We investigate the ground state of the irrationally frustrated Josephson junction array with a controlling anisotropy parameter $\lambda$ that is the ratio of the longitudinal Josephson coupling to the transverse one. We find that the ground state has one-dimensional periodicity whose reciprocal lattice vector depends on $\lambda$ and is incommensurate with the substrate lattice. Approaching the isotropic point $\lambda =1$, the so-called hull function of the ground state exhibits analyticity breaking similar to the Aubry transition in the Frenkel-Kontorova model. We find a scaling law for the harmonic spectrum of the hull functions, which suggests the existence of a characteristic length scale diverging at the isotropic point. This critical behavior is directly connected to the jamming transition previously observed in the current-voltage characteristics by a numerical simulation. On top of the ground state there is a gapless continuous band of metastable states, which exhibit the same critical behavior as the ground state.

The idea that a space-time metric emerges as a Fisher-Rao “information metric” of instanton moduli space has been examined in several field theories, such as the Yang-Mills theories and nonlinear $\sigma$ models. In this paper, we report that the flat Euclidean or Minkowskian metric, rather than an anti–de Sitter metric that generically emerges from instanton moduli spaces, can be obtained as the Fisher-Rao metric from a nontrivial solution of the massive Klein-Gordon field (a linear $\sigma$ model). This realization of the flat space from the simple field theory would be useful to investigate the ideas that relate the space-time geometry with the information geometry.

We investigate experimentally whether self-organized criticality (SOC) occurs in granular piles composed of different grains, namely, rice, lentils, quinoa, and mung beans. These four grains were selected to have different aspect ratios, from oblong to oblate. As a function of aspect ratio, we determined the growth ($\beta$) and roughness ($\alpha$) exponents, the avalanche fractal dimension ($D$), the avalanche size distribution exponent ($\tau$), the critical angle ($\gamma$), and its fluctuation. At superficial inspection, three types of grains seem to have power-law-distributed avalanches with a well-defined $\tau$. However, only rice is truly SOC if we take three criteria into account: a power-law-shaped avalanche size distribution, finite size scaling, and a universal scaling relation relating characteristic exponents. We study SOC as a spatiotemporal fractal; in particular, we study the spatial structure of criticality from local observation of the slope angle. From the fluctuation of the slope angle we conclude that greater fluctuation (and thus bigger avalanches) happen in piles consisting of grains with larger aspect ratio.

We analyze the geometric structure and mechanical stability of a complete set of isostatic and hyperstatic sphere packings obtained via exact enumeration. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and their diversity of structure and symmetry increases with increasing $N$ and decreases with increasing hyperstaticity $H\equiv N_c-N_{\text{ISO}}$, where $N_c$ is the number of pair contacts and $N_{\text{ISO}}=3N-6$. Maximally contacting packings are in general neither the densest nor the most symmetric. Analyses of local structure show that the fraction $f$ of nuclei with order compatible with the bulk (rhcp) crystal decreases sharply with increasing $N$ due to a high propensity for stacking faults, five- and near-fivefold symmetric structures, and other motifs that preclude rhcp order. While $f$ increases with increasing $H$, a significant fraction of hyperstatic nuclei for $N$ as small as 11 retain non-rhcp structure. Classical theories of nucleation that consider only spherical nuclei, or only nuclei with the same ordering as the bulk crystal, cannot capture such effects. Our results provide an explanation for the failure of classical nucleation theory for hard-sphere systems of $N\lesssim 10$ particles; we argue that in this size regime, it is essential to consider nuclei of unconstrained geometry. Our results are also applicable to understanding kinetic arrest and jamming in systems that interact via hard-core-like repulsive and short-ranged attractive interactions.

