We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot is reduces to the partition function of a $q$-state anisotropic Potts model with complex interactions, which is defined on a planar signed graph that corresponds to the knot. For any integer $q$, we cast this partition function into tensor network form, which inherits the interaction graph structure of the Potts model instance, and employ fast tensor network contraction protocols to obtain the exact tensor trace and thus the value of the Jones polynomial. By sampling random knots via a grid-walk procedure and computing the full tensor trace exactly, we demonstrate numerically that the Jones polynomial can be evaluated in time that scales subexponentially with the number of crossings in the typical case. This allows us to evaluate the Jones polynomial of knots that are too complex to be treated with other available methods. Our results establish tensor network methods as a practical tool for the study of knots.

The statistical properties of stochastic entropies in a discrete stationary one-dimensional Kardar-Parisi-Zhang system are numerically studied. As the usual time-independent solution of the associated Fokker-Planck equation is not strictly stationary, it is necessary to transform the current variables to other variables with zero spatial mean. We resorted to discrete representations in order to prove the statistical properties of entropies, and we performed a direct test of the fluctuation theorem. We discuss the connection between fluctuation theorems and the deviation from Gaussian distribution for the entropy.

Shell buckling is known for its extreme sensitivity to initial imperfections. It is generally understood that this sensitivity is caused by subcritical (unstable) buckling, whereby initial geometric imperfections rapidly erode the idealized buckling load of the perfect shell. However, it is less appreciated that subcriticality also creates a strong proclivity for spatially localized buckling modes. The spatial multiplicity of localizations implies a large set of possible trajectories to instability—also known as spatial chaos—with each trajectory affine to a particular imperfection. Using a toy model, namely a link system on a softening elastic foundation, we show that spatial chaos leads to a large spread in buckling loads even for seemingly indistinguishable random imperfections of equal amplitude. By imposing a dominant imperfection, the strong sensitivity to random imperfections is ameliorated. The ability to control the equilibrium trajectory to buckling via dominant imperfections or elastic tailoring creates interesting possibilities for designing imperfection-insensitive shells.

Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity appears in several systems, in static or quasistatic regimes, as well as close to transitions to absorbing states. Here, we show that a vibrated granular layer, at the critical point of the liquid-to-solid transition, displays dynamic hyperuniformity. Prior to the transition, patches of the solid phase form, with length scales and mean lifetimes that diverge critically at the transition point. When reducing the wave number, density fluctuations encounter increasingly more patches that block their propagation, resulting in a static structure factor that tends to zero for small wave numbers at the critical point, which is a signature of hyperuniformity. A simple model demonstrates that this coupling of a density field to a highly fluctuating scalar friction field gives rise to dynamic hyperuniform states. Finally, we show that the structure factor detects better the emergence of hyperuniformity, compared to the particle number variance.

Liquid flow in sessile evaporating droplets of ultrapure water typically results from two main contributions: a capillary flow pushing the liquid toward the contact line from the bulk and a thermal Marangoni flow pulling the drop free surface toward the summit. Current analytical and numerical models are in good qualitative agreement with experimental observations; however, they overestimate the interfacial velocity values by two to three orders of magnitude. This discrepancy is generally ascribed to contamination of the water samples with nonsoluble surfactants; however, an experimental confirmation of this assumption has not yet been provided. In this work, we show that a small “ionic contamination” can cause a significant effect in the flow pattern inside the droplet. To provide the proof, we compare the flow in evaporating droplets of ultrapure water with commercially available bottled water of different mineralization levels. Mineral waters are bottled at natural springs, are microbiologically pure, and contain only traces of minerals (as well as traces of other possible contaminants), and therefore one would expect a slower interfacial flow as the amount of “contaminants” increase. Surprisingly, our results show that the magnitude of the interfacial flow is practically the same for mineral waters with low content of minerals as that of ultrapure water. However, for waters with larger content of minerals, the interfacial flow tends to slow down due to the presence of ionic concentration gradients. Our results show a much more complex scenario than it has been typically suspected and therefore a deeper and more comprehensive analysis of the huge differences between numerical models and experiments is necessary.

We present a method of sound amplification and self-oscillation in high pressure partially ionized gas. Continuous microwaves incident on partially ionized gas may sustain and amplify an acoustic field if increased ionization during the sound field's adiabatic compression enhances rf power absorption. Amplifying sound in this way enables the generation of high amplitude sound in a cavity containing partially ionized gas without mechanical driving or precise knowledge of its resonance frequency. This method of amplification may open opportunities within thermoacoustics such as using three-dimensional geometries and volumetric gain mechanisms.

