To reveal the role of the quantumness in the Otto cycle and to discuss the validity of the thermodynamic uncertainty relation (TUR) in the cycle, we study the quantum Otto cycle and its classical counterpart. In particular, we calculate exactly the mean values and relative error of thermodynamic quantities. In the quasistatic limit, quantumness reduces the productivity and precision of the Otto cycle compared to that in the absence of quantumness, whereas in the finite-time mode, it can increase the cycle's productivity and precision. Interestingly, as the strength (heat conductance) between the system and the bath increases, the precision of the quantum Otto cycle overtakes that of the classical one. Testing the conventional TUR of the Otto cycle, in the region where the entropy production is large enough, we find a tighter bound than that of the conventional TUR. However, in the finite-time mode, both quantum and classical Otto cycles violate the conventional TUR in the region where the entropy production is small. This implies that another modified TUR is required to cover the finite-time Otto cycle. Finally, we discuss the possible origin of this violation in terms of the uncertainty products of the thermodynamic quantities and the relative error near resonance conditions.

We study the orientational order of an immobile fish school. Starting from the second Newton law, we show that the inertial dynamics of orientations is ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of alignment between neighboring fish in a shoal—a dynamics already used in the literature for mobile fish schools. First, in a fluid at rest, we calculate the global polarization (i.e., the mean orientation of the fish), which decreases rapidly as a function of noise. We show that the faster a fish is able to reorient itself the more the school can afford to reorder itself for important noise values. Second, in the presence of a stream, each fish tends to orient itself and swims against the flow: so-called rheotaxis. So, even in the presence of a flow, it results in an immobile fish school. By adding an individual rheotaxis effect to alignment interaction between fish, we show that in a noisy environment individual rheotaxis is enhanced by alignment interactions between fish.

The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolution of the infiltration. We study this problem in two- and three-dimensional lattices with randomly distributed porous sites at the critical percolation thresholds and with a border in contact with a reservoir of an aggressive solute. The solute infiltrates that medium by diffusion and the reactions with the impermeable sites produce new porous sites with a probability $r$, which is proportional to the ratio of reaction and diffusion rates at the scale of a lattice site. Numerical simulations for $r\ll 1$ show initial subdiffusive scaling and long time Fickean scaling of the infiltrated volumes or areas, but with an intermediate regime with time increasing rates of infiltration and reaction. The anomalous exponent of the initial regime agrees with a relation previously applied to infinitely ramified fractals. We develop a scaling approach that explains the subsequent time increase of the infiltration rate, the dependence of this rate on $r$, and the crossover to the Fickean regime. The exponents of the scaling relations depend on the fractal dimensions of the critical percolation clusters and on the dimensions of random walks in those clusters. The time increase of the reaction rate is also justified by that reasoning. As $r$ decreases, there is an increase in the number of time decades of the intermediate regime, which suggests that the time increasing rates are more likely to be observed is slowly reacting systems.

Networks of coupled oscillators show a wealth of fascinating dynamics and are capable of storing and processing information. In biological and social networks, the coupling is often asymmetric. We use the chirality of rotating spiral waves to introduce this asymmetry in an excitable reaction-diffusion model. The individual vortices are pinned to unexcitable disks and arranged at a constant spacing $L$ along straight lines or simple geometric patterns. In the case of periodic boundaries or pinning disks arranged along the edge of a closed shape, small $L$ values lead to synchronization via repeated wave collisions. The rate of synchronization as a function of $L$ shows a single maximum and is determined by the dispersion behavior of a continuous wave train traveling along the system boundary. For finite systems, spirals are affected by their upstream neighbor, and a single dominant spiral exists along each chain. Specific initial conditions can decouple neighboring vortices even for small $L$ values. We also present a time-delay differential equation that reproduces the phase dynamics in periodic systems.

