The long-time limit behavior of the positional distribution for an underdamped Brownian particle in a fluctuating harmonic potential well, which is simultaneously exposed to an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law-type memory kernel. The influence of a fluctuating environment is modeled by a multiplicative white noise (fluctuations of the stiffness of the trapping potential) and by an additive internal fractional Gaussian noise. The exact expressions of the second-order moments of the fluctuating position for the Brownian particle in the shear plane have been calculated. Also, shear-induced cross correlation between particle fluctuations along orthogonal directions as well as the angular momentum are found. It is shown that interplay of shear flow, memory, and multiplicative noise can generate a variety of cooperation effects, such as energetic instability, multiresonance versus the shear frequency, and memory-induced anomalous diffusion in the direction of the shear flow. Particularly, two different critical memory exponents have been found, which mark dynamical transitions from a stationary regime to a subdiffusive (or superdiffusive) regime of the system. Similarities and differences between the behaviors of the models with oscillatory and nonoscillatory shear flow are also discussed.

We present an inequality which holds in the thermodynamical processes with measurement and feedback controls and uses only the Helmholtz free energy and the entanglement of formation: $W_{\mathrm{ext}}\le -\Delta F-k_{B}T\Delta E_F$. The quantity $-\Delta E_F$, which is positive, expresses the amount of entanglement transfer from system $S$ to probe $P$ through the interaction ${\widehat{U}}_{SP}$ during the measurement. It is easier to achieve the upper bound in this inequality than in the Sagawa-Ueda inequality [Phys. Rev. Lett. 100, 080403 (2008)]. Our inequality has clear physical meaning: in the above thermodynamical processes, the work which we can extract from the thermodynamic system is greater than the upper bound in the conventional thermodynamics by the amount of the entanglement extracted by the measurement.

Consider a finite-sized, multidimensional system in parameter state a. The system is either at statistical equilibrium or general nonequilibrium, and may obey either classical or quantum physics. L. Hardy's mathematical axioms provide a basis for the physics obeyed by any such system. One axiom is that the number $N$ of distinguishable states a in the system obeys $N=\max$. This assumes that $N$ is known as deterministic prior knowledge. However, most observed systems suffer statistical fluctuations, for which $N$ is therefore only known approximately. Then what happens if the scope of the axiom $N=\max$ is extended to include such observed systems? It is found that the state a of the system must obey a principle of maximum Fisher information, $I=I_{\max }$. This is important because many physical laws have been derived, assuming as a working hypothesis that $I=I_{\max }$. These derivations include uses of the principle of extreme physical information (EPI). Examples of such derivations were of the De Broglie wave hypothesis, quantum wave equations, Maxwell's equations, new laws of biology (e.g., of Coulomb force-directed cell development and of in situ cancer growth), and new laws of economic fluctuation and investment. That the principle $I=I_{\max }$ itself derives from suitably extended Hardy axioms thereby eliminates its need to be assumed in these derivations. Thus, uses of $I=I_{\max }$ and EPI express physics at its most fundamental level, its axiomatic basis in math.

We investigate the dynamics of granular columns of point particles that interact via long-range hydrodynamic interactions and fall under the action of gravity. We investigate the influence of inertia using the Green's function for the Oseen equation. The initial conditions (density and aspect ratio) are systematically varied. Our results suggest that universal self-similar laws may be sufficient to characterize the temporal and structural evolution of the granular columns. A characteristic time above which an instability is triggered (which may enable the formation of clusters) is also retrieved and discussed.

We report on localized measurement of the longitudinal and transverse flow velocities in a colloidal suspension using optical coherence tomography. We present a model for the path-length resolved autocorrelation function including diffusion and flow, which we experimentally verify. For flow that is not perpendicular to the incident beam, the longitudinal velocity gradient over the coherence gate causes additional decorrelation, which is described by our model. We demonstrate simultaneous imaging of sample morphology and longitudinal and transverse flow at micrometer scale in a single measurement.

A liquid droplet resting on a soft gel substrate can deform that substrate to the point of material failure, whereby fractures develop on the gel surface that propagate outwards from the contact line in a starburst pattern. In this paper, we characterize (i) the initiation process, in which the number of arms in the starburst is controlled by the ratio of the surface tension contrast to the gel's elastic modulus, and (ii) the propagation dynamics showing that once fractures are initiated they propagate with a universal power law $L\propto t^{3/4}$. We develop a model for crack initiation by treating the gel as a linear elastic solid and computing the deformations within the substrate from the liquid-solid wetting forces. The elastic solution shows that both the location and the magnitude of the wetting forces are critical in providing a quantitative prediction for the number of fractures and, hence, an interpretation of the initiation of capillary fractures. This solution also reveals that the depth of the gel is an important factor in the fracture process, as it can help mitigate large surface tractions; this finding is confirmed with experiments. We then develop a model for crack propagation by considering the transport of an inviscid fluid into the fracture tip of an incompressible material and find that a simple energy-conservation argument can explain the observed material-independent power law. We compare predictions for both linear elastic and neo-Hookean solids, finding that the latter better explains the observed exponent.

