\mathrm{C}}_A$ liquid crystal phase.

Fundamental properties of an interface evolving on a domain of size $L$, such as its height distribution (HD) and two-point covariances, are known to assume universal but different forms depending on whether $L$ is fixed (flat geometry) or expands linearly in time (radial growth). The interesting situation where $L$ varies nonlinearly, however, is far less explored and it has never been tackled for two-dimensional (2D) interfaces. Here, we study discrete Kardar-Parisi-Zhang (KPZ) growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L=L_0+\omega t^{\gamma }$. Our numerical simulations reveal that the competition between the substrate expansion and the increase of the correlation length parallel to the substrate, $\xi \simeq c{t}^{1/z}$, gives rise to a number of interesting results. For instance, when $\gamma <1/z$ the interface becomes fully correlated, but its squared roughness, $W_2$, keeps increasing as $W_2\sim t^{2\alpha \gamma }$, as previously observed for one-dimensional (1D) systems. A careful analysis of this scaling, accounting for an intrinsic width on it, allows us to estimate the roughness exponent of the 2D KPZ class as $\alpha =0.387\left(1\right)$, which is very accurate and robust, once it was obtained averaging the exponents for different models and growth conditions (i.e., for various ${\gamma }^{\prime }\mathrm{s}$ and ${\omega }^{\prime }\mathrm{s}$). In this correlated regime, the HDs and covariances are consistent with those expected for the steady-state regime of the 2D KPZ class for flat geometry. For $\gamma \approx 1/z$, we find a family of distributions and covariances continuously interpolating between those for the steady-state and the growth regime of radial KPZ interfaces, as the ratio $\omega /c$ augments. When $\gamma >1/z$ the system stays forever in the growth regime and the HDs always converge to the same asymptotic distribution, which is the one for the radial case. The spatial covariances, on the other hand, are $(\gamma ,\omega )$-dependent, showing a trend towards the covariance of a random deposition in enlarging substrates as the expansion rate increases. These results considerably generalize our understanding of the height fluctuations in 2D KPZ systems, revealing a scenario very similar to the one previously found in the 1D case.

Various kinds of heterogeneity in solids, including atomistic discreteness, affect the fracture strength as well as the failure dynamics remarkably. Here we study the effects of an initial crack in a discrete model for fracture in heterogeneous materials, known as the fiber bundle model. We find three distinct regimes for fracture dynamics depending on the initial crack size. If the initial crack is smaller than a certain value, it does not affect the rupture dynamics and the critical stress, while for a larger initial crack, the growth of the crack leads to breakdown of the entire system, and the critical stress depends on the crack size in a power-law manner with a nontrivial exponent. The exponent, as well as the limiting crack size, depend on the strength of heterogeneity and the range of stress relaxation in the system.

We propose a setup for positron acceleration consisting of an electron driver and a laser pulse creating a twofold plasma column structure. The resulting wakefield is capable of accelerating positron bunches over long distances even when the evolution of the driver is considered. The scheme is studied by means of particle-in-cell simulations. Further, the analytical expression for the accelerating and focusing fields are obtained, showing the equilibrium lines along which the witness bunch is accelerated.

Long-lived mode (LLM) in rotating plasmas is studied by using a alternative dispersion relation. This work offers a theoretical interpretation of LLM observed in experiments [Heidbrink, Phys. Rev. Lett. 57, 835 (1986); Chapman, Nucl. Fusion 50, 045007 (2010)]. It is found that in rotating plasmas, LLM can transform from the fishbone mode. The real frequency of LLM, independent of the characteristic frequency of energetic ions (EIs), is proportional to the on-axis rotation frequency of bulk plasma. The key conditions to cause transition between the fishbone mode and LLM are weak magnetic shear (for both monotonic and nonmonotonic safety factor profile) and plasma rotation. The fishbone mode can evolve into LLM only when rotating speed is bigger than a critical value in low shear plasmas. The critical beta of EIs to induce LLM is very low. LLM is nonresonantly excited by EIs, and the driving sources mainly come from plasma inertia.

Understanding the role of classical and quantum correlations in work extraction is a problem of fundamental importance in thermodynamics. We approach this problem by considering that, in closed quantum systems, the maximum cyclic work extractable is equal to the ergotropy. Thus, we aim to identify and investigate the contributions to the ergotropy coming from different kinds of initial correlations (total, classical, discord, and entanglement correlations). By doing so, we have introduced and studied quantifiers of correlations which are based on ergotropy. In particular, our results suggest that only discord correlations always give a positive contribution to work extraction, whereas total, classical, and entanglement correlations can reduce the work extraction.

Overparametrized deep neural networks trained by stochastic gradient descent are successful in performing many tasks of practical relevance. One aspect of overparametrization is the possibility that the student network has a larger expressivity than the data generating process. In the context of a student-teacher scenario, this corresponds to the so-called over-realizable case, where the student network has a larger number of hidden units than the teacher. For online learning of a two-layer soft committee machine in the over-realizable case, we present evidence that the approach to perfect learning occurs in a power-law fashion rather than exponentially as in the realizable case. All student nodes learn and replicate one of the teacher nodes if teacher and student outputs are suitably rescaled and if the numbers of student and teacher hidden units are commensurate.