In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focus on the plume velocity, and not the whole velocity, and the temperature when studying the scaling behavior. In this paper, a phenomenological theory for the scaling behavior in the central region of confined turbulent thermal convection is presented. The spatial (temporal) plume velocity structure functions are found to have the same scaling behavior as the spatial (temporal) temperature structure functions. For $\tau ⩾{\tau }_b$, where the buoyant scale ${\tau }_b$ is determined in terms of measurable quantities, the scaling exponents of the temporal temperature structure functions and hence those of the temporal plume velocity structure functions are obtained. These results are checked against experimental measurements, and good agreement is found.

We investigate the probability density of rescaled sums of iterates of deterministic dynamical systems, a problem relevant for many complex physical systems consisting of dependent random variables. A central limit theorem (CLT) is valid only if the dynamical system under consideration is sufficiently mixing. For the fully developed logistic map and a cubic map we analytically calculate the leading-order corrections to the CLT if only a finite number of iterates is added and rescaled, and find excellent agreement with numerical experiments. At the critical point of period doubling accumulation, a CLT is not valid anymore due to strong temporal correlations between the iterates. Nevertheless, we provide numerical evidence that in this case the probability density converges to a $q$-Gaussian, thus leading to a power-law generalization of the CLT. The above behavior is universal and independent of the order of the maximum of the map considered, i.e., relevant for large classes of critical dynamical systems.

We present an analytical result for the evolution of the domain-size distribution during the growth of simultaneously nucleated domains. The final stage of this transformation is the well-known Poisson-Voronoi tessellation. The method can be easily extended to the calculation of the probability distribution of any other geometric characteristic. As far as we know, it is the first time that an exact result is given for this classic system.

We study bottle-brush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side chains with approximately 60 monomer units. The SLS and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a wormlike chain with a contour length of $380\mathrm{nm}$ and a persistence length of $17.5\mathrm{nm}$. An analysis of the DLS data confirms these model parameters. The scattering intensities taken at finite concentration can be modeled using the polymer reference interaction site model. It reveals a softening of the bottle-brush polymers caused by their mutual interaction. We demonstrate that the persistence decreases from $17.5\mathrm{nm}$ down to $5\mathrm{nm}$ upon increasing the concentration from dilute solution to the highest concentration $(40.59\mathrm{g}∕\mathrm{l})$ under consideration. The observed softening of the chains is comparable to the theoretically predicted decrease of the electrostatic persistence length of linear polyelectrolyte chains at finite concentrations.

Elastic and quasielastic neutron scattering experiments have been used to investigate the dynamics of methyl groups in a protein-model hydrophobic peptide in solution. The results suggest that, when the hydrophobic side chains are hydrated by a single hydration water layer, the only allowed motions are confined and attributed to librational and rotational movement associated with the methyl groups. They provide unique experimental evidence that the structural and dynamical properties of the interfacial water strongly influence the side-chain dynamics and the activation of diffusive motion.

Numerical and analytical studies of the onset of percolation in high-aspect-ratio fiber fiber systems such as nanotube reinforced polymers available in the literature have consistently modeled fibers as penetrable, straight, capped cylinders, also referred to as spherocylinders. In reality, however, fibers of very high-aspect ratio embedded in a polymer do not come into direct physical contact with each other, let alone exhibit any degree of penetrability. Further, embedded fibers of very high-aspect ratio are often actually wavy, rather than straight. In this two-part paper we address these critical differences between known physical systems, and the presently used spherocylinder percolation model. In Paper I we evaluate the effect of allowing penetration of the model fibers on simulation results by comparing the soft-core and the hard-core approaches to modeling percolation onset. We use Monte Carlo simulations to investigate the relationship between percolation threshold and excluded volume for both modeling approaches. Our results show that the generally accepted inverse proportionality between percolation threshold and excluded volume holds for both models. We further demonstrate that the error introduced by allowing the fibers to intersect is non-negligible, and is a function of both aspect ratio and tunneling distance. Thus while the results of both the soft-core model and hard-core assumptions can be matched to select experimental results, the hard-core model is more appropriate for modeling percolation in nanotubes-reinforced composites. The hard-core model can also potentially be used as a tool in calculating the tunneling distance in composite materials, given the fiber morphology and experimentally derived electrical percolation threshold. In Paper II we investigate the effect of the waviness of the fibers on the onset of percolation in fiber reinforced composites.