We study the effect of the sample thickness in planar crack front propagation in a disordered elastic medium using the random fuse model. We employ different loading conditions and we test their stability with respect to crack growth. We show that the thickness induces characteristic lengths in the stress enhancement factor in front of the crack and in the stress transfer function parallel to the crack. This is reflected by a thickness-dependent crossover scale in the crack front morphology that goes from from multiscaling to self-affine with exponents, in agreement with line depinning models and experiments. Finally, we compute the distribution of crack avalanches, which is shown to depend on the thickness and the loading mode.

Topological methods are indispensable in theoretical studies of particle physics, condensed matter physics, and gravity. These powerful techniques have also been applied to biological physics. For example, knowledge of DNA topology is pivotal to the understanding as to how living cells function. Here, the biophysical repertoire of topological methods is extended, with the aim to understand and characterize the global structure of a folded protein. For this, the elementary concept of winding number of a vector field on a plane is utilized to introduce a topological quantity called the folding index of a crystallographic protein. It is observed that in the case of high resolution protein crystals, the folding index, when evaluated over the entire length of the crystallized protein backbone, has a very clear and strong propensity towards integer values. The observation proposes that the way how a protein folds into its biologically active conformation is a structural self-organization process with a topological facet that relates to the concept of solitons. It is proposed that the folding index has a potential to become a useful tool for the global, topological characterization of the folding pathways.

Coherent diffractive imaging with x-ray free-electron lasers (XFEL) promises high-resolution structure determination of noncrystalline objects. Randomly oriented particles are exposed to XFEL pulses for acquisition of two-dimensional (2D) diffraction snapshots. The knowledge of their orientations enables 3D imaging by multiview reconstruction, combining 2D diffraction snapshots in different orientations. Here we introduce a globally optimal algorithm that can infer these orientations. We apply it to experimental XFEL data of nanoparticles and so determine their 3D electron density.

In fields such as robotics and sensor networks, synchronization among mobile and dynamic agents is a basic task. We articulate an effective strategy to achieve synchronization in dynamic networks of moving chaotic agents. Our counterintuitive idea is to restrict agents’ ability to interact with each other, which can be implemented by designating a finite number of fixed zones in the space, in which agents are allowed to interact with each other but agents outside the zones are deprived of the ability of mutual interaction. Our setting is thus different from the one used in existing works on synchronization of mobile agents where each agent is associated with an interacting zone that moves with the agent. We find, through a mathematical analysis, that an optimal interval exists in the interaction probability, where stable synchronization emerges. An inverse square-root scaling law is uncovered which relates the interval with the system size, i.e., the total number of moving agents. Extensive numerical support for physical spaces of one, two, and three dimensions is provided.

The emergence of explosive synchronization transitions in networks of phase oscillators recently has become one of the most interesting topics. It is widely believed that the large frequency mismatch of a pair of oscillators (also known as disassortativity in frequency) is a direct cause of an explosive synchronization. It is found that, besides the disassortativity in frequency, the disassortativity in node degree also shows up in connection with the first-order synchronization transition. In this paper, we simulate the Kuramoto model on top of a family of networks with different degree-degree and frequency-frequency correlation patterns. Results show that only when the degrees and natural frequencies of the network's nodes are both disassortative can an explosive synchronization occur.

We discuss the wave resistance in the case of an externally perturbed viscous liquid film of arbitrary thickness. Emphasis is placed on the dependence of the wave resistance on the film thickness $H$, the length scale $b$ characterizing the external perturbation, and its velocity $V$. In particular, the effectiveness of the mechanisms of capillary-gravity waves and the viscous dissipation localized in the vicinity of the perturbation are compared and discussed as functions of $H$ and $V$. We show that, in general, the wave resistance is a nonmonotonous function of $H$ with a maximum whose amplitude and position depend on $b$ and $V$. In the case of small $H$ the wave resistance depends on a parameter $S\propto V/H^3$. We find three different regimes of this parameter in which the wave resistance behaves like $S^r$ with the exponent $r$ equal to 1, 1/3, and $-1$. These results are also obtained independently within the thin liquid film approximation. This allows us to assess the range of validity of the thin liquid film approximation in various cases, in particular its dependence on the perturbation length scale $b$.

