Asymptotic Capture-Number and Island-Size Distributions for One-Dimensional Irreversible Submonolayer Growth

Using a set of evolution equations [J.G. Amar {\it et al}, Phys. Rev. Lett. {\bf 86}, 3092 (2001)] for the average gap-size between islands, we calculate analytically the asymptotic scaled capture-number distribution (CND) for one-dimensional irreversible submonolayer growth of point islands. The predicted asymptotic CND is in reasonably good agreement with kinetic Monte-Carlo (KMC) results and leads to a \textit{non-divergent asymptotic} scaled island-size distribution (ISD). We then show that a slight modification of our analytical form leads to an analytic expression for the asymptotic CND and a resulting asymptotic ISD which are in excellent agreement with KMC simulations. We also show that in the asymptotic limit the self-averaging property of the capture zones holds exactly while the asymptotic scaled gap distribution is equal to the scaled CND.Comment: 4 pages, 1 figure, submitted to Phys. Rev.

Universality in two-dimensional Kardar-Parisi-Zhang growth

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of the heights distribution are estimated. Results for the etching model, the ballistic deposition (BD) model and the temperature-dependent body-centered restricted solid-on-solid model (BCSOS) suggest the universality of the absolute value of the skewness S = W_3 / (W_2)^(3/2) and of the value of the kurtosis Q = W_4 / (W_2)^2 - 3. The sign of the skewness is the same of the parameter \lambda of the KPZ equation which represents the process in the continuum limit. The best numerical estimates, obtained from the etching model, are |S| = 0.26 +- 0.01 and Q = 0.134 +- 0.015. For this model, the roughness exponent \alpha = 0.383 +- 0.008 is obtained, accounting for a constant correction term (intrinsic width) in the scaling of the squared interface width. This value is slightly below previous estimates of extensive simulations and rules out the proposal of the exact value \alpha=2/5. The conclusion is supported by results for the ballistic deposition model. Independent estimates of the dynamical exponent and of the growth exponent are 1.605 <= z <= 1.64 and \beta = 0.229 +- 0.005, respectively, which are consistent with the relations \alpha + z = 2 and z = \alpha / \beta.Comment: 8 pages, 9 figures, to be published in Phys. Rev.

Deep Task-Based Analog-to-Digital Conversion

Analog-to-digital converters (ADCs) allow physical signals to be processed using digital hardware. Their conversion consists of two stages: Sampling, which maps a continuous-time signal into discrete-time, and quantization, i.e., representing the continuous-amplitude quantities using a finite number of bits. ADCs typically implement generic uniform conversion mappings that are ignorant of the task for which the signal is acquired, and can be costly when operating in high rates and fine resolutions. In this work we design task-oriented ADCs which learn from data how to map an analog signal into a digital representation such that the system task can be efficiently carried out. We propose a model for sampling and quantization that facilitates the learning of non-uniform mappings from data. Based on this learnable ADC mapping, we present a mechanism for optimizing a hybrid acquisition system comprised of analog combining, tunable ADCs with fixed rates, and digital processing, by jointly learning its components end-to-end. Then, we show how one can exploit the representation of hybrid acquisition systems as deep network to optimize the sampling rate and quantization rate given the task by utilizing Bayesian meta-learning techniques. We evaluate the proposed deep task-based ADC in two case studies: the first considers symbol detection in multi-antenna digital receivers, where multiple analog signals are simultaneously acquired in order to recover a set of discrete information symbols. The second application is the beamforming of analog channel data acquired in ultrasound imaging. Our numerical results demonstrate that the proposed approach achieves performance which is comparable to operating with high sampling rates and fine resolution quantization, while operating with reduced overall bit rate

Comment on ``Phase ordering in chaotic map lattices with conserved dynamics''

Angelini, Pellicoro, and Stramaglia [Phys. Rev. E {\bf 60}, R5021 (1999), cond-mat/9907149] (APS) claim that the phase ordering of two-dimensional systems of sequentially-updated chaotic maps with conserved ``order parameter'' does not belong, for large regions of parameter space, to the expected universality class. We show here that these results are due to a slow crossover and that a careful treatment of the data yields normal dynamical scaling. Moreover, we construct better models, i.e. synchronously-updated coupled map lattices, which are exempt from these crossover effects, and allow for the first precise estimates of persistence exponents in this case.Comment: 3 pages, to be published in Phys. Rev.

