arXiv subjects

Muhittin Mungan

Publications and source records attributed to Muhittin Mungan.

32 records · Page 2Linked to original sources

arXiv2013

Exact results for a toy model exhibiting dynamic criticality

In this article we discuss an exactly solvable, one-dimensional, periodic toy charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103}, 46002 (2013)]. In particular, driving the system with a uniform force, we show that the depinning threshold configuration is an explicit function of the underlying disorder, as is the evolution from the negative threshold to the positive threshold, the latter admitting a description in terms of record sequences. This evolution is described by an avalanche algorithm, which identifies a sequence of static configurations that are stable at successively stronger forcing, and is useful both for analysis and simulation. We focus in particular on the behavior of the polarization $P$, which is related to the cumulative avalanche size, as a function of the threshold force minus the current force $(F_{\mathrm{th}} - F)$, as this has been the focus of several prior numerical and analytical studies of CDW systems. The results presented are rigorous, with exceptions explicitly indicated, and show that the depinning transition in this model is indeed a dynamic critical phenomenon.

math-ph↗

arXiv2013

Subthreshold behavior and avalanches in an exactly solvable Charge Density Wave system

We present a toy charge density wave (CDW) model in 1d exhibiting a depinning transition with threshold force and configurations that are explicit. Due to the periodic boundary conditions imposed, the threshold configuration has a set of topological defects whose location and number depend on the realization of the random phases. Approaching threshold, these defects are relocated by avalanches whose size dependence on the external driving force $F$ is described by a record-breaking process. We find that the depinning transition in this model is a critical phenomenon, with the cumulative avalanche size diverging near threshold as $(F_{\rm th} - F)^{-2}$. The exact avalanche size distributions and their dependence on the control parameter $(F_{\rm th} - F)$ are obtained. Remarkably, the scaling exponents associated with the critical behavior depend on (1) the initial conditions and (2) the relationship between the system size and the pinning strength.

cond-mat.stat-mech↗

arXiv2010

Frenkel-Kontorova Models, Pinned Particle Configurations and Burgers Shocks

We analyze the relationship between the lowest energy configurations of an infinite harmonic chain of particles in a periodic potential and the evolution of characteristics in a periodically-forced inviscid Burgers equation. The shock discontinuities in the the Burgers evolution arise from thermodynamical considerations and play an important role as they separate out flows related to lowest energy configurations from those associated with higher energies. We study in detail the exactly solvable case of an external potential consisting of parabolic segments, and calculate analytically the lowest energy configurations, as well as excited states containing discommensurations.

cond-mat.stat-mech↗

arXiv2010

Stability of Maximum likelihood based clustering methods: exploring the backbone of classifications (Who is keeping you in that community?)

Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them, some of which involve inference methods using either Bayesian or Maximum Likelihood approaches. In this article, we study a statistical model designed for detecting clusters based on connection similarity. The basic assumption of the model is that the graph was generated by a certain grouping of the nodes and an Expectation Maximization algorithm is employed to infer that grouping. We show that the method admits further development to yield a stability analysis of the groupings that quantifies the extent to which each node influences its neighbors group membership. Our approach naturally allows for the identification of the key elements responsible for the grouping and their resilience to changes in the network. Given the generality of the assumptions underlying the statistical model, such nodes are likely to play special roles in the original system. We illustrate this point by analyzing several empirical networks for which further information about the properties of the nodes is available. The search and identification of stabilizing nodes constitutes thus a novel technique to characterize the relevance of nodes in complex networks.

physics.soc-ph↗

arXiv2009

Nanoepitaxy on quasicrystal surfaces

In film growth on quasicrystalline surfaces, the epitaxy-imposed ordering cannot compete with the stable bulk phases of thick films due to absence of translational order in the structure of the substrate. Energetically, this renders the formation of crystalline domains in the native structure of the film material more favorable while their global orientation is prescribed by the quasicrystalline order. We present experimental results on the dissociative chemisorption of oxygen on the decagonal surface of Al$_{70}$Co$_{15}$Ni$_{15}$ as well as molecular-dynamics simulations of the diffusion of adatoms on the surface of the partially covered substrate.

cond-mat.mtrl-sci↗

arXiv2008

Bulk and surface structure of the clean and adsorbate-covered decagonal Al-Co-Ni quasicrystal

We review our Al adsorption experiments on the tenfold-symmetry surface of the decagonal Al-Co-Ni quasicrystal and present computational simulations of adsorption on a structural model based on a fundamental Al-Co cluster with 20 Ådiameter, symmetry $\bar{10}2m$, and 8 Åperiodicity. This cluster is the building unit of $τ^2$-Al$_{13}$Co$_4$, from which, by a sequence of minor changes, the structures of the phases in the stability region of decagonal Al-Co-Ni can be derived. The model used for the decagonal Al$_{70}$Co$_{15}$Ni$_{15}$ is an idealized model with a two-layer periodicity (4 Å) and no chemical or structural disorder. We find that the bulk and surface properties of this model are in good agreement with experiments. Our molecular-dynamics simulations of Al adsorption reproduce the experimental results and show that by varying the thermal relaxation rates of the adsorbed layer, a variety of different surface morphologies can be achieved. We also present our recent experiments on dissociative adsorption of oxygen on the decagonal surface.

