The study of correlation structures in DNA sequences is of great interest because it allows us to obtain structural and functional information about underlying genetic mechanisms. In this paper we present a study of the correlation structure of protein coding sequences of DNA based on a recently developed mathematical representation of the genetic code. A fundamental consequence of such representation is that codons can be assigned a parity class (odd-even). Such parity can be obtained by means of a nonlinear algorithm acting on the chemical character of the codon bases. In the same setting the Rumer’s class can be naturally described and a new dichotomic class, the hidden class, can be defined. Moreover, we show that the set of DNA’s base transformations associated to the three dichotomic classes can be put in a compact group-theoretic framework. We use the dichotomic classes as a coding scheme for DNA sequences and study the mutual dependence between such classes. The same analysis is carried out also on the chemical dichotomies of DNA bases. In both cases, the statistical analysis is performed by using an entropy-based dependence metric possessing many desirable properties. We obtain meaningful tests for mutual dependence by using suitable resampling techniques. We find strong short-range correlations between certain combinations of dichotomic codon classes. These results support our previous hypothesis that codon classes might play an active role in the organization of genetic information.

We investigate the quantum kicked rotor in resonance subjected to momentum measurements with a Lévy waiting-time distribution. We find that the system has a sub-ballistic behavior. We obtain an analytical expression for the exponent of the power law of the variance as a function of the characteristic parameter of the Lévy distribution. We also connect the anomalous diffusion found with a fractional dynamics.

Methods to control the dynamics of coupled oscillators have been developed owing to various medical and technological demands. In this study, we develop a method to control coupled oscillators in which the coupling function expressed in a phase model is regulated by the multilinear feedback. The present method has wide applicability because we do not need to measure an individual output from each oscillator, but only measure the sum of the outputs from all the oscillators. Moreover, it allows us to easily control the coupling function up to higher harmonics. The validity of the present method is confirmed through a simulation.

An ion projectile stopping at a velocity smaller than the target electron thermal velocity in a strong magnetic field is investigated within a different diffusion formulation, based on Green-Kubo integrands evaluated in magnetized one component plasma models, respectively framed on target ions and electrons. Analytic expressions are reported for slowing down orthogonal and parallel to an arbitrary large magnetic field, which are free from the usual uncertainties plaguing the standard perturbative derivations. Magnetic and target temperature dependences of the low velocity slowing down are thoroughly detailed for dense plasmas of fast ignition concern and ultracold plasmas envisioned for ion beam cooling, as well.

The homogeneous nucleation in the dust-electron plasma, which is formed in the zone of metal powder combustion products in the premixed laminar two-phase flame, has been studied. The classical nucleation theory has been used to determine the free energy and the critical radius of the nucleus. The influence of nucleus charging as a result of interaction between the nucleus and the electronic component of the plasma on the free energy has been determined. The dependence of the nucleus’ critical radius on the plasma temperature and number density of the plasma’s dust component has been determined. The proposed theoretical model shows that nucleation in the thermal dust-electron plasma is a self-consistent process, which is opposed to changing of the plasma’s disperse structure.

The quasilinear theory of the Wigner-Poisson system in one spatial dimension is examined. Conservation laws and properties of the stationary solutions are determined. Quantum effects are shown to manifest themselves in transient periodic oscillations of the averaged Wigner function in velocity space. The quantum quasilinear theory is checked against numerical simulations of the bump-on-tail and two-stream instabilities. The predicted wavelength of the oscillations in velocity space agrees well with the numerical results.

In a preceding paper, Langer and Mukhopadhyay [Phys. Rev. E 77, 061505 (2008)] studied the diffusive motion of a tagged molecule in an heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation between heterogeneity and stretched-exponential decay of correlations, and we also confirmed that systems of this kind generally exhibit non-Gaussian diffusion on intermediate length and time scales. Here I extend this analysis to higher temperatures approaching the point where the heterogeneities disappear and thermal activation barriers become small. I start by modifying the continuous-time random-walk theory proposed in Langer and Mukhopadhyay and supplement this analysis with an extension of the excitation-chain theory of glass dynamics. I also use a key result from the shear-transformation-zone theory of viscous deformation of amorphous materials. Elements of each of these theories are then used to interpret experimental data for orthoterphenyl, specifially, the diffusion and viscosity coefficients and neutron-scattering measurements of the self-intermediate scattering function. Reconciling the theory with these data sets provides insights into the crossover between super-Arrhenius and Arrhenius dynamics, length scales of spatial heterogeneities, violation of the Stokes-Einstein relation in glass-forming liquids, and the origin of stretched-exponential decay of correlations.

