We report measurements of the bulk modulus of individual poly($N$-isopropylacrylamide) microgels along their swelling transition. The modulus is determined by measuring the volume deformation of the microgel as a function of osmotic pressure using dextran solutions. We find that the modulus softens through the transition, displaying a nonmonotonous behavior with temperature. This feature is correctly reproduced by the theory of Flory for polymer gels, once the concentration dependence of the solvency parameter is properly incorporated.

Within a mean-field treatment of the interaction between two oppositely charged plates in a salt-free solution, the distance at which a transition from an attractive to a repulsive regime appears can be computed analytically. The mean-field description, however, breaks down under strong Coulombic couplings, which can be achieved at room temperature with multivalent counterions and highly charged surfaces. Making use of the contact theorem and simple physical arguments, we propose explicit expressions for the equation of state in several situations at short distances. The possibility of Bjerrum pair formation is addressed and is shown to have profound consequences on the interactions. To complete the picture, we consider the large-distance limit, from which schematic phase diagram discriminating attractive from repulsive regions can be proposed.

Chaotic patterns in electroconvection of homeotropic nematics, soft-mode turbulence (SMT), and the related spatiotemporal chaos (STC) are discussed, and the quantitative definition of the patterns is considered. The order parameter $S$, obtained directly from the 2D spectra of the patterns, is introduced. The contribution of the Nambu-Goldstone mode and the increase in pattern regularity under the influence of an external magnetic field $\mathbf{H}$ are evaluated. We propose a schematic phase diagram of STC patterns based on the value of $S$.

We use the Maxwell stress tensor to calculate the dielectrophoretic force and electrorotational torque acting on a realistic four-shelled model of the yeast Saccharomyces cerevisiae in a nonuniform rotating electric field generated by four coplanar square electrodes. The comparison of these results with numerical calculations of the dipolar and quadrupolar contributions obtained from an integral equation for the polarization charge density shows the effect of the quadrupole contribution in the proximity of the electrode plane. We also show that under typical experimental conditions the substitution of the multilayered cell by an equivalent cell with homogeneous permittivity underestimates the quadrupole contribution to the force and torque by 1 order of magnitude.

All cells derive nutrition by absorbing some chemical and energy resources from the environment; these resources are used by the cells to reproduce the chemicals within them, which in turn leads to an increase in their volume. In this study we introduce a protocell model exhibiting catalytic reaction dynamics, energy metabolism, and cell growth. Results of extensive simulations of this model show the existence of four phases with regard to the rates of both the influx of resources and cell growth. These phases include an active phase with high influx and high growth rates, an inefficient phase with high influx but low growth rates, a quasistatic phase with low influx and low growth rates, and a death phase with negative growth rate. A mean field model well explains the transition among these phases as bifurcations. The statistical distribution of the active phase is characterized by a power law, and that of the inefficient phase is characterized by a nearly equilibrium distribution. We also discuss the relevance of the results of this study to distinct states in the existing cells.

The coarsening instability typically disrupts steady-state cluster-size distributions. We show that degradation coupled to the cluster size, such as arising from biological proteolysis, leads to a fixed-point cluster size. Stochastic evaporative and condensative fluxes determine the width of the fixed-point size distribution. At the fixed point, we show how the peak size and width depend on number, interactions, and proteolytic rate. This proteolytic size-control mechanism is consistent with the phenomenology of pseudopilus length control in the general secretion pathway of bacteria.

Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity ($S$) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with $1/S>0$. A large constant $S>0$ weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereas $S<0$ strengthens them; oscillations of $S$ further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked.

To develop and test theory-based procedures for modeling two-phase flow through fractures, it is important to be able to compare computational results for a fracture with experiments performed on the exact same fracture. Unfortunately for real fractures, any attempt to image the fracture and to produce a numerical model of the fracture accessible to computer modeling unavoidably results in a coarsening of the resolution, with the very small-scale features of the imaged fracture averaged to produce the numerical representation used in modeling. Contrary to the hope that these high-resolution features would be unimportant, several modeling efforts have shown that such changes in resolution do affect the flow. Therefore, the numerical representation is different from the real fracture because of this unavoidable coarsening of the resolution. To remove the problems caused by the use of different fractures in the experiment and in the model, the fracture used in our experiments was stereographically constructed from the same numerical representation used in the modeling so that the only difference between the experimental “fracture” and the modeling “fracture” is a manufacturing error of approximately 3% or less in the aperture sizes of the manufactured experimental model. Using several models not unlike others in the literature, we modeled injection of air into the water-saturated fracture. The modeling results are compared to experimental results for injection of air into the water-saturated stereolithographically constructed fracture. A comparison between modeling and experimental results for the essentially identical fractures shows a much better detailed agreement than obtained in other studies, which compared experimental flows on the real fracture with modeling results for a lower resolution representation of the real fracture. This suggests that many of the differences between experiment and modeling in previous work resulted from the differences between the experimental and modeling fractures. For our low capillary-number cases, the best agreement with experiment is for a modification of invasion percolation with trapping (IPwt) that included approximations to viscosity ratio effects and to the interfacial tension effects in reducing very short-range curvature.