cond-mat.mtrl-sci↗

arXiv2007

Inversion method for content-based networks

In this paper, we generalize a recently introduced Expectation Maximization (EM) method for graphs and apply it to content-based networks. The EM method provides a classification of the nodes of a graph, and allows to infer relations between the different classes. Content-based networks are ideal models for graphs displaying any kind of community or/and multipartite structure. We show both numerically and analytically that the generalized EM method is able to recover the process that led to the generation of such networks. We also investigate the conditions under which our generalized EM method can recover the underlying contents-based structure in the presence of randomness in the connections. Two entropies, Sq and Sc, are defined to measure the quality of the node classification and to what extent the connectivity of a given network is content-based. Sq and Sc are also useful in determining the number of classes for which the classification is optimal.

physics.soc-ph↗

arXiv2007

Deposition of Atoms on a Quasicrystalline Substrate: Molecular-Dynamics Study in 3 Dimensions

We study the three-dimensional structure formation when atoms are deposited onto a substrate with a decagonal quasicrystalline order. Molecular-dynamicscalculations show that the adsorbate layer consists of ordered nano-scale domains with orientations determined by the underlying substrate symmetry. Depending on the relative strength of the interactions of adsorbate atoms with each other and with the substrate atoms, different morphologies are observed ranging from layer-by-layer growth to cluster formation. We also find that the film thickness likewise affects the overall structure of the growing film: Depending on the relative strength of the interaction between adsorbate atoms, a structural transition of the configuration of the adsorbate layers closest to the substrate can occur as the number of deposited layers increases.

cond-mat.mtrl-sci↗

arXiv2007

Dynamics of Three Agent Games

We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games.

physics.soc-ph↗

arXiv2006

Spontaneous Self-Assembly of Transcription Factor Based Gene Regulation Networks

We model the transcription factor based regulation network of yeast using a content-based network model that mimicks the recognition of binding motifs on the regulatory regions of the genes. We are thereby able to faithfully reproduce many of the topological features of the gene regulatory network of yeast once the parameters of the yeast genome, in particular the distribution of information coded by the "binding sequences" within the promoter regions is provided as input. The length distribution for the promoter regions is fixed by comparing the k-core analysis of the model network with that of yeast. Our results strongly point to the possibility that the observed topological features are generic to networks formed via sequence-matching between random strings obeying certain length distributions.

q-bio.MN↗

arXiv2005

String Matching and 1d Lattice Gases

We calculate the probability distributions for the number of occurrences $n$ of a given $l$ letter word in a random string of $k$ letters. Analytical expressions for the distribution are known for the asymptotic regimes (i) $k \gg r^l \gg 1$ (Gaussian) and $k,l \to \infty$ such that $k/r^l$ is finite (Compound Poisson). However, it is known that these distributions do now work well in the intermediate regime $k \gtrsim r^l \gtrsim 1$. We show that the problem of calculating the string matching probability can be cast into a determining the configurational partition function of a 1d lattice gas with interacting particles so that the matching probability becomes the grand-partition sum of the lattice gas, with the number of particles corresponding to the number of matches. We perform a virial expansion of the effective equation of state and obtain the probability distribution. Our result reproduces the behavior of the distribution in all regimes. We are also able to show analytically how the limiting distributions arise. Our analysis builds on the fact that the effective interactions between the particles consist of a relatively strong core of size $l$, the word length, followed by a weak, exponentially decaying tail. We find that the asymptotic regimes correspond to the case where the tail of the interactions can be neglected, while in the intermediate regime they need to be kept in the analysis. Our results are readily generalized to the case where the random strings are generated by more complicated stochastic processes such as a non-uniform letter probability distribution or Markov chains. We show that in these cases the tails of the effective interactions can be made even more dominant rendering thus the asymptotic approximations less accurate in such a regime.

cond-mat.stat-mech↗

arXiv2005

Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.

q-bio.MN↗

arXiv1998

Determining Pair Interactions from Structural Correlations

We examine metastable configurations of a two-dimensional system of interacting particles on a quenched random potential landscape and ask how the configurational pair correlation function is related to the particle interactions and the statistical properties of the potential landscape. Understanding this relation facilitates quantitative studies of magnetic flux line interactions in type II superconductors, using structural information available from Lorentz microscope images or Bitter decorations. Previous work by some of us supported the conjecture that the relationship between pair correlations and interactions in pinned flux line ensembles is analogous to the corresponding relationship in the theory of simple liquids. The present paper aims at a more thorough understanding of this relation. We report the results of numerical simulations and present a theory for the low density behavior of the pair correlation function which agrees well with our simulations and captures features observed in experiments. In particular, we find that the resulting description goes beyond the conjectured classical liquid type relation and we remark on the differences.

cond-mat.supr-con↗

arXiv1993

q-Oscillators, q-Epsilon Tensor, q-Groups

Considering a multi-dimensional $q$-oscillator invariant under the (non quantum) group $U(n)$, we construct a $q$-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this $q$-epsilon tensor is shown to yield the quantum group $SL_{q}(n)$ and establishes the relationship of the $U(n)$ invariant $q$-oscillator to quantum groups and quantum group related oscillators. Furthermore the $q$-epsilon tensor provides the connection between $SL_{q}(n)$ and the volume element of the quantum hyper plane.

hep-th↗