A simulation model is presented, comprising elastic spheres with a short-range attraction. Besides conservative forces, radial and shear friction, and radial noise are added. The model can be used to simulate colloids, granular solids, and powders, and the parameters may be related to experimental systems via the range of attraction and the adhesion energy. The model shares the simplicity and speed of dissipative particle dynamics, yet the predictions are rather nontrivial. We demonstrate that the model predicts the correct scaling relations for fracture of granular solids, and we present a schematic phase diagram. This shows liquid-vapor coexistence for a sufficiently large interaction range, with a surface tension that follows Ising criticality. For smaller interaction range only solid-vapor coexistence is found, but for a very small attractive interaction range stable liquid-vapor coexistence reappears due to pathological stability of the solid phase. At very low temperature the model forms a glassy state.

Shear banding is an important feature of flow in complex fluids. Essentially, shear bands refer to the coexistence of flowing and nonflowing regions in driven material. Understanding the possible sources of shear banding has important implications for a wide range of flow applications. In this regard, quasi-two-dimensional flow offers a unique opportunity to study competing factors that result in shear bands. One proposal for interpretation and analysis is the competition between intrinsic dissipation and an external source of dissipation. In this paper, we report on the experimental observation of the transition between different classes of shear bands that have been predicted to exist in cylindrical geometry as the result of this competition [R. J. Clancy, E. Janiaud, D. Weaire, and S. Hutzlet, Eur. J. Phys. E 21, 123 (2006)].

The interaction between a phase separated polymer network and a liquid crystal was studied across the smectic-$A^{*}$ (Sm-$A^{*}$) to smectic-$C^{*}$ (Sm-$C^{*}$) phase transition of a polymer-stabilized ferroelectric liquid crystal polymerized in the Sm-$A^{*}$ phase. Using precise measurements of the tilt angle and the spontaneous polarization as functions of the external electric field and polymer concentration, the effective coefficients of the Landau expansion of the free energy of the Sm-$C^{*}$ phase have been determined experimentally. The observed polymer concentration dependence of the Landau expansion coefficients is explained using a more general theoretical model which incorporates the effect of polymer networks on the local liquid crystal director configuration. In particular, using experimental estimates of the penetration depth of the polymer network into the liquid crystal, it is shown that the $b$ coefficient calculated from the Landau model increases with polymer concentration, evidencing the relationship determined experimentally.

The shear-induced domain deformation in a lipid monolayer comprised of tilted molecules is studied as a mechanical balance between surface pressure, line tension, electrostatic energy due to the dipole-dipole interaction, hexatic-elastic stress, and viscous stress. It is found that a simple shear can deform a circular domain into an elliptic shape with the long axis inclined 45° from the shear direction. The “ellipse” is elongated in the long axis as shear rate increases, and evolves to a straight or kinked stripe, which was observed as a “shear band” by Fuller’s group [Science 274, 233 (1996)] and “avalanche-like fronts” by Schwaltz’s group [Langmuir 17, 3017 (2001)], at a threshold shear rate. The propagation of stripe-shaped domains is discussed in the context of electrostatic energy. The dependence of the threshold shear rate on surface pressure is predicted in good agreement with observation and can be used to estimate surface viscosity. The shear-induced domain deformation is maintained by the effect of the lattice elastic stress when shear ceases.

We investigate the influence of salt concentration, charge on viral proteins and the length of single-stranded RNA (ssRNA) molecule on the spontaneous assembly of viruses. Only the nonspecific interactions are assumed to guide the assembly, i.e., we exclude any chemical specificity that may lock the viral proteins and ssRNA in preferred configurations. We demonstrate that the electrostatic interactions screened by the salt in the solution impose strong limits on viral composition that can be achieved by spontaneous assembly. In particular, we show that viruses whose ssRNA carries more than twice the amount of charge that is located on the viral proteins, cannot be assembled spontaneously. We find that the spatial distribution of protein charge is important for the energetics of the assembly. We also show that the pressures that act on the viruses as a result of attractive protein-ssRNA electrostatic interactions are at least an order of magnitude smaller than is the case with bacteriophage viruses that contain double-stranded DNA molecule.

