Surface-Directed Spinodal Decomposition: A Molecular Dynamics Study

We use molecular dynamics (MD) simulations to study surface-directed spinodal decomposition (SDSD) in unstable binary ($AB$) fluid mixtures at wetting surfaces. The thickness of the wetting layer $R_1$ grows with time $t$ as a power-law ($R_1 \sim t^\theta$). We find that hydrodynamic effects result in a crossover of the growth exponent from $\theta\simeq 1/3$ to $\theta\simeq1$. We also present results for the layer-wise correlation functions and domain length scales.Comment: 29 pages, 13 figures, submitted to PR

Non-Equilibrium Quantum Dissipation

Dissipative processes in non-equilibrium many-body systems are fundamentally different than their equilibrium counterparts. Such processes are of great importance for the understanding of relaxation in single molecule devices. As a detailed case study, we investigate here a generic spin-fermion model, where a two-level system couples to two metallic leads with different chemical potentials. We present results for the spin relaxation rate in the nonadiabatic limit for an arbitrary coupling to the leads, using both analytical and exact numerical methods. The non-equilibrium dynamics is reflected by an exponential relaxation at long times and via complex phase shifts, leading in some cases to an "anti-orthogonality" effect. In the limit of strong system-lead coupling at zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with {\it voltage difference} activation. This is analogous to the equilibrium spin-boson model, where at strong coupling and high temperatures the spin excitation rate manifests temperature activated Gaussian behavior. We find that there is no simple linear relationship between the role of the temperature in the bosonic system and a voltage drop in a non-equilibrium electronic case. The two models also differ by the orthogonality-catastrophe factor existing in a fermionic system, which modifies the resulting lineshapes. Implications for current characteristics are discussed. We demonstrate the violation of pair-wise Coulomb gas behavior for strong coupling to the leads. The results presented in this paper form the basis of an exact, non-perturbative description of steady-state quantum dissipative systems

Exact solutions to the nonlinear dynamics of learning in deep linear neural networks

Despite the widespread practical success of deep learning methods, our theoretical understanding of the dynamics of learning in deep neural networks remains quite sparse. We attempt to bridge the gap between the theory and practice of deep learning by systematically analyzing learning dynamics for the restricted case of deep linear neural networks. Despite the linearity of their input-output map, such networks have nonlinear gradient descent dynamics on weights that change with the addition of each new hidden layer. We show that deep linear networks exhibit nonlinear learning phenomena similar to those seen in simulations of nonlinear networks, including long plateaus followed by rapid transitions to lower error solutions, and faster convergence from greedy unsupervised pretraining initial conditions than from random initial conditions. We provide an analytical description of these phenomena by finding new exact solutions to the nonlinear dynamics of deep learning. Our theoretical analysis also reveals the surprising finding that as the depth of a network approaches infinity, learning speed can nevertheless remain finite: for a special class of initial conditions on the weights, very deep networks incur only a finite, depth independent, delay in learning speed relative to shallow networks. We show that, under certain conditions on the training data, unsupervised pretraining can find this special class of initial conditions, while scaled random Gaussian initializations cannot. We further exhibit a new class of random orthogonal initial conditions on weights that, like unsupervised pre-training, enjoys depth independent learning times. We further show that these initial conditions also lead to faithful propagation of gradients even in deep nonlinear networks, as long as they operate in a special regime known as the edge of chaos.Comment: Submission to ICLR2014. Revised based on reviewer feedbac

Dynamical Local Chirality and Chiral Symmetry Breaking

We present some of the reasoning and results substantiating the notion that spontaneous chiral symmetry breaking (SChSB) in QCD is encoded in local chiral properties of Dirac eigenmodes. Such association is possible when viewing chirality as a dynamical effect, measured with respect to the benchmark of statistically independent left-right components. Following this rationale leads to describing local chiral behavior by a taylor-made correlation, namely the recently introduced correlation coefficient of polarization C_A. In this language, correlated modes (C_A>0) show dynamical preference for local chirality while anti-correlated modes (C_A<0) favor anti-chirality. Our conclusion is that SChSB in QCD can be viewed as dominance of low-energy correlation (chirality) over anti-correlation (anti-chirality) of Dirac sea. The spectral range of local chirality, chiral polarization scale Lambda_ch, is a dynamically generated scale in the theory associated with SChSB. One implication of these findings is briefly discussed.Comment: 8 pages, 4 figures. Talk given at "Quark Confinement and the Hadron Spectrum X", Munich, Germany, Oct. 8-12, 201

Sensory memory for odors is encoded in spontaneous correlated activity between olfactory glomeruli

Sensory memory is a short-lived persistence of a sensory stimulus in the nervous system, such as iconic memory in the visual system. However, little is known about the mechanisms underlying olfactory sensory memory. We have therefore analyzed the effect of odor stimuli on the first odor-processing network in the honeybee brain, the antennal lobe, which corresponds to the vertebrate olfactory bulb. We stained output neurons with a calcium-sensitive dye and measured across-glomerular patterns of spontaneous activity before and after a stimulus. Such a single-odor presentation changed the relative timing of spontaneous activity across glomeruli in accordance with Hebb's theory of learning. Moreover, during the first few minutes after odor presentation, correlations between the spontaneous activity fluctuations suffice to reconstruct the stimulus. As spontaneous activity is ubiquitous in the brain, modifiable fluctuations could provide an ideal substrate for Hebbian reverberations and sensory memory in other neural systems

Quantitative field theory of the glass transition

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.Comment: 6 pages, 2 figures + supplementary information -- a few minor errors of the published version have been fixe

Image Encryption Based on Diffusion and Multiple Chaotic Maps

In the recent world, security is a prime important issue, and encryption is one of the best alternative way to ensure security. More over, there are many image encryption schemes have been proposed, each one of them has its own strength and weakness. This paper presents a new algorithm for the image encryption/decryption scheme. This paper is devoted to provide a secured image encryption technique using multiple chaotic based circular mapping. In this paper, first, a pair of sub keys is given by using chaotic logistic maps. Second, the image is encrypted using logistic map sub key and in its transformation leads to diffusion process. Third, sub keys are generated by four different chaotic maps. Based on the initial conditions, each map may produce various random numbers from various orbits of the maps. Among those random numbers, a particular number and from a particular orbit are selected as a key for the encryption algorithm. Based on the key, a binary sequence is generated to control the encryption algorithm. The input image of 2-D is transformed into a 1- D array by using two different scanning pattern (raster and Zigzag) and then divided into various sub blocks. Then the position permutation and value permutation is applied to each binary matrix based on multiple chaos maps. Finally the receiver uses the same sub keys to decrypt the encrypted images. The salient features of the proposed image encryption method are loss-less, good peak signal-to-noise ratio (PSNR), Symmetric key encryption, less cross correlation, very large number of secret keys, and key-dependent pixel value replacement.Comment: 14 pages,9 figures and 5 tables; http://airccse.org/journal/jnsa11_current.html, 201