We have studied experimentally the angular distributions of fusion neutrons from plasmas of multi-keV ion temperature, created by $40\mathrm{fs}$, multi-TW laser pulses in dense plumes of ${\mathrm{D}}_2$ and ${\mathrm{CD}}_4$ clusters. A slight anisotropy in the neutron emission is observed. We attribute this anisotropy to the fact that the differential cross section for DD fusion is anisotropic even at low collision energies, and this, coupled with the geometry of the gas jet target, leads to beam-target neutrons that are slightly directed. The qualitative features of this anisotropy are confirmed by Monte Carlo simulations.

Soliton perturbation theory based on the inverse scattering transform method is applied to the derivative nonlinear Schrödinger equation, which describes nonlinear Alfvén waves propagating quasiparallel to the external magnetic field. Radiative effects are considered. Spectral distributions of the emitted energy and magnetic helicity rates (in the wave number domain) are calculated analytically. Several forms of perturbations are considered, including the finite electric conductivity, the effect of resonant particles (nonlinear Landau damping), and the influence of the random inhomogeneity of the plasma density. The space structure of the radiative field is determined for a perturbation in the form of the finite electric conductivity.

Combining dynamic renormalization with equation-free computational tools, we study the apparently asymptotically self-similar evolution of void distribution dynamics in the diffusion-deposition problem proposed by Stinchcombe and Depken [Phys. Rev. Lett. 88, 125701 (2002)]. We illustrate fixed point and dynamic approaches, forward as well as backward in time; these can be used to accelerate simulators of glassy dynamic phenomena.

The dynamics in the onset of a Hagen-Poiseuille flow of an incompressible liquid in a channel of circular cross section is well-studied theoretically. We use an eigenfunction expansion in a Hilbert space formalism to generalize the results to channels of an arbitrary cross section. We find that the steady state is reached after a characteristic time scale $\tau ={(\mathcal{A}∕\mathcal{P})}^2(1∕\nu )$, where $\mathcal{A}$ and $\mathcal{P}$ are the cross-sectional area and perimeter, respectively, and $\nu$ is the kinematic viscosity of the liquid. For the initial dynamics of the flow rate $Q$ for $t⪡\tau$ we find a universal linear dependence, $Q\left(t\right)=Q_{\infty }(\alpha ∕\mathcal{C})(t∕\tau )$, where $Q_{\infty }$ is the asymptotic steady-state flow rate, $\alpha$ is the geometrical correction factor, and $\mathcal{C}={\mathcal{P}}^2∕\mathcal{A}$ is the compactness parameter. For the long-time dynamics $Q\left(t\right)$ approaches $Q_{\infty }$ exponentially on the time scale $\tau$, but with a weakly geometry-dependent prefactor of order unity, determined by the lowest eigenvalue of the Helmholz equation.

Enyzme kinetics are cyclic. We study a Markov renewal process model of single-enzyme turnover in nonequilibrium steady state (NESS) with sustained concentrations for substrates and products. We show that the forward and backward cycle times have identical nonexponential distributions: ${\Theta }_{+}\left(t\right)={\Theta }_{-}\left(t\right)$. This equation generalizes the Haldane relation in reversible enzyme kinetics. In terms of the probabilities for the forward $\left(p_{+}\right)$ and backward $\left(p_{-}\right)$ cycles, $k_{B}T\ln (p_{+}∕p_{-})$ is shown to be the chemical driving force of the NESS, $\mathrm{\Delta }\mu$. More interestingly, the moment generating function of the stochastic number of substrate cycle $\nu \left(t\right)$, $⟨e^{-\lambda \nu \left(t\right)}⟩$, follows the fluctuation theorem in the form of Kurchan-Lebowitz-Spohn-type symmetry. When $\lambda =\mathrm{\Delta }\mu ∕k_{B}T$, we obtain the Jarzynski-Hatano-Sasa-type equality $⟨e^{-\nu \left(t\right)\mathrm{\Delta }\mu ∕k_{B}T}⟩$ $\equiv$ 1 for all $t$, where $\nu \mathrm{\Delta }\mu$ is the fluctuating chemical work done for sustaining the NESS. This theory suggests possible methods to experimentally determine the nonequilibrium driving force in situ from turnover data via single-molecule enzymology.

The equilibrium shapes of biological structures as diverse as plant tendrils and bacterial filaments can be altered by externally imposed stresses of sufficient duration. We study the simplest model for this morphoelasticity—a filament whose intrinsic curvatures relax to the local curvatures—and illustrate its properties in the context of dynamic Euler buckling and writhing. When a thrust or twist is ramped in time the effective elastic properties of the filament depend on the load rate. Slow ramps interrupted by removal of the external forces can leave in equilibrium any of a whole continuum of buckled shapes. Morphoelastic relaxation can also allow a filament to bypass a bifurcation.