The relativistically induced transparency acceleration (RITA) scheme of proton and ion acceleration using laser-plasma interactions is introduced, modeled, and compared to the existing schemes. Protons are accelerated with femtosecond relativistic pulses to produce quasimonoenergetic bunches with controllable peak energy. The RITA scheme works by a relativistic laser inducing transparency [Akhiezer and Polovin, Zh. Eksp. Teor. Fiz 30, 915 (1956); Kaw and Dawson, Phys. Fluids 13, 472 (1970); Max and Perkins, Phys. Rev. Lett. 27, 1342 (1971)] to densities higher than the cold-electron critical density, while the background heavy ions are stationary. The rising laser pulse creates a traveling acceleration structure at the relativistic critical density by ponderomotively [Lindl and Kaw, Phys. Fluids 14, 371 (1971); Silva et al., Phys. Rev. E 59, 2273 (1999)] driving a local electron density inflation, creating an electron snowplow and a co-propagating electrostatic potential. The snowplow advances with a velocity determined by the rate of the rise of the laser's intensity envelope and the heavy-ion-plasma density gradient scale length. The rising laser is incrementally rendered transparent to higher densities such that the relativistic-electron plasma frequency is resonant with the laser frequency. In the snowplow frame, trace density protons reflect off the electrostatic potential and get snowplowed, while the heavier background ions are relatively unperturbed. Quasimonoenergetic bunches of velocity equal to twice the snowplow velocity can be obtained and tuned by controlling the snowplow velocity using laser-plasma parameters. An analytical model for the proton energy as a function of laser intensity, rise time, and plasma density gradient is developed and compared to 1D and 2D PIC OSIRIS [Fonseca et al., Lect. Note Comput. Sci. 2331, 342 (2002)] simulations. We model the acceleration of protons to GeV energies with tens-of-femtoseconds laser pulses of a few petawatts. The scaling of proton energy with laser power compares favorably to other mechanisms for ultrashort pulses [Schreiber et al., Phys. Rev. Lett. 97, 045005 (2006); Esirkepov et al., Phys. Rev. Lett. 92, 175003 (2004); Silva et al., Phys. Rev. Lett. 92, 015002 (2004); Fiuza et al., Phys. Rev. Lett. 109, 215001 (2012)].

Quantum ion-acoustic solitary waves are studied by considering the effects of exchange and correlation for the electrons. Starting from one-dimensional quantum hydrodynamic equations, including the term of exchange correlation for electrons, we obtain a model in which two dimensionless parameters appear (in addition to the parameter measuring the quantum diffraction) measuring the exchange and the correlation. A new deformed Korteweg–de Vries equation is derived. The effect of exchange and correlation is reflected in the phase speed as well as in the nonlinear and dispersion terms. Its solution shows that the exchange-correlation effects modify the amplitude as well as the width of the weak solitary waves. In the arbitrary amplitude regime, and as may be expected, a pseudopotential analysis shows that the exchange-correlation effects may change the nature (compressive or rarefactive) of the quantum ion-acoustic solitary waves. Our results complement and give new insight into the previously published work on this problem.

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behavior via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks.

We study by simulation and theory how the addition of insulating spherical particles affects the conductivity of fluids of conducting rods, modeled by spherocylinders. The electrical connections are implemented as tunneling processes, leading to a more detailed and realistic description than a discontinuous percolation approach. We find that the spheres enhance the tunneling conductivity for a given concentration of rods and that the enhancement increases with rod concentration into the regime where the conducting network is well established. By reformulating the network of rods using a critical path analysis, we quantify the effect of depletion-induced attraction between the rods due to the spheres. Furthermore, we show that our conductivity data are quantitatively reproduced by an effective-medium approximation, which explicitly relates the system tunneling conductance to the structure of the rod-sphere fluid.

We employ the nonperturbative functional renormalization group to study models with an $\mathrm{O}\left(N_1\right)\oplus \mathrm{O}\left(N_2\right)$ symmetry. Here different fixed points exist in three dimensions, corresponding to bicritical and tetracritical behavior induced by the competition of two order parameters. We discuss the critical behavior of the symmetry-enhanced isotropic, the decoupled and the biconical fixed point, and analyze their stability in the $N_1,N_2$ plane. We study the fate of nontrivial fixed points during the transition from three to four dimensions, finding evidence for a triviality problem for coupled two-scalar models in high-energy physics. We also point out the possibility of noncanonical critical exponents at semi-Gaussian fixed points and show the emergence of Goldstone modes from discrete symmetries.

We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, ${\chi }_4$, which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.

Breakage is generally understood in mechanical terms, yet nanostructures can rupture not only under external loads but also via thermal activation. Here we treat in a general framework the statistical mechanics of thermally induced breakage at the nanoscale for one-dimensional systems. We test it on a simple approximation and find that the probability of breakage controls distinct regimes, characterized by sharp crossovers and narrow peaks in the thermal fluctuations and specific heat. Our work provides predictions on clustering of new phases, of relevance in nanofabrication.

We consider a toy model that captures the short-time nondiffusive behavior seen in many physical systems, to study the extraction of self-diffusivity from particle trajectories. We propose and evaluate a simple method to automatically detect the transition to diffusive behavior. We simulate the toy model to generate data sets of varying quality and test different methods of extracting the self-diffusion coefficient and characterizing its uncertainty. We find that weighted least-squares with statistical bootstrap is the most accurate and efficient means for analyzing the trajectory data. The analysis suggests an iterative recipe for designing simulations to conform to a specified level of accuracy.