The absorption dynamics of two model chromophores of the photoactive yellow protein were studied in gas-phase experiments. Using different time-resolving techniques with an overall sensitivity ranging from seconds down to a few nanoseconds, complex dynamics were revealed for the $p$-coumaric acid anion, involving both fragmentation and electron detachment as possible photoresponse channels. For the trans-thiophenyl-$p$-coumarate model, despite its more complex molecular structure, simpler decay dynamics showing only fragmentation were observed.

A class of conservation laws containing Hamilton’s action integral is introduced for Lagrangian dynamical systems with a single degree of freedom and for the case when the Lagrangian function depends on the second time derivative of the coordinate. The action conservation laws are derived from the invariant properties of the Lagrange-D’Alembert differential variational principle with respect to infinitesimal transformations of the generalized coordinate and time by supposing that the generators of infinitesimal transformations depend on time, a generalized coordinate, and its first and second derivatives with respect to time. These action integral conservation laws are applied to the stability of columns, heat transfer, Thomas-Fermi problems, and other physical phenomena. A direct method for the approximate solution of these problems is combined with the Ritz variational method in order to obtain results of high accuracy.

The moment propagation (MP) method was used to study the transport of a passive scalar by a turbulent fluid. Numerical results show that the MP method does not accurately capture the evolution of a scalar field at moderate Reynolds numbers. A theoretical analysis proves that the diffusivity derived from the MP model depends on fluid velocity, which limits the range of Péclet number. We describe an improved MP model (MP2) which eliminates the velocity-dependent diffusion, leading to more accurate predictions of scalar transport in high-velocity flows; at low velocities both methods give similar results. We test the model for a variety of simple flows and find that accurate results can be obtained at grid Péclet numbers in excess of 10.

This paper is a generalization of the models considered in J. Stat. Phys. 128, 1365 (2007). Using an analogy with free fermions, we compute exactly the large deviation function (LDF) of the energy injected up to time $t$ in a one-dimensional dissipative system of classical spins, where a drift is allowed. The dynamics are $T=0$ asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely, a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the LDF. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.

We propose a mechanism by which wave fronts emanating from a spiral may break far from the spiral core due to intrinsic spatial inhomogeneities. A series of computer simulations are presented to demonstrate how coupling domains, which on their own would not cause breakup, may cause a single spiral to break into many spirals.

Capillary discharge $Z$ pinches have been shown to be efficient drivers for x-ray lasers (XRLs). In this work we examine the possibility of realizing a ${\mathrm{H}}_{\alpha }$ nitrogen recombination laser ($3\to 2$ transition) at $\lambda =13.4\mathrm{nm}$, using a capillary discharge $Z$ pinch. A pulsed power generator with $60\mathrm{kA}$ peak current and $70\mathrm{ns}$ quarter period have been used to generate $Z$-pinch plasma in a $90\text{−}\mathrm{mm}$-long and $5\text{−}\mathrm{mm}$-diameter capillary. The plasma conditions were evaluated experimentally, using a filtered x-ray diode detector and time-integrated spectroscopy. The conditions required for the XRL were analytically estimated based on simple steady-state rate equations and then compared to experimental results. We demonstrated above 10% ${\mathrm{N}}^{7+}$ abundance at pinch time, while at least 50% is required. Then, in the expansion phase, the plasma is cooled in a time less than $5\mathrm{ns}$ to temperatures below $60\mathrm{eV}$, as needed for the recombination laser. These results suggest that the required conditions for nitrogen-recombination lasing could be achieved in a capillary discharge $Z$ pinch, but a higher-power driver might be needed.

Interacting populations often create complicated spatiotemporal behavior, and understanding it is a basic problem in the dynamics of spatial systems. We study the two-species case by simulations of a host-parasitoid model. In the case of coexistence, there are spatial patterns leading to noise-sustained oscillations. We introduce a measure for the patterns, and explain the oscillations as a consequence of a time-scale separation and noise. They are linked together with the patterns by letting the spreading rates depend on instantaneous population densities. Applications are discussed.

Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green’s function for the Laplacian in a three-dimensional (3D) domain with a Dirac mass on the boundary. In addition to the usual 3D Coulomb singularity, this Green’s function also has an additional weaker logarithmic singularity. By calculating the coefficient of this logarithmic singularity, we calculate the second term in the asymptotic expansion of the narrow escape time and in the expansion of the principal eigenvalue of the Laplace equation with mixed Dirichlet-Neumann boundary conditions, with small Dirichlet and large Neumann parts. We also determine the leakage flux of Brownian particles that diffuse from a source to an absorbing target on a reflecting boundary of a domain, if a small perforation is made in the reflecting boundary.