We propose a computationally simple and efficient network-based method for approximating topological entropy of low-dimensional chaotic systems. This approach relies on the notion of an ordinal partition. The proposed methodology is compared to the three existing techniques based on counting ordinal patterns—all of which derive from collecting statistics about the symbolic itinerary—namely (i) the gradient of the logarithm of the number of observed patterns as a function of the pattern length, (ii) direct application of the definition of topological permutation entropy, and (iii) the outgrowth ratio of patterns of increasing length. In contrast to these alternatives, our method involves the construction of a sequence of complex networks that constitute stochastic approximations of the underlying dynamics on an increasingly finer partition. An ordinal partition network can be computed using any scalar observable generated by multidimensional ergodic systems, provided the measurement function comprises a monotonic transformation if nonlinear. Numerical experiments on an ensemble of systems demonstrate that the logarithm of the spectral radius of the connectivity matrix produces significantly more accurate approximations than existing alternatives—despite practical constraints dictating the selection of low finite values for the pattern length.

The final size reached by an epidemic, measured in terms of the total number of fatalities, is an extremely relevant quantity. It has been recently claimed that the size distribution of major epidemics in human history is “strongly fat-tailed,” i.e., a power law asymptotically, which has important consequences for risk management. From the point of view of statistical physics and complex-systems modeling this is not an unexpected outcome, nevertheless, strong empirical evidence is also necessary to support such a claim. Reanalyzing previous data, we find that, although the fatality distribution may be compatible with a power-law tail, these results are not conclusive, and other distributions, not fat-tailed, could explain the data equally well. As an example, simulation of a log-normally distributed random variable provides synthetic data whose statistics are undistinguishable from the statistics of the empirical data. Theoretical reasons justifying a power-law tail as well as limitations in the current available data are also discussed.

Graph embedding methods are becoming increasingly popular in the machine learning community, where they are widely used for tasks such as node classification and link prediction. Embedding graphs in geometric spaces should aid the identification of network communities as well because nodes in the same community should be projected close to each other in the geometric space, where they can be detected via standard data clustering algorithms. In this paper, we test the ability of several graph embedding techniques to detect communities on benchmark graphs. We compare their performance against that of traditional community detection algorithms. We find that the performance is comparable, if the parameters of the embedding techniques are suitably chosen. However, the optimal parameter set varies with the specific features of the benchmark graphs, like their size, whereas popular community detection algorithms do not require any parameter. So, it is not possible to indicate beforehand good parameter sets for the analysis of real networks. This finding, along with the high computational cost of embedding a network and grouping the points, suggests that, for community detection, current embedding techniques do not represent an improvement over network clustering algorithms.

Mushroom species display distinctive morphogenetic features. For example, Amanita muscaria and Mycena chlorophos grow in a similar manner, their caps expanding outward quickly and then turning upward. However, only the latter finally develops a central depression in the cap. Here we use a mathematical approach unraveling the interplay between physics and biology driving the emergence of these two different morphologies. The proposed growth elastic model is solved analytically, mapping their shape evolution over time. Even if biological processes in both species make their caps grow turning upward, different physical factors result in different shapes. In fact, we show how for the relatively tall and big A. muscaria a central depression may be incompatible with the physical need to maintain stability against the wind. In contrast, the relatively short and small M. chlorophos is elastically stable with respect to environmental perturbations; thus, it may physically select a central depression to maximize the cap volume and the spore exposure. This work gives fully explicit analytic solutions highlighting the effect of the growth parameters on the morphological evolution, providing useful insights for novel bio-inspired material design.

Solutions of microgels have been widely used as model systems to gain insight into atomic condensed matter and complex fluids. We explore the thermodynamic phase behavior of hollow microgels, which are distinguished from conventional colloids by a central cavity. Small-angle neutron and x-ray scattering are used to probe hollow microgels in crowded environments. These measurements reveal an interplay among deswelling, interpenetration, and faceting and an unusual absence of crystals. Monte Carlo simulations of model systems confirm that, due to the cavity, solutions of hollow microgels more readily form a supercooled liquid than for microgels with a cross-linked core.

We extend the replica liquid theory in order to describe the multiple glass transitions of binary mixtures with large size disparities, by taking into account the two-step replica symmetry breaking (2RSB). We determine the glass phase diagram of the mixture of large and small particles in the large-dimension limit where the mean-field theory becomes exact. When the size ratio of particles is beyond a critical value, the theory predicts three distinct glass phases; (i) the one-step replica symmetery breaking (1RSB) double glass where both components vitrify simultaneously, (ii) the 1RSB single glass where only large particles are frozen while small particles remain mobile, and (iii) a glass phase called the 2RSB double glass where both components vitrify simultaneously but with an energy landscape topography distinct from the 1RSB double glass.

