We study diffusion with a bias toward a target node in networks. This problem is relevant to efficient routing strategies in emerging communication networks like optical networks. Bias is represented by a probability $p$ of the packet or particle to travel at every hop toward a site that is along the shortest path to the target node. We investigate the scaling of the mean first passage time (MFPT) with the size of the network. We find by using theoretical analysis and computer simulations that for random regular (RR) and Erdős-Rényi networks, there exists a threshold probability, $p_{\mathrm{th}}$, such that for $p<p_{\mathrm{th}}$ the MFPT scales anomalously as $N^{\alpha }$, where $N$ is the number of nodes, and $\alpha$ depends on $p$. For $p>p_{\mathrm{th}}$, the MFPT scales logarithmically with $N$. The threshold value $p_{\mathrm{th}}$ of the bias parameter for which the regime transition occurs is found to depend only on the mean degree of the nodes. An exact solution for every value of $p$ is given for the scaling of the MFPT in RR networks. The regime transition is also observed for the second moment of the probability distribution function, the standard deviation. For the case of scale-free (SF) networks, we present analytical bounds and simulations results showing that the MFPT scales at most as $\ln N$ to a positive power for any finite bias, which means that in SF networks even a very small bias is considerably more efficient in comparison to unbiased walk.

Some epidemic spreading models are usually applied to analyze the propagation of opinions or news. However, the dynamics of epidemic spreading and information or behavior spreading are essentially different in many aspects. Centola's experiments [Science 329, 1194 (2010)] on behavior spreading in online social networks showed that the spreading is faster and broader in regular networks than in random networks. This result contradicts with the former understanding that random networks are preferable for spreading than regular networks. To describe the spreading in online social networks, a unknown-known-approved-exhausted four-status model was proposed, which emphasizes the effect of social reinforcement and assumes that the redundant signals can improve the probability of approval (i.e., the spreading rate). Performing the model on regular and random networks, it is found that our model can well explain the results of Centola's experiments on behavior spreading and some former studies on information spreading in different parameter space. The effects of average degree and network size on behavior spreading process are further analyzed. The results again show the importance of social reinforcement and are accordant with Centola's anticipation that increasing the network size or decreasing the average degree will enlarge the difference of the density of final approved nodes between regular and random networks. Our work complements the former studies on spreading dynamics, especially the spreading in online social networks where the information usually requires individuals' confirmations before being transmitted to others.

We study the Bouchaud-Mézard model on a regular random network. By assuming adiabaticity and independency, and utilizing the generalized central limit theorem and the Tauberian theorem, we derive an equation that determines the exponent of the probability distribution function of the wealth as $x\to \infty$. The analysis shows that the exponent can be smaller than 2, while a mean-field analysis always gives the exponent as being larger than 2. The results of our analysis are shown to be in good agreement with those of the numerical simulations.

We investigate the collective motion of symmetric self-propelled objects that are driven by a difference in the surface tension. The objects move around an annular water channel spontaneously and interact through the camphor layer that develops on the water surface. We found that two collective motion modes, discrete and continuous density waves, are generated depending on the number of self-propelled objects. The two modes are characterized by examining the local and global dynamics, and the collective motion mechanism is discussed in relation to the distribution of camphor concentration in the annular water channel. We conclude that the difference between these two modes originates from that of the driving mechanism that pushes a camphor paper away from a cluster, through which mechanism density waves are generated and maintained.

Time- and space-resolved visible-emission spectroscopy measurements are applied to study plasma parameters in nanosecond electrical discharges in He gas at pressure of ${10}^5$ Pa, using a 150 kV, 5 ns duration high-voltage pulse. The plasma evolution during the discharge is investigated by applying line-shape analysis of several He i spectral transitions, with the Stark and opacity effects accounted for. The analysis shows that the discharge plasma is not in equilibrium and that significant electric fields of several kV/cm are present in the plasma during the discharge. Regions of plasma with significantly different electron densities are identified and a qualitative model of the plasma formation and evolution is proposed.

We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures.

We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent novel all-pair exchange method. We compare the resulting schemes and measure specific heat errors and efficiency using the two-dimensional (2D) Ising model. Our tests suggest that an earlier proposal for using numbers of local moves related to the canonical correlation times is one of the key ingredients for increasing efficiency, and protocols using cluster algorithms are found to be very effective. Some of the protocols are also tested for efficiency and ground state production in 3D spin-glass models where we find that a simple nearest-neighbor approach using a local $n$-fold-way algorithm is the most effective. Finally, we present evidence that the asymptotic limits of the ground state energy for the isotropic case and for an anisotropic case of the 3D spin-glass model are very close and may even coincide.

This Rapid Communication presents a simple closure for the two-point correlation transport equation in decaying isotropic turbulence. It relies essentially on an eddy viscosity ${\nu }_t$ which exhibits some remarkable universal facets over an impressively wide range of scales. This allows us to model the third-order structure functions in different decaying flows covering a large extent of Reynolds numbers. The model is numerically time integrated to predict the decay of second-order structure functions and compared to experiments in grid turbulence. Agreement between predictions and measurements is satisfactory.

