It is shown that solitary-wave, kinklike structures can propagate superluminally in two- and four-level amplifying media with strongly damped oscillations of coherences. This is done by solving analytically the Maxwell-Bloch equations in the kinetic limit. It is also shown that the true wave fronts—unlike the pseudo wave fronts of the kinks—must propagate with velocity $c$, so that no violation of special relativity is possible. The conditions of experimental verification are discussed.

We study the stripe rearrangements in microwrinkles subjected to gradual changes in the compression direction. The spatially averaged stripe orientation follows the changing compression direction with a deviation of 3°–4°. Meanwhile, the local stripe orientation stays constant for a certain period and a dislocation gliding nearby causes it to jump suddenly in the direction of compression. This sequence repeatedly occurs over the surface. The regular pattern transiently appears in the stripe orientation as a result of the organized glide motions, indicating the interaction between dislocations.

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. We discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions $1<d⩽4$, in contrast with the mean-field theory, which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.

Key residues in proteins are important to their stability, folding, and functions. They usually are highly conserved and can be identified by sequence or structure alignments. However, these methods can only determine the locations of key residues in sequences and structures and give less information about their physical characters. In this paper, we try to identify key residues by analyzing their inter-residue interactions. The model we study is the ${\mathrm{G}}_{\beta }$ protein domain from transducin. We show that the usual Gaussian network analysis and distance-based contact analysis have difficultly identifying the key residues in this protein, but the contact energies can do it well. We find that most key residues can be located by the lowest contact energies. This enables us to predict and analyze the key residues in other proteins. Our results suggest that contact energy analysis may provide an alternative approach to investigating the folding and stability of proteins.

We present Monte Carlo (MC) simulations of the stretching of a single $30\mathrm{nm}$ chromatin fiber. The model approximates the DNA by a flexible polymer chain with Debye-Hückel electrostatics and uses a two-angle zigzag model for the geometry of the linker DNA connecting the nucleosomes. The latter are represented by flat disks interacting via an attractive Gay-Berne potential. Our results show that the stiffness of the chromatin fiber strongly depends on the linker DNA length. Furthermore, changing the twisting angle between nucleosomes from 90° to 130° increases the stiffness significantly. An increase in the opening angle from 22° to 34° leads to softer fibers for small linker lengths. We observe that fibers containing a linker histone at each nucleosome are stiffer compared to those without the linker histone. The simulated persistence lengths and elastic moduli agree with experimental data. Finally, we show that the chromatin fiber does not behave as an isotropic elastic rod, but its rigidity depends on the direction of deformation: Chromatin is much more resistant to stretching than to bending.

Dynamics of three identical solid spheres falling under gravity in low-Reynolds-number fluid flow is investigated. Stationary solutions are found. Their stability is discussed. Phase portraits for two types of symmetric motions are calculated.

We demonstrate an approach for fabricating photonic crystals with large three-dimensional photonic band gaps (PBG’s) using single-exposure, single-beam, optical interference lithography based on diffraction of light through an optical phase mask. The optical phase mask (OPM) consists of two orthogonally oriented binary gratings joined by a thin, solid layer of homogeneous material. Illuminating the phase mask with a normally incident beam produces a five-beam diffraction pattern which can be used to expose a suitable photoresist and produce a photonic crystal template. Optical-phase-mask Lithography (OPML) is a major simplification from the previously considered multibeam holographic lithography of photonic crystals. The diffracted five-beam intensity pattern exhibits isointensity surfaces corresponding to a diamondlike (face-centered-cubic) structure, with high intensity contrast. When the isointensity surfaces in the interference patterns define a silicon-air boundary in the resulting photonic crystal, with dielectric contrast 11.9 to 1, the optimized PBG is approximately 24% of the gap center frequency. The ideal index contrast for the OPM is in the range of 1.7–2.3. Below this range, the intensity contrast of the diffraction pattern becomes too weak. Above this range, the diffraction pattern may become too sensitive to structural imperfections of the OPM. When combined with recently demonstrated polymer-to-silicon replication methods, OPML provides a highly efficient approach, of unprecedented simplicity, for the mass production of large-scale three-dimensional photonic band-gap materials.

The propagation of high-power large-aperture laser beams in a Kerr medium is considered. A statistical approach is developed for the growth of filaments from small-amplitude small-scale initial modulations. Closed-form expressions are derived for the intensity distribution, contrast, and maximal beam intensity, which are valid up to the blowup of the most intense filament. Numerical experiments are found to be in good agreement with theoretical predictions.

We propose an effective permittivity model to homogenize an array of long thin $ϵ$-negative rods arranged in a periodic lattice. It is proven that the effect of spatial dispersion in this electromagnetic crystal cannot be neglected, and that the medium supports dispersionless modes that guide the energy along the rod axes. It is suggested that this effect may be used to achieve subwavelength imaging at the infrared and optical domains. The reflection problem is studied in detail for the case in which the rods are parallel to the interfaces. Full wave numerical simulations demonstrate the validity and accuracy of the new model.

It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. The most obvious case is the isothermal Rayleigh-Taylor instability when a heavy fluid is placed on top of a light one. In the nonisothermal case, while heating from above, the density stratification is stable in a pure liquid. However, unstable density stratification might be established in a binary mixture with a negative Soret effect in the case of heating from above: the heavier liquid is accumulated on the top of the lighter one. Due to the large differences between viscous, thermal, and diffusion times the system has a tendency to fingering buoyant instabilities. At some moment the flow may be initiated. Near the onset of convection the flow pattern has a columnar convective structure: for a relatively low applied temperature difference $\mathrm{\Delta }T$ the lighter and colder liquid is drawn up in the central part of the cell and the heavier liquid flows down along the walls. For finite size systems the situation is reversed at higher $\mathrm{\Delta }T$. Here we present results of three-dimensional direct numerical simulations of heat and mass transfer in a system with a negative Soret effect. While the development of Soret-induced convection is similar for a wide class of liquids: water based mixtures, colloidal, and polymer solutions, the parameters of the chosen system correspond to a realistic binary mixture of water (90%) and isopropanol (10%) enabling comparison of theoretical predictions with planned experimental studies.