The linear stability of a jet propagating under an electric field is analyzed under nonisothermal conditions. The electrified jet of a Newtonian fluid is modeled as a slender filament, and the leaky dielectric model is used to account for the Maxwell stresses within the fluid. The convective heat transfer from high-temperature jet to the surroundings results in formation of thicker fibers owing to increased viscosity upon cooling. The jet exhibiting substantial thinning under the action of tangential electric field is examined for stability toward axisymmetric nonperiodic disturbances. This is in contrast to most prior studies which analyzed the stability of a cylindrical jet of uniform radius without thinning under extensional flow by examining only periodic disturbances. Two case studies of reference fluids differing in viscosity and electrical properties are examined. The spectrum of discrete growth rates for axisymmetric disturbances reveal qualitatively distinct instabilities for the two fluids. For a fluid with high electrical conductivity, the conducting mode driven by the coupling of surface charges and an external electric field is found to be the dominant mode of instability. On the contrary, for low conductivity materials, the surface-tension-driven capillary mode is found to be the most critical mode. Heat transfer from the jet to the surroundings tends to stabilize both types of instability mode. Under sufficiently strong heat transfer, the axisymmetric instability, which is believed to be responsible for producing nanofibers with diametric oscillations in electrospinning process, is suppressed. The stabilization is attributed to the enhancement of viscous stress in the thinning jet upon cooling. It is observed that the stabilization effect is relatively more pronounced in a thinning jet compared to the cylindrical jet of uniform radius. The effects of various material and process parameters on the stability behavior is also examined.

While the majority of fusion energy research is focused on magnetic confinement, there have been several alternative confinement methods aimed at the development of smaller and less expensive reactors. A number of these alternative reactors are based on a spherically convergent beam of recirculating ions and include designs such as inertial electrostatic confinement (IEC), multigrid IEC, and the periodically oscillating plasma sphere concept. Here, a fully time-dependent GPU-based Vlasov solver was developed in order to study these spherically convergent devices. This code solves the Vlasov equation for a spherically symmetric system using a finite-volume method with a modified flux to account for electrode transparency. The solver accounts for secondary electron emission, interactions between the charged particles, and collisional effects such as ionization and charge exchange. This code was used to investigate a system similar to the ion-injected device described by Hirsch (see [R. L. Hirsch, J. Appl. Phys. 38, 4522 (1967)]), who had reported a neutron production rate for deuterium-deuterium reactions in the range of ${10}^6\mathrm{to}{10}^7$ neutrons per second, which was attributed to the formation of a virtual electrode structure near the center of the chamber. Attempts to reproduce this experiment [B. J. Egle, Ph.D. thesis, 2010] yielded similar fusion rates, though the majority of the reactions were found not to occur near the center of the chamber. The results of this Vlasov solver, considering only beam-beam and beam-background fusion reactions, show that beam-background reactions would be dominant in such an ion-injected device. This result is consistent with work by Baxter and Stuart, who proposed a simplified steady-state Boltzmann model. However, the result of both models are inconsistent with the experimental results, which indicate a higher neutron production rate, and an inverse pressure scaling trend. It is shown that the higher experimental rates may be explained by beam-target fusion between the ion beam and deuterium embedded on the inner surface of the cathode.

Maxwell refrigerator as a device that can transfer heat from a cold to hot temperature reservoir making use of information reservoir was introduced by Mandal et al. [Phys. Rev. Lett. 111, 030602 (2013)]. The model has a two-state demon and a bit stream interacting with two thermal reservoirs simultaneously. We work out a simpler version of the refrigerator where the demon and bit system interact with the reservoirs separately and for a duration long enough to establish equilibrium. The efficiency, $\eta$, of the device when working as an engine as well as the coefficient of performance (COP) when working as a refrigerator are calculated. It is shown that the maximum efficiency matches that of a Carnot engine/refrigerator working between the same temperatures, as expected. The COP, when cooling per cycle is a maximum, decreases as $\frac{1}{T_h}$ when $T_h>T_c\gg \mathrm{\Delta }E$ $(k_B=1)$, where $T_h$ and $T_c$ are the temperatures of the hot and cold reservoirs, respectively, and $\mathrm{\Delta }E$ is the level spacing of the demon. $\eta$, when work per cycle is a maximum, is found to be $\frac{T_h}{0.779+T_h}$ when $T_c\ll \mathrm{\Delta }E$ and $T_h\gg \mathrm{\Delta }E$.