Beating of a broad laser reference beam with a quite general focused object beam inside a plasma volume generates a dynamic plasma hologram. Both beams may be of moderate intensity. The volume hologram can be read out by an ultraintense main beam (of similar structure as the reference beam) producing an object beam replica. For the latter, intensity in the focus may become extremely large. As an application, the possibility of a read-out focused Gaussian laser pulse with intensity of several ${10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ in focus is shown by three-dimensional numerical simulations. Besides the focusing possibility, the hologram may also act as a mode converter for high-intensity laser pulses. Generating a plasma hologram with a focused Laguerre-Gaussian object beam results in a staggered plasma density grating, allowing the production of high-intensity vortex beam replica.

Pattern interaction has so far been restricted to systems with relatively complex reaction schemes, such as activator-inhibitor systems, that lead to rich spatio-temporal dynamics. Surprisingly, a simple second-order chemical reaction is capable of generating similar complex phenomena, such as attractive or repulsive interaction modes between the localized reaction zones (or fronts). We illustrate the latter statement both analytically and numerically with two initially separated $A+B\to C$ reaction-diffusion fronts when the solution of $B$ is initially confined between two solutions of $A$. The nature of the front-front interaction changes from an attractive type to a repulsive one above a critical distance separating the two fronts initially. The complexity of the pattern dynamics emerges here due to finite-size effects. A scaling law relating the critical distance $d_c$ above which the repulsion occurs and kinetic parameters gives insights into (i) extracting those parameters from experiments for bimolecular reactions and (ii) the control strategy of periodic patterns.

It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths. It has been found that if a given state is kept at a sufficiently low temperature compared to the other, the system shows one kind of logic behavior (say, or). Interestingly, the system's response turns into the other kind (say, and) if the temperature of the initial low-temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value. However, the reliability of the second kind of logical response (and) is not as good as the first kind (or) and depends on the amplitude of the inputs. Still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low-temperature well.

We numerically demonstrate heat rectification for linear chains of ions in trap lattices with graded trapping frequencies, in contact with thermal baths implemented by optical molasses. To calculate the local temperatures and heat currents we find the stationary state by solving a system of algebraic equations. This approach is much faster than the usual method that integrates the dynamical equations of the system and averages over noise realizations.

A new model of search based on stochastic resetting is introduced, wherein rate of resets depends explicitly on time elapsed since the beginning of the process. It is shown that rate inversely proportional to time leads to paradoxical diffusion which mixes self-similarity and linear growth of the mean-square displacement with nonlocality and non-Gaussian propagator. It is argued that such resetting protocol offers a general and efficient search-boosting method that does not need to be optimized with respect to the scale of the underlying search problem (e.g., distance to the goal) and is not very sensitive to other search parameters. Both subdiffusive and superdiffusive regimes of the mean-squared displacement scaling are demonstrated with more general rate functions.

In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address these two questions, we investigate the response of complex networks of coupled oscillators to local perturbations. We quantify the magnitude of the resulting excursion away from the unperturbed synchronous state through quadratic performance measures in the angle or frequency deviations. We find that the most fragile oscillators in a given network are identified by centralities constructed from network resistance distances. Further defining the global robustness of the system from the average response over ensembles of homogeneously distributed perturbations, we find that it is given by a family of topological indices known as generalized Kirchhoff indices. Both resistance centralities and Kirchhoff indices are obtained from a spectral decomposition of the stability matrix of the unperturbed dynamics and can be expressed in terms of resistance distances. We investigate the properties of these topological indices in small-world and regular networks. In the case of oscillators with homogeneous inertia and damping coefficients, we find that inertia only has small effects on robustness of coupled oscillators. Numerical results illustrate the validity of the theory.

Collective cell migration underlies morphogenesis, tissue regeneration, and cancer progression. How the biomechanical coupling between epithelial cells triggers and coordinates the collective migration is an open question. Here, we develop a one-dimensional model for an epithelial monolayer which predicts that after the onset of migration at an open boundary, cells in the bulk of the epithelium are gradually recruited into outward-directed motility, exhibiting traveling-wave-like behavior. We find an exact formula for the speed of this motility wave proportional to the square root of the cells' contractility, which accounts for cortex tension and adhesion between adjacent cells.

We have studied the kinetics of the interaction between antimicrobial peptide nisin and Langmuir monolayers of phospholipids DPPC and DPPG at the air-water interface using the surface manometry technique. The charge on the nisin and the lipid molecules is controlled by varying the pH of the subphase, and the interactions between them are studied by measuring the surface pressure of the lipid monolayer as a function of time after injecting the nisin in the subphase. A model based on the diffusion of particles under the influence of a constant force is developed to obtain an analytical expression for surface pressure as a function of time. The expression was found to fit well with the experimental data. The average hydrodynamic radius and the translational diffusion constant of the nisin molecules are calculated from the fit parameters for the different subphase pH solutions.