We investigate the triangular-lattice antiferromagnetic Ising model with a spatially anisotropic next-nearest-neighbor ferromagnetic coupling, which was first discussed by Kitatani and Oguchi. By employing the effective geometric factor, we analyze the scaling dimensions of the operators around the Berezinskii-Kosterlitz-Thouless (BKT) transition lines, and determine the global phase diagram. Our numerical data exhibit that two types of BKT-transition lines separate the intermediate critical region from the ordered and disordered phases, and they do not merge into a single curve in the antiferromagnetic region. We also estimate the central charge and perform some consistency checks among scaling dimensions in order to provide the evidence of the six-state clock universality. Further, we provide an analysis of the shapes of boundaries based on the crossover argument.

The fractional translational diffusion of a particle in a double-well potential (excluding inertial effects) is considered. The position correlation function and its spectrum are evaluated using a fractional probability density diffusion equation (based on the diffusion limit of a fractal time random walk). Exact and approximate solutions for the dynamic susceptibility describing the position response to a small external field are obtained. The exact solution is given by matrix continued fractions while the approximate solution relies on the exponential separation of the time scales of the fast “intrawell” and low overbarrier relaxation processes associated with the bistable potential. It is shown that knowledge of the characteristic relaxation times for normal diffusion allows one to predict accurately the anomalous relaxation behavior of the system for all relevant time scales.

We investigate the dynamics of granular materials confined in a radial Hele-Shaw cell, during central air injection. The behavior of this granular system, driven by its interstitial fluid, is studied both experimentally and numerically. This allows us to explore the associated pattern formation process, characterize its features and dynamics. We classify different hydrodynamic regimes as function of the injection pressure. The numerical model takes into account the interactions between the granular material and the interstitial fluid, as well as the solid-solid interactions between the grains and the confining plates. Numerical and experimental results are comparable, both to reproduce the hydrodynamical regimes experimentally observed, as well as the dynamical features associated to fingering and compacting.

Using computer simulations, we establish an approach for creating defect-free, periodically ordered polymeric materials. The system involves $ABC$ ternary mixtures where the $A$ and $B$ components undergo a reversible photochemical reaction. In addition, all three components are mutually immiscible and undergo phase separation. Through the simulations, we model the effects of illuminating a three-dimensional (3D) sample with spatially and temporally dependent light irradiation. Experimentally, this situation can be achieved by utilizing both a uniform background light and a spatially localized, higher intensity light, and then rastering a higher-intensity light over the 3D sample. We first focus on the case where the higher-intensity light is held stationary and focused in a distinct region within the system. The $C$ component is seen to displace the $A$ and $B$ within this region and replicate the pattern formed by the higher-intensity light. In effect, one can write a pattern of $C$ onto the $AB$ binary system by focusing the higher-intensity light in the desired arrangement. We isolate the conditions that are necessary for producing clearly written patterns of $C$ (i.e., for obtaining sharp interfaces between the $C$ and $A∕B$ domains). We next consider the effect of rastering a higher-intensity light over this sample and find that this light “combs out” defects in the $AB$ blend as it moves through the system. The resulting material displays a defect-free structure that encompasses both a periodic ordering of the $A$ and $B$ domains and a well-defined motif of $C$. In this manner, one can create hierarchically patterned materials that exhibit periodicity over two distinct length scales. The approach is fully reversible, noninvasive, and points to a novel means of patterning with homopolymers, which normally do not self-assemble into periodic structures.

Building upon our previous report [Veum et al., Phys. Rev. E 17, 020701(R) (2005)] involving two compounds, we have performed a systematic study of the temperature variation of film tension above the bulk isotropic transition in freestanding films to include a total of six smectic liquid-crystal compounds. Consistent with the previous results, the tension increases sharply with temperature above the transition, the tension-temperature slope is proportional to the film’s thickness, and the data can be interpreted in the context of theoretical models for layer thinning. Our data suggest that both molecular weight and bulk phase appearing below its isotropic phase play important roles in the slope values.

Over the last $15\text{years}$, the possible existence of a cubatic mesophase, possessing cubic orientational order (i.e., along three mutually orthogonal axes) but no translational one, has been addressed theoretically, and predicted in some cases, where the investigated interaction models involved hard-core repulsion only; on the other hand, no experimental realizations of such a phase are known at the time being. The present paper addresses a very simple cubatic mesogenic lattice model, involving continuous interactions; we consider particles possessing $O_h$ symmetry, whose centers of mass are associated with a three-dimensional simple-cubic lattice; the pair potential is taken to be isotropic in orientation space, and restricted to nearest neighboring sites; let the two orthonormal triads {${\mathbf{u}}_j$, $j=1,2,3$} and {${\mathbf{v}}_k$, $k=1,2,3$} define orientations of a pair of interacting particles, and let $f_{jk}={\mathbf{v}}_j\bullet {\mathbf{u}}_k$. The interaction model studied here is defined by the simplest nontrivial (quartic) polynomial in the scalar products $f_{jk}$, consistent with the assumed symmetry and favoring orientational order; it is, so to speak, the cubatic counterpart of the Lebwohl-Lasher model for uniaxial nematics. The model was investigated by mean field theory and Monte Carlo simulation, and found to produce a low-temperature cubatically ordered phase, undergoing a first order transition to the isotropic phase at higher temperature; the mean field treatment yielded results in reasonable qualitative agreement with simulation.