The onset of electrical percolation in nanotube-reinforced composites is often modeled by considering the geometric percolation of a system of penetrable, straight, rigid, capped cylinders, or spherocylinders, despite the fact that embedded nanotubes are not straight and do not penetrate one another. In Part I of this work we investigated the applicability of the soft-core model to the present problem, and concluded that the hard-core approach is more appropriate for modeling electrical percolation onset in nanotube-reinforced composites and other high-aspect-ratio fiber systems. In Part II, we investigate the effect of fiber waviness on percolation onset. Previously, we studied extensively the effect of joint morphology and waviness in two-dimensional nanotube networks. In this work, we present the results of Monte Carlo simulations studying the effect of waviness on the percolation threshold of randomly oriented fibers in three dimensions. The excluded volumes of fibers were found numerically, and relationships between these and percolation thresholds for two different fiber morphologies were found. We build on the work of Part I, and extend the results of our soft-core, wavy fiber simulations to develop an analytical solution using the more relevant hard-core model. Our results show that for high- aspect-ratio fibers, the generally accepted inverse proportionality between percolation threshold and excluded volume holds, independent of fiber waviness. This suggests that, given an expression for excluded volume, an analytical solution can be derived to identify the percolation threshold of a system of high-aspect-ratio fibers, including nanotube-reinforced composites. Further, we show that for high aspect ratios, the percolation threshold of the wavy fiber networks is directly proportional to the analytical straight fiber solution and that the constant of proportionality is a function of the nanotube waviness only. Thus the onset of percolation can be adequately modeled by applying a factor based on fiber geometry to the analytical straight fiber solution.

Rotational constraint representing a local external bias generally has a nontrivial effect on the critical behavior of lattice statistical models in equilibrium critical phenomena. In order to study the effect of rotational bias in an out-of-equilibrium situation like self-organized criticality, a two state “quasideterministic” rotational sandpile model is developed here imposing rotational constraint on the flow of sand grains. An extended set of critical exponents are estimated to characterize the avalanche properties at the nonequilibrium steady state of the model. The probability distribution functions are found to obey usual finite size scaling supported by negative time autocorrelation between the toppling waves. The model exhibits characteristics of both deterministic and stochastic sandpile models.

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams (‘‘clouds’’), as the system approaches a nonequilibrium steady state from a disordered initial state. We monitor the dynamic structure factor $S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of the form $S(0,k_y;t)=t^{\beta }\tilde{S}\left(k_y{t}^{\alpha }\right)$. Over a significant range of times, we observe excellent data collapse with $\alpha =1∕2$ and $\beta =1$. The effects of varying filling fraction and driving force are discussed.

We present an exact calculation of the probability density for the work done by an external agent on a two-level system. Due to the external drive, both the transition rates between the two states and their energies depend on time. Within this setting we calculate the probability of every possible sample path of the system evolution and also the work done along any such path. The general procedure yields an evolution equation for the characteristic function of the work. Assuming that the energies change with constant rates, the properties of the work distribution are controlled by a single parameter representing the ratio of the time scales of the driving protocol, and of the internal dynamics, respectively. We calculate the mean work and characterize those sample paths which are not in agreement with the second law. In the slow driving limit, the probability density for the work collapses to a delta function localized at the reversible work. In the strongly nonequilibrium regime, the most probable work is smaller and the mean work is bigger than the reversible work.

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for nonrelativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems, which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It still has the $r^{-6}$ decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.

We study the effect of the interaction’s range on the structural and kinetic properties of a computer-simulated two-dimensional aggregating colloidal system. For this purpose, we considered that the particles of the system interact through a repulsive Yukawa potential which depends on two parameters: the value of the interaction potential between particles in contact $V_0$ and the range of the interaction $\kappa d$. We observed that the increase of the interaction range or $V_0$ provokes the arrangement of the small aggregates in linear structures. The repulsive interactions have also a strong influence on the kinetic behavior of the coagulation process. Indeed, they induce the formation of three different time-separated aggregation regimes. In the first regime (at early states) the aggregation is dominated by the range of the repulsive forces, and the cluster-cluster repulsion increases with the cluster size. The second regime (at intermediate times) is reached when the average cluster size is larger than the interaction range. Here, the cluster-cluster repulsions do not grow anymore with the cluster size, so the probability of overcoming the repulsive barrier is the same for all clusters. This corresponds with the so-called reaction-limited-cluster-aggregation regime, where more than one collision between the clusters is needed to form a bond. The third aggregation regime is found at long aggregation times. In this region the coagulation is mainly determined by the diffusion time and the kinetics becomes diffusion controlled. A physical interpretation for the transition between chain structures and the typical fractals aggregates from the point of view of the range of the interactions is discussed. Moreover, a method has been developed in order to obtain the effect of the interactions with a non-negligible range over the aggregation rates directly from the simulations. The relation between these different regions with the parameters of the interaction potential $V_0$ and $\kappa d$ is analyzed.

