arXiv subjects

Joseph O. Indekeu

Publications and source records attributed to Joseph O. Indekeu.

29 records · Page 2Linked to original sources

arXiv2014

Magnetic hierarchical deposition

We consider random deposition of debris or blocks on a line, with block sizes following a rigorous hierarchy: the linear size equals $1/λ^n$ in generation $n$, in terms of a rescaling factor $λ$. Without interactions between the blocks, this model is described by a logarithmic fractal, studied previously, which is characterized by a constant increment of the length, area or volume upon proliferation. We study to what extent the logarithmic fractality survives, if each block is equipped with an Ising (pseudo-)spin $s=\pm 1$ and the interactions between those spins are switched on (ranging from antiferromagnetic to ferromagnetic). It turns out that the dependence of the surface topology on the interaction sign and strength is not trivial. For instance, deep in the ferromagnetic regime, our numerical experiments and analytical results reveal a sharp crossover from a Euclidean transient, consisting of aggregated domains of aligned spins, to an asymptotic logarithmic fractal growth. In contrast, deep into the antiferromagnetic regime the surface roughness is important and is shown analytically to be controlled by vacancies induced by frustrated spins. Finally, in the weak interaction regime, we demonstrate that the non-interacting model is extremal in the sense that the effect of the introduction of interactions is only quadratic in the magnetic coupling strength. In all regimes, we demonstrate the adequacy of a mean-field approximation whenever vacancies are rare. In sum, the logarithmic fractal character is robust with respect to the introduction of spatial correlations in the hierarchical deposition process.

cond-mat.dis-nn↗

arXiv2014

Degree-dependent network growth: From preferential attachment to explosive percolation

We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities $p_k$. To illustrate the techniques and support our findings using Monte-Carlo simulations, we introduce the exemplary linking rule $p_k$ proportional to $k^{-α}$, with $α$ between -1 and plus infinity. This parameter may be used to interpolate between different regimes. For negative $α$, links are most likely attached to high-degree nodes. On the other hand, in case $α>0$, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.

cond-mat.stat-mech↗

arXiv2013

Efficiency at maximum power of a chemical engine

A cyclically operating chemical engine is considered that converts chemical energy into mechanical work. The working fluid is a gas of finite-sized spherical particles interacting through elastic hard collisions. For a generic transport law for particle uptake and release, the efficiency at maximum power $η$ takes the form 1/2+cΔμ+ O(Δμ^2), with 1/2 a universal constant and $Δμ$ the chemical potential difference between the particle reservoirs. The linear coefficient c is zero for engines featuring a so-called left/right symmetry or particle fluxes that are antisymmetric in the applied chemical potential difference. Remarkably, the leading constant in $η$ is non-universal with respect to an exceptional modification of the transport law. For a nonlinear transport model we obtain η= 1/(θ+1), with θ>0 the power of $Δμ$ in the transport equation

physics.chem-ph↗

arXiv2011

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E_c. Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.

cond-mat.stat-mech↗

arXiv2010

Percolation on bipartite scale-free networks

Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with probability proportional to (kq)^(-alpha), where alpha is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.

cond-mat.stat-mech↗

arXiv2009

Biased Percolation on Scale-free Networks

Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in which the probability for an edge between nodes $i$ and $j$ to be retained is proportional to $(k_ik_j)^{-α}$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating functions method. The theory is found to agree quite well with simulations. By introducing an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well described by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous couplings.

cond-mat.stat-mech↗

arXiv2008

How to make a fragile network robust and vice versa

We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-γ}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$ through $p_{ij}\propto(k_{i}k_{j})^{-α}$. By varying the exponent $α$, we interpolate between random ($α=0$) and systematic failure. For $α>0 $ ($<0$) the most (least) connected nodes are depreciated first. This topological bias introduces a characteristic scale in $P(k)$ of the depreciated network, marking a crossover between two distinct power laws. The critical percolation threshold, at which global connectivity is lost, depends both on $γ$ and on $α$. As a consequence, network robustness or fragility can be controlled through fine tuning of the topological bias in the failure process.

cond-mat.dis-nn↗

arXiv2003

Transition temperatures and contact angles in the sequential-wetting scenario of n-alkanes on (salt) water

Alkanes of medium chain length show an unusual wetting behavior on (salt) water, exhibiting a sequence of two changes in the wetting state. When deposited on the water surface at low temperatures, the liquid alkane forms discrete droplets that are interconnected only by a molecularly thin film. On increase of the temperature, there occurs a sudden jump of the film thickness and, at this first-order transition, a mesoscopically thick layer of liquid alkane is formed. Heating the system further leads to a divergence of the film thickness in a continuous manner. While the long-range forces between substrate and adsorbate are responsible for the critical transition, which occurs at the temperature at which the Hamaker constant changes sign, it is primarily the short-range components of the forces that bring about the first-order transition. We calculate the Hamaker constant of the system and show how, within a modified Cahn theory, accurate predictions of the first-order transition temperatures can be obtained for n-alkanes (pentane and hexane) on water and even on brine. Furthermore, we study the variation of the contact angle as a function of temperature.

cond-mat.stat-mech↗

arXiv2003

Specific Heat Discontinuity in Impure Two-Band Superconductors

The Ginzburg-Landau coefficients, and the jump of the specific heat are calculated for a disordered two-band superconductor. We start with the analysis of a more general case arbitrary anisotropy. While the specific heat discontinuity at the critical temperature T_c decreases with increasing disorder, its ratio to the normal state specific heat at T_c increases and slowly converges to the isotropic value. For a strong disorder the deviation from the isotropic value is proportional to the elastic electron scattering time. In the case of a two-band superconductor we apply a simplified model of the interaction independent on momentum within a band. In the framework of this model all thermodynamic values can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific heat discontinuity in MgB_2 and the influence of the disorder on the critical temperature.

cond-mat.supr-con↗

arXiv2003

Effect of ion hydration on the first-order transition in the sequential wetting of hexane on brine

In recent experiments, a sequence of changes in the wetting state (`wetting transitions') has been observed upon increasing the temperature in systems consisting of pentane on pure water and of hexane on brine. This sequence of two transitions is brought about by an interplay of short-range and long-range interactions between substrate and adsorbate. In this work, we argue that the short-range interaction (contact energy) between hexane and pure water remains unchanged due to the formation of a depletion layer (a thin `layer' of pure water which is completely devoid of ions) at the surface of the electrolyte and that the presence of the salt manifests itself only in a modification of the long-range interaction between substrate and adsorbate. In a five-layer calculation considering brine, water, the first layer of adsorbed hexane molecules, liquid hexane, and vapor, we determine the new long-range interaction of brine with the adsorbate {\em across} the water `layer'. According to the recent theory of the excess surface tension of an electrolyte by Levin and Flores-Mena, this water `layer' is of constant, i.e.\ salt-concentration independent, thickness $δ$, with $δ$ being the hydrodynamic radius of the ions in water. Our results are in good agreement with the experimental ones.

cond-mat.stat-mech↗

arXiv2002

Comment on "Anisotropic s-wave superconductivity in MgB_2"

An analytical result for renormalization of the jump of the heat capacity Delta C/C_N by the anisotropy of the order parameter is derived in the framework of the model proposed by Haas and Maki [Phys. Rev. B 65, 020502(R) (2001)], for both prolate and oblate anisotropy. The graph of Delta C/C_N versus the ratio of the gaps on the equator and the pole, Delta_e/Delta_p, of the Fermi surface allows a direct determination of the gap anisotropy parameter Delta_e/Delta_p using data from specific heat measurements.

cond-mat.supr-con↗