Inspired by recent atomic force microscope (AFM) images of plasmids deposited on oppositely charged supported lipid bilayers from salt free solution, we propose a model for strongly adsorbed supercoiled cyclic stiff polyelectrolytes. We discuss how the excess linking number Lk of the deposited cycle is shared between writhe Wr and twist Tw at equilibrium and obtain the typical number of self-crossings in the deposited cycle as a function of surface charge density. The number of crossings at equilibrium is simply determined by the crossing penalty which is a local quantity and by the excess linking number. The number of crossings is well defined despite versatile plasmid shapes. For moderate numbers of crossings the loops are rather small and localized along the primary cycle, as expected from entropic loops. In the regime of many crossings, the cycle takes the shape of a regular flat ply ruled by local stiffness. The model allows for a semiquantitative comparison with the AFM images of deposited plasmids which are strongly charged.

We study the synchronization and phase lag of fluctuations in the number of infected individuals in a network of cities between which individuals commute. The frequency and amplitude of these oscillations is known to be very well captured by the van Kampen system-size expansion, and we use this approximation to compute the complex coherence function that describes their correlation. We find that, if the infection rate differs from city to city and the coupling between them is not too strong, these oscillations are synchronized with a well-defined phase lag between cities. The analytic description of the effect is shown to be in good agreement with the results of stochastic simulations for realistic population sizes.

The competition between Na${}^{+}$ and Rb${}^{+}$ ions in the minor groove of a synthetic B-DNA dodecamer d (CGCGAATTCGCG) is studied using molecular dynamics simulations as the ratio of these two ions changing from 9:1 to 1:9 with the DNA merged into the solvent of water molecule at 298 K. When the concentration of Rb${}^{+}$ ions increases, from minority to majority, Na${}^{+}$ ions are gradually released from the A tract, and the binding sites in the minor groove are occupied by Rb${}^{+}$ ions, extending from the A tract to the whole minor groove. Comparing Na${}^{+}$ with Rb${}^{+}$ ions, the conformation of the minor groove is influenced strongly by Na${}^{+}$ ions.

Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases.

We develop a continuum elastic approach to examining the bending mechanics of semiflexible filaments with a local internal degree of freedom that couples to the bending modulus. We apply this model to study the nonlinear mechanics of a double-stranded DNA oligomer (shorter than its thermal persistence length) whose free ends are linked by a single-stranded DNA chain. This construct, studied by H. Qu and G. Zocchi [Europhys. Lett. 94, 18003 (2011)], displays nonlinear strain softening associated with the local melting of the double-stranded DNA under applied torque and serves as a model system with which to study the nonlinear elasticity of DNA under large energy deformations. We show that one can account quantitatively for the observed bending mechanics using an augmented wormlike chain model, the helix-coil wormlike chain. We also predict that the highly bent and partially molten dsDNA should exhibit particularly large end-to-end fluctuations associated with the fluctuation of the length of the molten region, and propose appropriate experimental tests. We suggest that the augmented wormlike chain model discussed here is a useful analytic approach to the nonlinear mechanics of DNA or other biopolymer systems.

Globalization facilitates our communication with each other, while it magnifies problems such as overharvesting of natural resources and human-induced climate change. Thus people all over the world are involved in a global social dilemma which calls for worldwide cooperation to reduce the risks of these extreme events and disasters. A collective target (threshold) is required to prevent such events. Everyone may lose their wealth once their total individual contributions fail to reach the threshold. To this end, we establish a model of threshold public goods games in a group-structured population and investigate its evolutionary process. We study multilevel public goods games with defectors, local cooperators, and global cooperators and are primarily concerned with how the global cooperative behavior evolves. We find that, compared with the standard public goods games, the strategy of global cooperation accounts for a bigger proportion in the stationary distribution of threshold public goods games. On the other hand, the fixation time of the global cooperation strategy is greatly shortened with increase of the probability of disaster striking. Therefore, global risks induced by the threshold can effectively promote global cooperation in environmental investment and the reduction of greenhouse gas emissions.

