Formation of ion clusters in aqueous NaCl solutions at $25°\mathrm{C}$ is investigated with dynamics simulations in the $0.1–3\mathrm{M}$ concentration range. The medium is found to be highly structured even at moderate concentrations, and clusters of over 20 ions are observed above $\sim 2\mathrm{M}$. The medium can be viewed as a multicomponent fluid, composed of reacting particles with well-defined average populations, shapes, sizes, and charge distributions. Clusters show substantial morphological variations that are here characterized by their hydrodynamic radii and internal charge distributions. Clusters can be described as prolate spheroids in the subnanometer length scale. The hydrodynamic radius and the radius of gyration follow simple power laws with the number of ions in the cluster. Dipole moment distributions show characteristic peaks in the $\sim 10–60\text{debye}$ range that reflect conformational preferences modulated by electrostatic and liquid-structure forces.

Dynamics of surface roughness during polycrystalline pure iron electrodissolution is investigated at constant current density by means of ex situ atomic force microscopy. The scaling of the local surface width reveals that surface kinetic roughening is anomalous with both the exponents of local roughness, ${\alpha }_{\mathrm{loc}}$, and growth, $\beta$, close to 1 pointing out that interface evolution is unstable. We show that this anomalous unstable behavior results from the development of a faceted surface structure exposing different crystal orientations. The presence of smooth faceted walls is consistent with the value ${\alpha }_{\text{local}}\sim 1$, whereas the difference in the dissolution rates on the different crystallographic planes account for the nonlocal effects causing the unstable growth. Results are discussed in the context of a recently reported anomalous scaling which accounts for dynamics of self-organized depinning models displaying faceted interfaces. The influence of the electrode potential on the dissolution rates of the different crystallographic planes, along with its effect on the mobility of metal adatoms, are discussed to be behind the complex behavior of local roughness when the current density is varied.

Small-angle neutron scattering (SANS) and dynamic light scattering (DLS) have been used to study conformational changes in protein bovine serum albumin (BSA) due to perturbation in its native structure as induced by varying temperature and pressure, and in presence of protein denaturating agents urea and surfactant. BSA has prolate ellipsoidal shape at ambient temperature and we observe no effect of temperature on its structure up to a temperature of about $60°\mathrm{C}$. At temperatures beyond $60°\mathrm{C}$, protein denaturation leads to aggregation. The protein solution exhibits a fractal structure at temperatures above $64°\mathrm{C}$, and its fractal dimension increases with temperature. This is an indication of aggregation followed by gelation that evolves with increasing temperature. It is known for some of the proteins (e.g., Staphylococcal Nuclease) that pressure of $200\mathrm{MPa}$ can unfold the protein, whereas BSA does not show any protein unfolding even up to the pressure of $450\mathrm{MPa}$. In presence of urea, the BSA protein unfolds for urea concentrations greater than $4M$ and acquires a random coil configuration. We make use of the dilution method to show the reversibility of protein unfolding with urea. The addition of surfactant denaturates the protein by the formation of micellelike aggregates of surfactants along the unfolded polypeptide chains of the protein. We show such structure of the protein-surfactant complex can be stabilized at higher temperatures, which is not the case for pure protein.

Using the multivariate long memory (LM) model and Taylor expansions, we find the conditions for convergence of the wavelet correlations between two LM processes on an asymptotic value at low frequencies. These mathematical results, and a least squares estimator of LM parameters, are validated in simulations and applied to neurophysiological (human brain) and financial market time series. Both brain and market systems had multivariate LM properties including a “fractal connectivity” regime of scales over which wavelet correlations were invariantly close to their asymptotic value. This analysis provides efficient and unbiased estimation of long-term correlations in diverse dynamic networks.

Triangles with sides given by consecutive integers ($N$, $N+1$, $N+2$) are fully irrational (all angles irrational with $\pi$) if $3<N<\infty$. Rational approximations to their angles and the Hurwitz theorem in number theory are used to define a parameter $h$ that quantifies the irrationality of each triangle. The energy level statistics [spacing distribution $p\left(s\right)$ and spectral rigidity ${\Delta }_3\left(L\right)$] of quantum billiards from this one-parameter family of triangles are investigated. The behavior of $h$ with varying $N$ and the numerically calculated level dynamics are found to be closely related: $h$ exhibits a local maximum at $N=10$, around which agreement with Gaussian orthogonal ensemble (GOE) spectral fluctuations is observed. As $N$ is increased, $h$ decreases and the statistics depart from GOE. Structures appear in $p\left(s\right)$ for $N>120$ and eventually the occurrence of gaps in the distribution for $N\sim 180$ define the onset of a long crossover towards the sequence observed in the integrable limit of the equilateral triangle $(N\to \infty )$.