A phenomenological model is proposed to analyze the influence of the incident light intensity on the photoinduced anisotropy of an azobenzene-containing polymer film. The optical anisotropy was generated in the films by the incidence of linearly polarized light and monitored by transmittance measurements.

The fluctuation theorems for the currents and the dissipated work are considered for molecular motors which are driven out of equilibrium by chemical reactions. Because of the molecular fluctuations, these nonequilibrium processes are described by stochastic models based on a master equation. Analytical expressions are derived for the fluctuation theorems, allowing us to obtain predictions on the work dissipated in the motor as well as on its rotation near and far from thermodynamic equilibrium. We show that the fluctuation theorems provide a method to determine the affinity or thermodynamic force driving the motor. This affinity is given in terms of the free enthalpy of the chemical reactions. The theorems are applied to the ${\mathrm{F}}_1$ rotary motor which turns out to be a stiff system typically functioning in the nonlinear regime of nonequilibrium thermodynamics. We show that this nonlinearity confers a robustness to the functioning of the molecular motor.

Our experiments on viscous fingering of air into oil contained between closely spaced plates reveal two selection rules for the fjords of oil that separate fingers of air. (Fjords are the building blocks of solutions of the zero-surface-tension Laplacian growth equation.) Experiments in rectangular and circular geometries yield fjords with base widths ${\lambda }_c∕2$, where ${\lambda }_c$ is the most unstable wavelength from a linear stability analysis. Further, fjords open at an angle of $8.0°\pm 1.0°$. These selection rules hold for a wide range of pumping rates and fjord lengths, widths, and directions.

A modular structure, in which groups of tightly connected nodes could be resolved as separate entities, is a property that can be found in many complex networks. In this paper, we propose a algorithm for identifying communities in networks. It is based on a local measure, so-called loop coefficient that is a generalization of the clustering coefficient. Nodes with a large loop coefficient tend to be core inner community nodes, while other vertices are usually peripheral sites at the borders of communities. Our method gives satisfactory results for both artificial and real-world graphs, if they have a relatively pronounced modular structure. This type of algorithm could open a way of interpreting the role of nodes in communities in terms of the local loop coefficient, and could be used as a complement to other methods.

This paper reports an experimental study on the correlation between the deviation from Gaussianity of the probability density function (PDF) of a fluctuating scalar and the dependence of the scalar dissipation on the scalar itself in turbulent flows. The study demonstrates that the departure of the scalar PDF from Gaussianity reflects the degree to which the dissipation rate depends statistically on the scalar. Of important significance, present results obtained from wake and jet flows, together with those deduced from previous work on various turbulent flows, appear to point to a generic expression for the total correlation. This expression suggests that the analytical result of O’Brien and Jiang [Phys. Fluids A 3, 3121 (1991)], derived for homogeneous turbulence, should be also valid for inhomogeneous turbulence. That is, the statistical independence of the scalar dissipation and the scalar itself appears to act as the sufficient and necessary condition for the scalar PDF to be Gaussian in any stationary turbulence. It follows that the independence assumption, often used in combustion modeling, is reasonable only in the flow region where the scalar PDF is closely Gaussian.

We investigated adiabatic changes in a near-critical fluid on acoustic time scales using an ultrasensitive interferometer. A sound emitted by very weak continuous heating caused a stepwise adiabatic change at its front with a density change of order ${10}^{-7}\mathrm{g}∕{\mathrm{cm}}^3$ and a temperature change of order ${10}^{-5}\mathrm{K}$. Very small heat inputs at a heater produced short acoustic pulses with width of order $10\mathrm{\mu }\mathrm{s}$, which were broadened as they moved through the cell and interacted with the boundaries. The pulse broadening became enhanced near the critical point. We also examined theoretically how sounds are emitted from a heater and how applied heat is transformed into mechanical work. Our predictions agree well with our data.

This paper considers the time evolution of disperse systems in which binary coagulation and a source of fresh particles govern the temporal changes to the particle mass spectra. The source is assumed to produce fresh particles at a constant rate. The Smoluchowski equation describing the time evolution of the particle mass spectrum is solved exactly for the coagulation kernel proportional to the product of masses of two coalescing particles. It is shown that after a critical time $t_c$ a gel forms in the system and the sol spectrum becomes an algebraic function of the particle mass at $t=t_c$. It begins to shrink after the critical time due to the mass loss supporting the growth of the gel mass. The pre- and post-critical behavior of the mass spectrum and its integral characteristics (total particle number and mass concentrations) are investigated for the source productivity $I\left(g\right)$ dropping down algebraically with the particle mass $g$ as $I\left(g\right)\propto g^{-\gamma }$. The critical particle mass spectrum is proved to be a universal function of $g$ (it drops down as $g^{-5∕2}$) if the third moment of $I\left(g\right)$ is finite $(\gamma >4)$. Otherwise $(3<\gamma \le 4)$ this and other critical exponents begin to depend on $\alpha$. Still the mass spectrum remains self-similar, i.e., it depends on a combination of $g$ and $t$. At smaller $\gamma$ the gelation process is shown to begin at $t=0$. All critical characteristics of the particle mass spectrum are determined for this case.