Increasingly accessible financial data allow researchers to infer market-dynamics-based laws and to propose models that are able to reproduce them. In recent years, several stylized facts have been uncovered. Here we perform an extensive analysis of foreign exchange data that leads to the unveiling of a statistical financial law. First, our findings show that, on average, volatility increases more when the price exceeds the highest (or lowest) value, i.e., breaks the resistance line. We call this the breaking-acceleration effect. Second, our results show that the probability $P\left(T\right)$ to break the resistance line in the past time $T$ follows power law in both real data and theoretically simulated data. However, the probability calculated using real data is rather lower than the one obtained using a traditional Black-Scholes (BS) model. Taken together, the present analysis characterizes a different stylized fact of financial markets and shows that the market exceeds a past (historical) extreme price fewer times than expected by the BS model (the resistance effect). However, when the market does, we predict that the average volatility at that time point will be much higher. These findings indicate that any Markovian model does not faithfully capture the market dynamics.

Three-dimensional numerical simulation using the front-tracking method is presented on the dynamics of a vesicle in a linear shear flow. The focus here is to elucidate the parametric dependence and the self-similarity of the vesicle dynamics, quantification of vesicle deformation, and the analysis of shape dynamics. A detailed comparison of the numerical results is made with various theoretical models and experiments. It is found that the applicability of the theoretical models is limited despite some general agreement with the simulations and experiments. The deviations between the perturbative results and the simulation results occur even in the absence of thermal noise. Specifically, we find that the vesicle dynamics does not follow a self-similar behavior in a two-parameter phase space, as proposed in a theoretical model. Rather, the dynamics is governed by three controlling parameters, namely, the excess area, viscosity ratio, and dimensionless shear rate. Additionally, we find that a linear scaling of the tank-treading angle, as proposed in the theoretical model, is possible only for nearly spherical vesicles. The breakdown of the scaling occurs at higher values of the excess area even in the absence of thermal noise. We find that the vesicle deformation saturates at large shear rates, and the asymptotic deformation matches well with a theoretical prediction for nearly spherical vesicles. The dependence of the critical viscosity ratio associated with the onset of unsteady dynamics on the vesicle excess area is in excellent agreement with the experimental observation. We show that near the transition between the tank-treading and tumbling dynamics, both the vacillating-breathing-like motion characterized by a smooth ellipsoidal shape and the trembling-like motion characterized by a highly deformed shape are possible. For the trembling-like motion, the shape is highly three-dimensional with concavities and lobes, and the vesicle deforms more in the vorticity direction than in the shear plane. A Fourier spectral analysis of the vesicle shape shows the presence of the odd harmonics and higher order modes beyond fourth order.

We propose that the rheological properties of background fluid play an important role in the interaction of microorganisms with the flow field. The viscoelastic-induced migration of microorganisms in a vortical flow leads to the emergence of a limit cycle. The shape and formation rate of patterns depend on motility, vorticity strength, and rheological properties of the background fluid. Given the inherent viscoelasticity of exopolysaccharides secreted by microorganisms, our results can suggest new mechanisms leading to the vital behavior of microorganisms such as bacterial aggregation and biofilm formation.

Ultrashort-pulse laser intensities can reach ${10}^{22}$ W/cm${}^2$. In this case the electron motion becomes ultrarelativistic and significant bremsstrahlung occurs. The radiation causes a dissipative effect, which is called a radiation reaction. It has been shown in the literature that the radiation reaction force causes phase-space contraction when the motion of electrons in a laser field is considered. The effect of the radiation reaction force is smaller for electron propagation in the direction of a propagating plane wave compared to counterpropagation. In the case of two colliding laser beams with sufficiently large amplitudes, stochastic heating is an important process that will be influenced by the radiation reaction. It is shown here that the radiation reaction causes attractors and in certain parameter regimes electron motion converges to regular attractors. This causes a significant reduction of stochastic heating. The forms of the attractors are presented. The results confirm the general prediction of phase-space contraction and provide quantitative results for the speed of contraction as well as the type of attracted motion.

A modified Colpitts oscillator (MCO) associated with a nonlinear transmission line (NLTL) with intersite nonlinearity is introduced as a self-sustained generator of a train of modulated dark signals with compact shape. Equations of state describing the dynamics of the MCO part are derived and the stationary state is obtained. Using the Routh-Hurwitz criterion, the result of a stability analysis indicates the existence of a limit cycle in certain parameter regimes and there the oscillation of the circuit delivers pulselike electrical signals. The train of generated signals is then transformed into a train of compact modulated dark voltage solitons by the NLTL. The exactness of this analytical analysis is confirmed by numerical simulations performed on the circuit equations. Finally, simulations show the capacity of this circuit to work as a generator of compactlike dark voltage solitons. The performance of the generator, namely, the pulse width and the repetition rate, is controlled by the magnitude of the characteristic parameters of the electronic components of the device.