The method of one-dimensional maps was recently introduced as a means of generating exceptional discretizations of the ${\varphi }^4$ theory, i.e., discrete ${\varphi }^4$ models which support kinks centered at a continuous range of positions relative to the lattice. In this paper, we employ this method to obtain exceptional discretizations of the sine-Gordon equation (i.e., exceptional Frenkel-Kontorova chains). We also use one-dimensional maps to construct a discrete sine-Gordon equation supporting kinks which move with arbitrary velocities without emitting radiation.

In a toroidal plasma confined by a purely toroidal magnetic field with a weak vertical field superimposed a system of convection cells are generated spontaneously, interacting with a background electron density gradient. The dynamics of this interaction is low-dimensional, chaotic, and consistent with solutions of the Lorenz equations in the diffusionless limit.

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of $\rho \simeq 0.64$ without introducing some partial crystallization. The nature of this “random-close-packing” limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of “quasiperfect tetrahedra” grows with the density up to a saturation fraction of $\sim 30\%$ reached at the RCP limit. At this limit the fraction of aggregate “polytetrahedral” structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit ${\rho }_K\simeq 0.66$. Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed.

Dipolar colloidal particles self-assemble into a rich variety of microstructures ranging from co-crystals of unusual symmetry, to open networks (gels) of cross-linked chains of particles. We use molecular dynamics computer simulation to explore the self-assembly, structure, crystallization and/or gelation of systems of colloid particles with permanent dipole moments immersed in a high-dielectric solvent. Particle-particle interactions are modeled with a discontinuous potential. The phase diagram in the temperature-packing fraction plane is calculated. Several types of phases are found in our simulations: ordered phases including face-centered-cubic, hexagonal-close-packed, and body-centered-tetragonal at high packing fractions, and fluid, string-fluid, and gel phases at low packing fractions. The very low volume fraction gel phases and the well-ordered crystal phases are promising for advanced materials applications.

The expression of the surface tension using the virial route has been reinvestigated in order to establish a local version of the surface tension and of its long-range corrections. In fact, giving a local surface tension is very important for the simulation from a methodological viewpoint. It is also of basic interest to associate the profile of the intrinsic part of the surface tension with that of the long-range corrections to make the surface tension calculation consistent between the different approaches that can be used. Working expressions for two-phase systems interacting through dispersion-repulsion (Lennard-Jones) and Coulombic (Ewald summation) interactions are proposed. Different operational expressions of the surface tension are compared in the cases of $n$-pentane, carbon dioxide, and water liquid-vapor equilibria for which the orders of magnitude between the electrostatic and dispersion forces are different.

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.

We suggest that the activation of a single fault by means of preseismic electromagnetic emissions (PEME) is well-described by recently introduced models for earthquake (EQ) dynamics, which have been rooted in a nonextensive framework starting from first principles. The analysis implies that the activation of a single fault is (i) a reduced self-affine image of the regional seismicity covering many geological faults, and (ii) a magnified image of the laboratory seismicity by means of acoustic and electromagnetic emissions. Finally, we study whether characteristic signatures emerged in PEME indicating the transition to the last phase of the EQ preparation process. We use the $q$-Tsallis entropy as a measure of organization. Tsallis entropy gives evidence of state changes leading to the point of global instability: it detects the pattern of alterations in the preseismic electromagnetic signals and is able to discriminate between “injury levels” of the focal area. Importantly, a significant organization increase can be confirmed at the tail of the recorded PEME by means of Tsallis entropy, which is also accompanied by the appearance of persistency. We argue that these footprints may indicate the fracture of the backbone of strong entities that hinders the relative motion of the fault planes.

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent $m$ can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime $t_f$ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life $t_f$ and the characteristic time $t_m$ of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of $t_f$ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of $m$. On the microlevel the distribution of waiting times is found to have a power law behavior with $m$-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements.