It is numerically demonstrated by means of a magnetohydrodynamics code that precession can trigger the dynamo effect in a cylindrical container. When the Reynolds number, based on the radius of the cylinder and its angular velocity, increases, the flow, which is initially centrosymmetric, loses its stability and bifurcates to a quasiperiodic motion. This unsteady and asymmetric flow is shown to be capable of sustaining dynamo action in the linear and nonlinear regimes. The magnetic field thus generated is unsteady and quadrupolar. These numerical evidences of dynamo action in a precessing cylindrical container may be useful for an experiment now planned at the Dresden sodium facility for dynamo and thermohydraulic studies in Germany.

We investigate numerically the dynamics of two-dimensional Euler and ideal magnetohydrodynamics (MHD) flows in systems with a finite number of modes, up to ${4096}^2$, for which several quadratic invariants are preserved by the truncation and the statistical equilibria are known. Initial conditions are the Orszag-Tang vortex with a neutral X point centered on a stagnation point of the velocity field in the large scales. In MHD, we observe that the total energy spectra at intermediate times and intermediate scales correspond to the interactions of eddies and waves, $E_T(k)~k^{-3/2}$. Moreover, no pseudodissipative range is visible for either Euler or ideal MHD in two dimensions. In the former case, this may be linked to the existence of a vanishing turbulent viscosity whereas in MHD, the numerical resolution employed may be insufficient. When imposing a uniform magnetic field to the flow, we observe a lack of saturation of the formation of small scales together with a significant slowing down of their equilibration, with however a cutoff independent partial thermalization being reached at intermediate scales.

The oscillation spectrum of a one-dimensional vertical dust string formed inside a glass box on top of the lower electrode in a gaseous electronics conference (GEC) reference cell was studied. A mechanism for creating a single vertical dust string is described. It is shown that the oscillation amplitudes, resonance frequencies, damping coefficients, and oscillation phases of the dust particles separate into two distinct groups. One group exhibits low damping coefficients, increasing amplitudes, and decreasing resonance frequencies for dust particles closer to the lower electrode. The other group shows high damping coefficients but anomalous resonance frequencies and amplitudes. At low oscillation frequencies, the two groups are also separated by a π phase difference. One possible cause for the difference in behavior between the two groups is discussed.

At the GSI Helmholtz center for heavy-ion research combined experiments with heavy ions and laser-produced plasmas are investigated. As a preparation to utilize indirectly heated targets, where a converter hohlraum provides thermal radiation to create a more homogeneous plasma, this converter target has to be characterized. In this paper the latest results of these measurements are presented. Small spherical cavities with diameters between 600 and 750 $\mu$m were heated with laser energies up to 30 J at 532-nm wavelength. Radiation temperatures could be determined by time-resolved as well as time-integrated diagnostics, and maximum values of up to 35 eV were achieved.

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schrödinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.

The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic nonstationary statistical properties of its fluctuations. Here we study this formalism through a statistical mechanics approach, that is, with an auxiliary counting process that maximizes an entropy function associated with the thermodynamic potential. We show that the realizations of this auxiliary process can be obtained after applying a conditional measurement scheme to the original ones, providing is this way an alternative measurement interpretation of the thermodynamic approach. General results are obtained for renewal counting processes, that is, those where the time intervals between consecutive events are independent and defined by a unique waiting time distribution. The underlying statistical mechanics is controlled by the same waiting time distribution, rescaled by an exponential decay measured by the free energy function. A scale invariance, shift closure, and intermittence phenomena are obtained and interpreted in this context. Similar conclusions apply for nonrenewal processes when the memory between successive events is induced by a stochastic waiting time distribution.