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)]. We derive the nonhomogeneous in space and time, hyperbolic partial differential equation for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable parameter in our theory, allowing us to answer what the differences are between this description and the mean-field theory i.e., the fully connected theory. We have considered the random network random field Ising model where the spin exchange interaction as well as the RF are random variables following a Gaussian distribution. The results were found within the replica symmetric (RS) approximation, whose stability is obtained using the two-replica method. This also puts our work in the context of a broader discussion, which is the RS stability as a function of the connectivity. In particular, our results show that for small connectivity there is a region at zero temperature where the RS solution remains stable above a given value of the magnetic field no matter the strength of RF. Consequently, our results show important differences with the crossover between the RF and SG regimes predicted by the fully connected theory.

The critical behavior of three-dimensional weakly diluted quenched Ising model is examined on the base of six-loop renormalization group expansions obtained within the minimal subtraction scheme in $4-\varepsilon$ space dimensions. For this purpose the ${\varphi }^4$ field theory with cubic symmetry was analyzed in the replica limit $n\to 0$. Along with renormalization group expansions in terms of renormalized couplings the $\sqrt{\varepsilon }$ expansions of critical exponents are presented. Corresponding numerical estimates for the physical, three-dimensional system are obtained by means of different resummation procedures applied both to the $\sqrt{\varepsilon }$ series and to initial renormalization group expansions. The results given by the latter approach are in a good agreement with their counterparts obtained experimentally and within the Monte Carlo simulations, while resumming of $\sqrt{\varepsilon }$ series themselves turned out to be disappointing.

Gene expression is a complex biochemical process involving multiple reaction steps, creating molecular memory because the probability of waiting time between consecutive reaction steps no longer follows exponential distributions. What effect the molecular memory has on metastable states in gene expression remains not fully understood. Here, we study transition paths of switching between bistable states for a non-Markovian model of gene expression equipped with a self-regulation. Employing the large deviation theory for this model, we analyze the optimal transition paths of switching between bistable states in gene expression, interestingly finding that dynamic behaviors in gene expression along the optimal transition paths significantly depend on the molecular memory. Moreover, we discover that the molecular memory can prolong the time of switching between bistable states in gene expression along the optimal transition paths. Our results imply that the molecular memory may be an unneglectable factor to affect switching between metastable states in gene expression.

There is growing evidence that suggests the importance of astrocytes as elements for neural information processing through the modulation of synaptic transmission. A key aspect of this problem is understanding the impact of astrocytes in the information carried by compound events in neurons across time. In this paper, we investigate how the astrocytes participate in the information integrated by individual neurons in an ensemble through the measurement of “integrated information.” We propose a computational model that considers bidirectional communication between astrocytes and neurons through glutamate-induced calcium signaling. Our model highlights the role of astrocytes in information processing through dynamical coordination. Our findings suggest that the astrocytic feedback promotes synergetic influences in the neural communication, which is maximized when there is a balance between excess correlation and spontaneous spiking activity. The results were further linked with additional measures such as net synergy and mutual information. This result reinforces the idea that astrocytes have integrative properties in communication among neurons.

Molecular dynamics simulations of crystallization in a supercooled liquid of Lennard-Jones particles with different range of attractions shows that the inclusion of the attractive forces from the first, second, and third coordination shell increases the trend to crystallize systematic. The bond order $Q_6$ in the supercooled liquid is heterogeneously distributed with clusters of particles with relative high bond order for a supercooled liquid, and a systematic increase of the extent of heterogeneity with increasing range of attractions. The onset of crystallization appears in such a cluster, which together explains the attractive forces influence on crystallization. The mean-square displacement and self-diffusion constant exhibit the same dependence on the range of attractions in the dynamics and shows, that the attractive forces and the range of the forces plays an important role for bond ordering, diffusion, and crystallization.