The observation that real complex networks have internal structure has important implication for dynamic processes occurring on such topologies. Here we investigate the impact of community structure on a model of information transfer able to deal with both search and congestion simultaneously. We show that networks with fuzzy community structure are more efficient in terms of packet delivery than those with pronounced community structure. We also propose an alternative packet routing algorithm which takes advantage of the knowledge of communities to improve information transfer and show that in the context of the model an intermediate level of community structure is optimal. Finally, we show that in a hierarchical network setting, providing knowledge of communities at the level of highest modularity will improve network capacity by the largest amount.

It is known that the free surface of an axisymmetric viscous film flowing down the outside of a thin vertical fiber under the influence of gravity becomes unstable to interfacial perturbations. We present an experimental study using fluids with different densities, surface tensions, and viscosities to investigate the growth and dynamics of these interfacial perturbations and to test the assumptions made by previous authors. We find that the initial perturbation growth is exponential, followed by a slower phase as the amplitude and wavelength saturate in size. Measurements of the perturbation growth for experiments conducted at low and moderate Reynolds numbers are compared to theoretical predictions developed from linear stability theory. Excellent agreement is found between predictions from a long-wave Stokes flow model [Craster and Matar, J. Fluid Mech. 553, 85 (2006)] and data, while fair to excellent agreement (depending on fiber size) is found between predictions from a moderate-Reynolds-number model [Sisoev et al., Chem. Eng. Sci. 61, 7279 (2006)] and data. Furthermore, we find that a known transition in the longer-time perturbation dynamics from unsteady to steady behavior at a critical flow rate $Q_c$ is correlated with a transition in the rate at which perturbations naturally form along the fiber. For $Q<Q_c$ (steady case), the rate of perturbation formation is constant. As a result, the position along the fiber where perturbations form is nearly fixed, and the spacing between consecutive perturbations remains constant as they travel 2 m down the fiber. For $Q>Q_c$ (unsteady case), the rate of perturbation formation is modulated. As a result, the position along the fiber where perturbations form oscillates irregularly, and the initial speed and spacing between perturbations varies, resulting in the coalescence of neighboring perturbations further down the fiber.

We investigate the band structure of a class of photonic crystals made from only thin wires. Using a different method, we demonstrate that a complete photonic band gap is possible for such materials. Band gap materials normally consist of space filling dielectric or metal, whereas thin wires occupy a very small fraction of the volume. We show that this is related to the large increase in scattering at the Brillouin zone boundary. The method we developed brings together the calculation techniques in three different fields. The first is the calculation of scattering from periodic, tilted antennas, which we improve upon. The second is the standard technique for frequency selective surface design. The third is obtained directly from low energy electron diffraction theory. Good agreements with experiments for left handed materials, negative materials, and frequency selective surfaces are demonstrated.

The relationship between capillary pressure and saturation in a porous medium often exhibits a power-law dependence. The physical basis for this relation has been substantiated by assuming that capillary pressure is directly related to the pore radius. When the pore space of a medium exhibits fractal structure this approach results in a power-law relation with an exponent of $3-D_v$, where $D_v$ is the pore volume fractal dimension. However, larger values of the exponent than are realistically allowed by this result have long been known to occur. Using a thermodynamic formulation for equilibrium capillary pressure we show that the standard result is a special case of the more general exponent $(3-D_v)∕(3-D_s)$ where $D_s$ is the surface fractal dimension of the pores. The analysis reduces to the standard result when $D_s=2$, indicating a Euclidean relationship between a pore’s surface area and the volume it encloses, and allows for a larger value for the exponent than the standard result when $D_s>2$.

Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity-dependent increase upon initial contact and a similarly sharp depth-dependent decrease as the impacting object comes to rest. Examination of the measured forces on the sphere in the vicinity of these features leads to an experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.

We study the distribution of volume fluctuations in experiments and numerical simulations concerning equal-sized sphere packings prepared with different techniques. We show that the distribution of the local volumes (Voronoï cells) and also the distributions of the global volumes (whole samples) follow remarkably well a shifted and rescaled Gamma distribution that we name a $k\text{-Gamma}$ distribution. Such agreement is robust over a broad range of packing fractions and it is observed for several distinct systems. This distribution is characterized by the average packing fraction and a shape parameter “$k$” which is very sensitive to changes in the structural organization. A statistical mechanics approach predicts such $k\text{-Gamma}$ distribution at statistical equilibrium and it links the parameter $k$ with the number of elementary cells which are exchanging volume during the system preparation. The thermodynamical equivalent of $k$ and its relation with the “granular temperature” are also discussed.