We investigate confining mechanisms for Lévy flights under premises of the principle of detailed balance. In this case, the master equation of the jump-type process admits a transformation to the Lévy-Schrödinger semigroup dynamics akin to a mapping of the Fokker-Planck equation into the generalized diffusion equation. This sets a correspondence between above two stochastic dynamical systems, within which we address a (stochastic) targeting problem for an arbitrary stability index $\mu \in (0,2)$ of symmetric Lévy drivers. Namely, given a probability density function, specify the semigroup potential, and thence the jump-type dynamics for which this PDF is actually a long-time asymptotic (target) solution of the master equation. Here, an asymptotic behavior of different $\mu$-motion scenarios ceases to depend on $\mu$. That is exemplified by considering Gaussian and Cauchy family target PDFs. A complementary problem of the reverse engineering is analyzed: given a priori a semigroup potential, quantify how sensitive upon the choice of the $\mu$ driver is an asymptotic behavior of solutions of the associated master equation and thus an invariant PDF itself. This task is accomplished for so-called $\mu$ family of Lévy oscillators.

We investigate the dynamic quantum tunneling between two attractors of a mesoscopic driven Duffing oscillator. We find that, in addition to inducing a remarkable quantum shift of the bifurcation point, the mesoscopic nature also results in a perfect linear scaling behavior for the tunneling rate with the driving distance to the shifted bifurcation point.

Responses of small open oscillator systems to applied external forces have been studied with the use of an exactly solvable classical Caldeira-Leggett model in which a harmonic oscillator (system) is coupled to finite $N$-body oscillators (bath) with an identical frequency (${\omega }_n={\omega }_o$ for $n=1$ to $N$). We have derived exact expressions for positions, momenta, and energy of the system in nonequilibrium states and for work performed by applied forces. A detailed study has been made on an analytical method for canonical averages of physical quantities over the initial equilibrium state, which is much superior to numerical averages commonly adopted in simulations of small systems. The calculated energy of the system which is strongly coupled to a finite bath is fluctuating but nondissipative. It has been shown that the Jarzynski equality is valid in nondissipative nonergodic open oscillator systems regardless of the rate of applied ramp force.

We perform extensive computational studies of two-dimensional static bidisperse disk packings using two distinct packing-generation protocols. The first involves thermally quenching equilibrated liquid configurations to zero temperature over a range of thermal quench rates $r$ and initial packing fractions followed by compression and decompression in small steps to reach packing fractions ${\phi }_J$ at jamming onset. For the second, we seed the system with initial configurations that promote micro- and macrophase-separated packings followed by compression and decompression to ${\phi }_J$. Using these protocols, we generate more than ${10}^4$ static packings over a wide range of packing fraction, contact number, and compositional and positional order. We find that disordered, isostatic packings exist over a finite range of packing fractions in the large-system limit. In agreement with previous calculations, the most dilute mechanically stable packings with ${\phi }_{\min }\approx 0.84$ are obtained for $r>r^{*}$, where $r^{*}$ is the rate above which ${\phi }_J$ is insensitive to rate. We further compare the structural and mechanical properties of isostatic versus hyperstatic packings. The structural characterizations include the contact number, several order parameters, and mixing ratios of the large and small particles. We find that the isostatic packings are positionally and compositionally disordered (with only small changes in a number of order parameters), whereas bond-orientational and compositional order increase strongly with contact number for hyperstatic packings. In addition, we calculate the static shear modulus and normal mode frequencies (in the harmonic approximation) of the static packings to understand the extent to which the mechanical properties of disordered, isostatic packings differ from partially ordered packings. We find that the mechanical properties of the packings change continuously as the contact number increases from isostatic to hyperstatic.

We investigate experimentally the behavior of liquid foams pumped at a given flow rate through a single pore, in the situation where the pore diameter is smaller than the bubble diameter. Results reveal that foam invasion can be observed only within a restricted range of values for the dimensionless flow rate and the foam liquid fraction. Within this foam invasion regime, the liquid content of invading foams is measured to be three times higher than the initial liquid content. Outside this regime, both gas alone and liquid alone invasion regimes can be observed. The gas invasion regime results from the rupture of foam films during local T1, during bubble rearrangements events induced by foam flow, whereas the liquid invasion regime is allowed by the formation of a stable cluster of jammed bubbles at the pore's opening.