Salt crusts forming at the surface of a porous medium can dynamically evolve with crust displacements leading to the formations of domes and blisters or simply to the upward migration of the crust. However, the mechanisms explaining the displacements are unclear. It has been conjectured that they could be related to dissolution-precipitation phenomena and/or to mechanical effects associated with the concept of crystallization pressure. We present a simple experiment where the crust upward migration is significant and can be entirely explained from the consideration of dissolution-precipitation phenomena. Equations governing the crust displacement are derived, leading to quite good agreement with the experimental results.

In the present study, three different electronic state-to-state methods are proposed to analyze nonequilibrium air plasma flows behind a strong shock wave. In the first approach representing the conventional method, a two-temperature model combined with the electronic quasi-steady-state assumption is adopted. In the second and the third methods, atomic and molecular electronic master equations are coupled with a conservation equation to describe the electronic state-to-state kinetics. State-of-the-art electronic transition rates for atmospheric gas species are compiled with comparisons of existing data. A prediction of the measured nonequilibrium radiation is made for the flow conditions of recent electric-arc shock tube experiments. In a comparison with the measured spectrum, the present electronic master equation coupling methods are more accurate than the conventional approach when used to estimate the initial rising rate and peak value of the diatomic intensity and small amounts of atomic radiation when the diatomic nonequilibrium condition is dominant. Moreover, the spatial distributions of the intensity and electron number density are more accurately predicted by the present methods when the flow fields are dominated by atomic nonequilibrium.

Numerical simulations and finite-size scaling analysis have been carried out to study the problem of inverse site percolation by the removal of $k\times k$ square tiles ($k^2$-mers) from square lattices. The process starts with an initial configuration, where all lattice sites are occupied and, obviously, the opposite sides of the lattice are connected by occupied sites. Then the system is diluted by removing $k^2$-mers of occupied sites from the lattice following a random sequential adsorption mechanism. The process finishes when the jamming state is reached and no more objects can be removed due to the absence of occupied sites clusters of appropriate size and shape. The central idea of this paper is based on finding the maximum concentration of occupied sites, $p_{c,k}$, for which the connectivity disappears. This particular value of the concentration is called the inverse percolation threshold and determines a well-defined geometrical phase transition in the system. The results obtained for $p_{c,k}$ show that the inverse percolation threshold is a decreasing function of $k$ in the range $1\le k\le 4$. For $k\ge 5$, all jammed configurations are percolating states, and consequently, there is no nonpercolating phase. In other words, the lattice remains connected even when the highest allowed concentration of removed sites is reached. The jamming exponent ${\nu }_j$ was measured, being ${\nu }_j=1$ regardless of the size $k$ considered. In addition, the accurate determination of the critical exponents $\nu$, $\beta$, and $\gamma$ reveals that the percolation phase transition involved in the system, which occurs for $k$ varying between one and four, has the same universality class as the standard percolation problem.

We study the localization properties, energy spectra, and coin-position entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is described by spatially dependent quantum coins distributed on the lattice, whose distribution is neither periodic (Bloch-like) nor random (Anderson-like). Within transport properties we identified delocalized and localized quantum walks mediated by a proper adjusting of aperiodic parameter. Both scenarios are studied by exploring typical quantities (inverse participation ratio, survival probability, and wave packet width), as well as the energy spectra of an associated effective Hamiltonian. By using the energy spectra analysis, we show that the early stage the inhomogeneity leads to a vanishing gap between two main bands, which justifies the predominantly delocalized character observed for $\nu <0.5$. With increase of $\nu$ arise gaps and flat bands on the energy spectra, which corroborates the suppression of transport detected for $\nu >0.5$. For $\nu$ high enough, we observe an energy spectra, which resembles that described by the one-dimensional Anderson model. Within coin-position entanglement, we show many settings in which an enhancement in the ability to entangle is observed. This behavior brings new information about the role played by aperiodicity on the coin-position entanglement for static inhomogeneous systems, reported before as almost always reducing the entanglement when comparing with the homogeneous case. We extend the analysis in order to show that systems with static inhomogeneity are able to exhibit asymptotic limit of entanglement.

With the advent of quantum technologies comes the requirement of building quantum components able to store energy to be used whenever necessary, i.e., quantum batteries. In this paper we exploit an adiabatic protocol to ensure a stable charged state of a three-level quantum battery which allows one to avoid the spontaneous discharging regime. We study the effects of the most relevant sources of noise on the charging process, and, as an experimental proposal, we discuss superconducting transmon qubits. In addition we study the self-discharging of our quantum battery where it is shown that spectrum engineering can be used to delay such phenomena.