We derive a self-similarity criterion that must hold if a planar electric double layer (EDL) can be captured by a local-density approximation (LDA), without specifying any specific LDA. Our procedure generates a similarity coordinate from EDL profiles (measured or computed), and all LDA EDL profiles for a given electrolyte must collapse onto a master curve when plotted against this similarity coordinate. Noncollapsing profiles imply the inability of any LDA theory to capture EDLs in that electrolyte. We demonstrate our approach with molecular simulations, which reveal dilute electrolytes to collapse onto a single curve, and semidilute ions to collapse onto curves specific to each electrolyte, except where size-induced correlations arise.

We consider diffusion-controlled evolution of the $A$-particle island–semi-infinite $B$-particle sea system at propagation of the sharp annihilation front $A+B\to 0$. We show that at a large initial number of island particles the system evolution is described by the universal scaling laws with nonmonotonous front trajectory and a constant velocity of the island center motion. We demonstrate that asymptotically the island moves self-similarly retaining its velocity, shape and width.

We solve exactly a model of monodispersed rigid rods of length $k$ with repulsive interactions on the random locally tree-like layered lattice. For $k\ge 4$ we show that with increasing density, the system undergoes two phase transitions: first, from a low-density disordered phase to an intermediate density nematic phase and, second, from the nematic phase to a high-density reentrant disordered phase. When the coordination number is four, both phase transitions are continuous and in the mean field Ising universality class. For an even coordination number larger than four, the first transition is discontinuous, while the nature of the second transition depends on the rod length $k$ and the interaction parameters.

Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model. Significantly, it is shown that the free energy barrier is a lower bound to the true finite temperature migration barrier for this general and popular system. Numerical simulation confirms the analysis, while effective migration potentials implied by the bounds are employed to give a surprisingly accurate prediction of the nonlinear response.

We explore how a frozen background metric affects the mechanical properties of planar membranes with a shear modulus. We focus on a special class of “warped membranes” with a preferred random height profile characterized by random Gaussian variables $h\left(\mathbf{q}\right)$ in Fourier space with zero mean and variance ${\langle \left|h\left(\mathbf{q}\right)\right|}^2\rangle \sim q^{-d_h}$ and show that in the linear response regime the mechanical properties depend dramatically on the system size $L$ for $d_h\ge 2$. Membranes with $d_h=4$ could be produced by flash polymerization of lyotropic smectic liquid crystals. Via a self-consistent screening approximation we find that the renormalized bending rigidity increases as ${\kappa }_R\sim L^{(d_h-2)/2}$ for membranes of size $L$, while the Young and shear moduli decrease according to $Y_R,{\mu }_R\sim L^{-(d_h-2)/2}$ resulting in a universal Poisson ratio. Numerical results show good agreement with analytically determined exponents.

We investigate the universal orientation-dependent interactions between nonspherical colloidal particles immersed in a critical solvent by studying the instructive paradigm of a needle embedded in bounded two-dimensional Ising models at bulk criticality. For a needle in an Ising strip, the interaction on mesoscopic scales depends on the width of the strip and the length, position, and orientation of the needle. By lattice Monte Carlo simulations we evaluate the free-energy difference between needle configurations being parallel and perpendicular to the strip. We concentrate on $\mathit{small}$ but nonetheless mesoscopic needle lengths for which analytic predictions are available for comparison. All combinations of boundary conditions for the needles and boundaries are considered which belong to either the “normal” or the “ordinary” surface universality class, i.e., which induce local order or disorder, respectively. We also derive exact results for needles of arbitrary mesoscopic length, in particular for needles embedded in a half plane and oriented perpendicularly to the corresponding boundary as well as for needles embedded at the center line of a symmetric strip with parallel orientation.

If the rates, $K(x,y)$, at which particles of size $x$ coalesce with particles of size $y$ is known, then the mean-field evolution of the particle size distribution of an ensemble of irreversibly coalescing particles is described by the Smoluchowski equation. We study the corresponding inverse problem which aims to determine the coalescence rates $K(x,y)$ from measurements of the particle size distribution. We assume that $K(x,y)$ is a homogeneous function of its arguments, a case which occurs commonly in practice. The problem of determining $K(x,y)$, a function to two variables, then reduces to the simpler problem of determining a function of a single variable plus two exponents, $\mu$ and $\nu$, which characterize the scaling properties of $K(x,y)$. The price of this simplification is that the resulting least-squares problem is nonlinear in the exponents $\mu$ and $\nu$. We demonstrate the effectiveness of the method on a selection of coalescence problems arising in polymer physics, cloud science, and astrophysics. The applications include examples in which the particle size distribution is stationary owing to the presence of sources and sinks of particles and examples in which the particle size distribution is undergoing self-similar relaxation in time.

Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8–14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1–3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values.

In order to describe and to study the processes of cold compaction within the discrete element method a three-dimensional model of nanosized powder is developed. The elastic forces of repulsion, the tangential forces of “friction” (Cattaneo-Mindlin), and the dispersion forces of attraction (van der Waals–Hamaker), as well as the formation and destruction of hard bonds between the individual particles are taken into account. The monosized powders with the size of particles in the range 10–40 nm are simulated. The simulation results are compared to the experimental data of the alumina nanopowders compaction. It is shown that the model allows us to reproduce experimental data reliably and, in particular, describes the size effect in the compaction processes. A number of different external loading conditions is used in order to perform the theoretical and experimental researches. The uniaxial compaction (the closed-die compaction), the biaxial (radial) compaction, and the isotropic compaction (the cold isostatic pressing) are studied. The real and computed results are in a good agreement with each other. They reveal a weak sensitivity of the oxide nanopowders to the loading condition (compaction geometry). The application of the continuum theory of the plastically hardening porous body, which is usually used for the description of powders, is discussed.

We investigate the structure of crystalline particle arrays on constant mean curvature (CMC) surfaces of revolution. Such curved crystals have been realized physically by creating charge-stabilized colloidal arrays on liquid capillary bridges. CMC surfaces of revolution, classified by Delaunay in 1841, include the 2-sphere, the cylinder, the vanishing mean curvature catenoid (a minimal surface), and the richer and less investigated unduloid and nodoid. We determine numerically candidate ground-state configurations for 1000 pointlike particles interacting with a pairwise-repulsive $1/r^3$ potential, with distance $r$ measured in three-dimensional Euclidean space ${\mathbb{R}}^3$. We mimic stretching of capillary bridges by determining the equilibrium configurations of particles arrayed on a sequence of Delaunay surfaces obtained by increasing or decreasing the height at constant volume starting from a given initial surface, either a fat cylinder or a square cylinder. In this case, the stretching process takes one through a complicated sequence of Delaunay surfaces, each with different geometrical parameters, including the aspect ratio, mean curvature, and maximal Gaussian curvature. Unduloids, catenoids, and nodoids all appear in this process. Defect motifs in the ground state evolve from dislocations at the boundary to dislocations in the interior to pleats and scars in the interior and then isolated sevenfold disclinations in the interior as the capillary bridge narrows at the waist (equator) and the maximal (negative) Gaussian curvature grows. We also check theoretical predictions that the isolated disclinations are present in the ground state when the surface contains a geodesic disk with integrated Gaussian curvature exceeding $-\pi /3$. Finally, we explore minimal energy configurations on sets of slices of a given Delaunay surface, and we obtain configurations and defect motifs consistent with those seen in stretching.

Protein translocation from the cytosol to the endoplasmic reticulum (ER) or vice versa, an essential process for cell function, includes the transport of preproteins destined to become secretory, luminal, or integral membrane proteins (translocation) or misfolded proteins returned to the cytoplasm to be degraded (retrotranslocation). An important aspect in this process that has not been fully studied is the molecular crowding at both sides of the ER membrane. By using models of polymers crossing a membrane through a pore, in an environment crowded by either static or dynamic spherical agents, we computed the following transport properties: the free energy, the activation energy, the force, and the transport times for translocation and retrotranslocation. Using experimental protein crowding data for the cytoplasm and ER sides, we showed that dynamic crowding, which resembles biological environments where proteins are translocated or retrotranslocated, increases markedly all the physical properties of translocation and retrotranslocation as compared with translocation in a diluted system. By contrast, transport properties in static crowded systems were similar to those in diluted conditions. In the dynamic regime, the effects of crowding were more notorious in the transport times, leading to a huge difference for large chains. We indicate that this difference is the result of the synergy between the free energy and the diffusivity of the translocating chain. That synergy leads to translocation rates similar to experimental measures in diluted systems, which indicates that the effects of crowding can be measured. Our data also indicate that effects of crowding cannot be neglected when studying translocation because protein dynamic crowding has a relevant steric contribution, which changes the properties of translocation.

The goal of this work was to analyze the propulsion of multiflagellated microorganisms, and to draw insight to the underlying physics and biology of the movement. Giardia lamblia was chosen as the model organism due to its unique ability to mechanically attach to various surfaces, its rapid movement, and its fine control over steering and navigation. In this work, a mechanics model was utilized to study the mechanics and propulsive contribution of the ventral and anterior flagella in Giardia. It was discovered that energy is supplied mainly at the proximal portion of these flagella, supporting the hypothesis that a decreasing adenosine triphosphate (ATP) gradient along the length of the flagella would not affect the motion observed. Similarly, the elasticity of the flagella allows the energy input at the proximal portion to be transferred to the distal portion, where the majority of thrust is generated. Specifically, we found that the ventral flagella are the driving force for planar propulsion and turning, while the anterior flagella are used for steering and control.