Early stage scaling in phase ordering kinetics

A global analysis of the scaling behaviour of a system with a scalar order parameter quenched to zero temperature is obtained by numerical simulation of the Ginzburg-Landau equation with conserved and non conserved order parameter. A rich structure emerges, characterized by early and asymptotic scaling regimes, separated by a crossover. The interplay among different dynamical behaviours is investigated by varying the parameters of the quench and can be interpreted as due to the competition of different dynamical fixed points.Comment: 21 pages, latex, 7 figures available upon request from [email protected]

Particle currents and the distribution of terrace sizes in unstable epitaxial growth

A solid-on-solid model of epitaxial growth in 1+1 dimensions is investigated in which slope dependent upward and downward particle currents compete on the surface. The microscopic mechanisms which give rise to these currents are the smoothening incorporation of particles upon deposition and an Ehrlich-Schwoebel barrier which hinders inter-layer transport at step edges. We calculate the distribution of terrace sizes and the resulting currents on a stepped surface with a given inclination angle. The cancellation of the competing effects leads to the selection of a stable magic slope. Simulation results are in very good agreement with the theoretical findings.Comment: 4 pages, including 3 figure

Multiscaling to Standard Scaling Crossover in the Bray-Humayun Model for Phase Ordering Kinetics

The Bray-Humayun model for phase ordering dynamics is solved numerically in one and two space dimensions with conserved and non conserved order parameter. The scaling properties are analysed in detail finding the crossover from multiscaling to standard scaling in the conserved case. Both in the nonconserved case and in the conserved case when standard scaling holds the novel feature of an exponential tail in the scaling function is found.Comment: 21 pages, 10 Postscript figure

Coarsening of Surface Structures in Unstable Epitaxial Growth

We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is observed. For the lateral size of mounds we obtain $\xi \sim t^{1/z}$ with $z \geq 4$. An analytic treatment within a self-consistent mean-field approximation predicts multiscaling of the height-height correlation function, while the direct numerical solution of the continuum equation shows conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR

Fast coarsening in unstable epitaxy with desorption

Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small amount of desorption dramatically speeds up the coarsening of the mound array, leading to coarsening exponents between 1/3 and 1/2. The underlying mechanism is the faster growth of larger mounds due to their lower evaporation rate.Comment: 4 pages, 4 PostScript figure

Exponents appearing in heterogeneous reaction-diffusion models in one dimension

We study the following 1D two-species reaction diffusion model : there is a small concentration of B-particles with diffusion constant $D_B$ in an homogenous background of W-particles with diffusion constant $D_W$; two W-particles of the majority species either coagulate ($W+W \longrightarrow W$) or annihilate ($W+W \longrightarrow \emptyset$) with the respective probabilities $p_c=(q-2)/(q-1)$ and $p_a=1/(q-1)$; a B-particle and a W-particle annihilate ($W+B \longrightarrow \emptyset$) with probability 1. The exponent $\theta(q,\lambda=D_B/D_W)$ describing the asymptotic time decay of the minority B-species concentration can be viewed as a generalization of the exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D $q$-state Potts model starting from a random initial condition : the W-particles represent domain walls, and the exponent $\theta(q,\lambda)$ characterizes the time decay of the probability that a diffusive "spectator" does not meet a domain wall up to time $t$. We extend the methods introduced by Derrida, Hakim and Pasquier ({\em Phys. Rev. Lett.} {\bf 75} 751 (1995); Saclay preprint T96/013, to appear in {\em J. Stat. Phys.} (1996)) for the problem of persistent spins, to compute the exponent $\theta(q,\lambda)$ in perturbation at first order in $(q-1)$ for arbitrary $\lambda$ and at first order in $\lambda$ for arbitrary $q$.Comment: 29 pages. The three figures are not included, but are available upon reques