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet–de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

The effectiveness of the actual annealing strategy in finite-time optimization by simulated annealing (SA) is analyzed by focusing on the search function of the relaxation dynamics observed in the multimodal landscape of the cost function. The rate-cycling experiment, which was introduced in the previous study [M. Hasegawa, Phys. Rev. E 83, 036708 (2011)] to examine the role of the relaxation dynamics in optimization, and the temperature-cycling experiment, which was developed for a laboratory experiment on relaxation-related phenomena, are conducted on two types of random traveling salesman problems (TSPs). In each experiment, the SA search starting from a quenched solution is performed systematically under a nonmonotonic temperature control used in the actual heat treatment of metals and glasses. The results show that, as in the previous monotonic cooling from a random solution, the optimizing ability is enhanced by allocating a lot of time to the search performed near an effective intermediate temperature irrespective of the annealing technique. In this productive phase, the relaxation dynamics successfully function as an optimizer and the relevant characteristics analogous to the stabilization phenomenon and the acceleration of relaxation, which are observed in glass-forming materials, play favorable roles in the present optimization. This nonmonotonic approach also has the advantage of a wider operation range of the effective relaxation dynamics, and in conclusion, the actual annealing strategy is useful and more workable than the conventional slow-cooling strategy, at least for the present TSPs. Further discussion is given of an illuminating aspect of computational physics analysis in the optimization algorithm research.

A molecular dynamics (MD) parallel to the control volume (CV) formulation of fluid mechanics is developed by integrating the formulas of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] over a finite cubic volume of molecular dimensions. The Lagrangian molecular system is expressed in terms of an Eulerian CV, which yields an equivalent to Reynolds’ transport theorem for the discrete system. This approach casts the dynamics of the molecular system into a form that can be readily compared to the continuum equations. The MD equations of motion are reinterpreted in terms of a Lagrangian-to-control-volume ($\mathcal{LCV}$) conversion function ${\vartheta }_i$ for each molecule $i$. The $\mathcal{LCV}$ function and its spatial derivatives are used to express fluxes and relevant forces across the control surfaces. The relationship between the local pressures computed using the volume average [Lutsko, J. Appl. Phys. 64, 1152 (1988)] techniques and the method of planes [Todd et al., Phys. Rev. E 52, 1627 (1995)] emerges naturally from the treatment. Numerical experiments using the MD CV method are reported for equilibrium and nonequilibrium (start-up Couette flow) model liquids, which demonstrate the advantages of the formulation. The CV formulation of the MD is shown to be exactly conservative and is, therefore, ideally suited to obtain macroscopic properties from a discrete system.

To date there are several iterative techniques that enjoy moderate success when reconstructing phase information, where only intensity measurements are made. There remains, however, a number of cases in which conventional approaches are unsuccessful. In the last decade, the theory of compressed sensing has emerged and provides a route to solving convex optimisation problems exactly via ${\ell }_1$-norm minimization. Here the application of compressed sensing to phase retrieval in a nonconvex setting is reported. An algorithm is presented that applies reweighted ${\ell }_1$-norm minimization to yield accurate reconstruction where conventional methods fail.

We demonstrate stable synchronous chaos in a delay coupled network of time continuous dynamical system using the framework of master stability formalism (MSF). It is further shown that conjugate coupling, i.e., coupling using dissimilar variables, can substitute delay coupling of similar variables in retrieving delay-induced phenomena. By exploiting the MSF, we show that delayed conjugate coupling in an arbitrary network is capable of both inducing synchronization where there is no synchronization at all and enhancing synchronization to a large parameter space, which even the conjugate coupling without delay is incapable of. The above results are demonstrated using the paradigmatic Rössler system and Hindmarsh-Rose neuron.