The microrheology of viscoelastic fluids containing light-scattering inclusions is measured by depolarized dynamic light scattering (DDLS) from optically anisotropic spherical colloidal probes. The anisotropy of the probes allows us to measure both their translational and the rotational mean squared displacements simultaneously, and DDLS allows us to suppress the light scattered from the inclusions. The storage and loss moduli are determined from both mean squared displacements and the results compared with mechanical measurements.

The three-dimensional structure that causes the coloration of the tropical weevil Pachyrrhynchus congestus pavonius was studied, using a combination of electron microscopy, optical spectroscopy, and numerical modeling. The orange scales that cover the colored rings on the animal’s body were opened, to display the structure responsible for the coloration. This structure is a three-dimensional photonic polycrystal, each grain of which showing a face-centered cubic symmetry. The measured lattice parameter and the observed filling fraction of this structure explain the dominant reflected wavelength in the reddish orange. The long-range disorder introduced by the grain boundaries explains the paradoxical observation that the reflectance, although generated by a photonic crystal, is insensitive to changes in the viewing angle.

Numerical simulations for electrically induced, intracellular calcium release from the endoplasmic reticulum are reported. A two-step model is used for self-consistency. Distributed electrical circuit representation coupled with the Smoluchowski equation yields the ER membrane nanoporation for calcium outflow based on a numerical simulation. This is combined with the continuum Li-Rinzel model and drift diffusion for calcium dynamics. Our results are shown to be in agreement with reported calcium release data. A modest increase (rough doubling) of the cellular calcium is predicted in the absence of extra-cellular calcium. In particular, the applied field of $15\mathrm{kV}∕\mathrm{cm}$ with $60\mathrm{ns}$ pulse duration makes for a strong comparison. No oscillations are predicted and the net recovery period of about $5\min$ are both in agreement with published experimental results. A quantitative explanation for the lack of such oscillatory behavior, based on the density dependent calcium fluxes, is also provided.

We study the role of the surface of the globule and the role of interactions with the solvent for designed-sequence heteropolymers using the random energy model. We investigate the ground-state energy and surface-monomer composition distribution. By comparing the freezing transition in random and designed-sequence heteropolymers, we discuss the effects of design. Based on our results, we are able to show under which conditions the solvation effect improves the quality of the sequence design. Finally, we study sequence-space entropy and discuss the number of available sequences as a function of the imposed requirements for design quality.

Reentrant condensation of DNA in the presence of spermidine (SPD) is studied by gel electrophoresis (GEP). It is found that the reentrant condensation of DNA induced by SPD can produce a reentrant jamming of DNA molecules at the liquid-gel interface during GEP. However, not all the DNA are jammed at the interface indicating that there are different forms of condensed DNA. A model of condensed DNA consisting of two conformations can be used to explain the experimental observations. A phase diagram of the reentrant condensation based on the jamming states of DNA in terms of the length of DNA $\left(L\right)$ and concentration of SPD is constructed. Furthermore, no charge inversion is observed during the reentrant transition.

We examine the quasistatic thermocapillary migration of a gas bubble normal to a solidified interface. The analysis accounts for the deformation of the solid-liquid interface caused by the bubble’s presence. An expression for the distance between the bubble surface and the crystal-melt interface is derived, and used to quantify the dependence of the bubble’s migration velocity on the processing variables and material properties of the directional solidification process.

Inspired by the structure of technological weblike systems, we discuss network evolution mechanisms which give rise to topological properties found in real spatial networks. Thus, we suggest that the peculiar structure of transport and distribution networks is fundamentally determined by two factors. These are the dependence of the spatial interaction range of vertices on the vertex attractiveness (or importance within the network) and on the inhomogeneous distribution of vertices in space. We propose and analyze numerically a simple model based on these generating mechanisms which seems, for instance, to be able to reproduce known structural features of the Internet.

The bouncing-ball billiard is a low-dimensional system with which transport properties of real physical systems can be studied theoretically. We study the bouncing-ball billiard with nonconvex scatterers and small slopes. We show that between the horizontal and vertical motion there is a separation of time scales, which is controlled by the slope of the billiard. We apply the theory of time-scale separation developed by Kantz et al. Physica D 187, 200 (2004). If the vertical motion is chaotic, the horizontal motion is diffusive, but if the vertical motion is (quasi)periodic, there is no diffusion. We confirm the results with numerical simulations. Hence, the order-chaos transition in the vertical degrees of freedom translates into a localization-delocalization transition for the horizontal motion.