A study—based on simulations and experiments as well as analytical derivations—of the internal structure of the fragmented (“mixed”) state induced by the Rayleigh-Taylor instability at the interface between two fluids is presented. The distribution of sizes and the energy spectrum in the fragmented state are derived from the symmetries exhibited by the data and by dimensional analysis.

We present experimental and theoretical results for the phase behavior of mixtures of oppositely charged globular protein molecules in aqueous solutions containing monovalent salt. These colloidal mixtures are interesting model systems, on the one hand for electrolyte solutions (“colloidal ionic liquids”), and on the other for mixtures of oppositely charged (bio)macromolecules, colloids, micelles, etc., with the range of the electrostatic interactions (Debye length) easily tunable from much smaller to much larger than the particle size, simply by adding different amounts of monovalent salt. In this paper we investigate the phase behavior of such mixtures in the case that equally sized colloids have a large difference in charge magnitude. This is possible at any mixing ratio because small ions compensate any colloidal charge asymmetry. Our experimental system is based on lysozyme, a positively charged “hard” globular protein molecule, and succinylated lysozyme, a chemical modification of lysozyme which is negatively charged. By changing the solution $p\mathrm{H}$ we can adjust the ratio of charge between the two molecules. To describe phase separation into a dilute phase and a dense “complex” phase, a thermodynamic model is set up in which we combine the Carnahan–Starling–van der Waals equation of state with a heterogeneous Poisson-Boltzmann cell model and include the possibility that protein molecules adjust their charge when they move from one phase to the other (charge regulation). The theory uses the nonelectrostatic attraction strength as the only adjustable parameter and reasonably well reproduces the data in that complexation is only possible at intermediate $p\mathrm{H}$, not too asymmetric mixing ratios, and low enough ionic strength and temperature.

By decomposing the Coulomb interaction into a long-distance component appropriate for mean-field theory, and a non-mean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short-distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.

Nervous systems under periodic stimuli display rich dynamical states including mode-locking and chaotic responses, which have been a subject of intense studies in neurodynamics. The bifurcation structure of the Hodgkin-Huxley neuron under sinusoidal stimulus is studied in detail. The mechanisms of the firing onset and rich firing dynamics are studied with the help of the codimension-2 bifurcations, which play the role of the organizing center for myriads of saddle-node, period-doubling, and inverse-flip bifurcations forming the boundaries of the complex mode-locking structure. This study provides a useful insight into the organization of similar bifurcation structures in excitable systems such as neurons under periodic forcing.

The Delaunay tessellation of several sets of real and simplified model protein structures has been used to explore graph theoretic properties of residue contact networks. The system of contacts defined by residues joined by edges in the Delaunay simplices can be thought of as a graph or network and analyzed using techniques from elementary graph theory and the theory of complex networks. Such analysis indicates that protein contact networks have small world character, but technically are not small world networks. This approach also indicates that networks formed by native structures and by most misfolded decoys can be differentiated by their respective graph properties. The characteristic features of residue contact networks can be used for the detection of structural elements in proteins, such as the ubiquitous closed loops consisting of 22–32 consecutive residues, where terminal residues are Delaunay neighbors.

We study numerically the variability of the outbreak of diseases on complex networks. We use a susceptible-infected model to simulate the disease spreading at short times in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time of a node on its degree and its distance to the seed. In particular, we show that the infection time of hubs have non-negligible fluctuations which limit their reliability as early detection stations. Finally, we discuss the effect of the multiplicity of paths between two nodes on the infection time. In particular, we demonstrate that the existence of even long paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies.

Exact theoretical results for the violation of time-dependent fluctuation-dissipation relations in driven dissipative systems are presented. The ratio of the correlation to delayed response in the stochastic model introduced in [Phys. Rev. Lett. 93, 240601 (2004)] is shown to depend on measurement time. The fluctuation temperature defined by this ratio differs both from the temperature of the environment performing the driving, and from other effective temperatures of the system, such as the average energy (or “granular temperature”). General explanations are given for the time independence of the fluctuation temperature for simple measurements or long measurement times.

Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying continuous-time random walk. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.

In wave chaotic scattering, statistical fluctuations of the scattering matrix $S$ and the impedance matrix $Z$ depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, ${\Xi }_z$ and ${\Xi }_s$, where ${\Xi }_z=\mathrm{Var}\left[Z_{ij}\right]∕{\left\{\mathrm{Var}\left[Z_{ii}\right]\mathrm{Var}\left[Z_{jj}\right]\right\}}^{1∕2}$, ${\Xi }_s=\mathrm{Var}\left[S_{ij}\right]∕{\left\{\mathrm{Var}\left[S_{ii}\right]\mathrm{Var}\left[S_{jj}\right]\right\}}^{1∕2}$, and Var[∙] denotes variance. ${\Xi }_z$ is shown to be a universal function of distributed losses within the scatterer. That is, ${\Xi }_z$ is independent of nonuniversal coupling details. This contrasts with ${\Xi }_s$ for which universality applies only in the large loss limit. Explicit results are given for ${\Xi }_z$ for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, Phys. Rev. E 70, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, Phys. Rev. E 59, 2010 (1999); P. B. Warren, J. Chem. Phys. 112, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of de-ionized suspensions.