Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as $R = [B \tau]^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(\delta t,\bar{t})$, where $\delta t = k^{1/n} B |\tau_2-\tau_1|$ and $\bar{t} = k^{1/n} B (\tau_1+\tau_2)/2$. Both analytically and numerically, the covariance is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the small-$\bar{t}$ limit and $\delta t/\bar{t} ^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{\tau_1^{2n}+\tau_2^{2n}}),\tau_1/\tau_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $\lambda \approx 4.47$, violating an upper bound conjectured by Fisher and Huse.Comment: RevTex: 11 pages + 12 figures, submitted to PR

Electron Tomography Analysis of Thylakoid Assembly and Fission in Chloroplasts of a Single-Cell C4 plant, Bienertia sinuspersici

Bienertia sinuspersici is a single-cell C4 plant species of which chlorenchyma cells have two distinct groups of chloroplasts spatially segregated in the cytoplasm. The central vacuole encloses most chloroplasts at the cell center and confines the rest of the chloroplasts near the plasma membrane. Young chlorenchyma cells, however, do not have large vacuoles and their chloroplasts are homogenous. Therefore, maturing Bienertia chlorenchyma cells provide a unique opportunity to investigate chloroplast proliferation in the central cluster and the remodeling of chloroplasts that have been displaced by the vacuole to the cell periphery. Chloroplast numbers and sizes increased, more notably, during later stages of maturation than the early stages. Electron tomography analyses indicated that chloroplast enlargement is sustained by thylakoid growth and that invaginations from the inner envelope membrane contributed to thylakoid assembly. Grana stacks acquired more layers, differentiating them from stroma thylakoids as central chloroplasts matured. In peripheral chloroplasts, however, grana stacks stretched out to a degree that the distinction between grana stacks and stroma thylakoids was obscured. In central chloroplasts undergoing division, thylakoids inside the cleavage furrow were kinked and severed. Grana stacks in the division zone were disrupted, and large complexes in their membranes were dislocated, suggesting the existence of a thylakoid fission machinery.11Ysciescopu

Information capacity in the weak-signal approximation

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.Comment: 11 pages, 4 figures; accepted for publication in Physical Review

Oscillator model for dissipative QED in an inhomogeneous dielectric

The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantised electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.Comment: 24 pages, 1 figur

Stability of a Nonequilibrium Interface in a Driven Phase Segregating System

We investigate the dynamics of a nonequilibrium interface between coexisting phases in a system described by a Cahn-Hilliard equation with an additional driving term. By means of a matched asymptotic expansion we derive equations for the interface motion. A linear stability analysis of these equations results in a condition for the stability of a flat interface. We find that the stability properties of a flat interface depend on the structure of the driving term in the original equation.Comment: 14 pages Latex, 1 postscript-figur

Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.Comment: To appear in PRE, figures available on reques

Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction

The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived, from which the density and correlation functions can be calculated. We find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for $d < 4$, with \D = n_0-C^\prime n_0^{d/2} + \dots, where $C$ is a universal constant, and $C^\prime$ is non-universal. The calculation is extended to the case of unequal diffusion constants $D_A \neq D_B$, resulting in a new amplitude but the same exponent. For $d \le 2$ a controlled calculation is not possible, but a heuristic argument is presented that the results above give at least the leading term in an $\epsilon = 2-d$ expansion. Finally, we address reaction zones formed in the steady-state by opposing currents of $A$ and $B$ particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq. (6.12) corrected, and a moderate rewriting of the introduction. Accepted for publication in J. Stat. Phy

Ocean acidification reduces hardness and stiffness of the Portuguese oyster shell with impaired microstructure: a hierarchical analysis

The rapidly intensifying process of ocean acidification (OA) due to anthropogenic CO2 is not only depleting carbonate ions necessary for calcification but also causing acidosis and disrupting internal pH homeostasis in several marine organisms. These negative consequences of OA on marine calcifiers, i.e. oyster species, have been very well documented in recent studies; however, the consequences of reduced or impaired calcification on the end-product, shells or skeletons, still remain one of the major research gaps. Shells produced by marine organisms under OA are expected to show signs of dissolution, disorganized microstructure and reduced mechanical properties. To bridge this knowledge gap and to test the above hypothesis, we investigated the effect of OA on juvenile shells of the commercially important oyster species, Magallana angulata, at ecologically and climatically relevant OA levels (using pH 8.1, 7.8, 7.5, 7.2). In lower pH conditions, a drop of shell hardness and stiffness was revealed by nanoindentation tests, while an evident porous internal microstructure was detected by scanning electron microscopy. Crystallographic orientation, on the other hand, showed no significant difference with decreasing pH using electron back-scattered diffraction (EBSD). These results indicate the porous internal microstructure may be the cause of the reduction in shell hardness and stiffness. The overall decrease of shell density observed from micro-computed tomography analysis indicates the porous internal microstructure may run through the shell, thus inevitably limiting the effectiveness of the shell's defensive function. This study shows the potential deterioration of oyster shells induced by OA, especially in their early life stage. This knowledge is critical to estimate the survival and production of edible oysters in the future ocean