arXiv subjects

H. J. Herrmann

Publications and source records attributed to H. J. Herrmann.

At least 73 records · Page 4Linked to original sources

arXiv2013

Percolation with long-range correlated disorder

Long-range power-law correlated percolation is investigated using Monte Carlo simulations. We obtain several static and dynamic critical exponents as function of the Hurst exponent $H$ which characterizes the degree of spatial correlation among the occupation of sites. In particular, we study the fractal dimension of the largest cluster and the scaling behavior of the second moment of the cluster size distribution, as well as the complete and accessible perimeters of the largest cluster. Concerning the inner structure and transport properties of the largest cluster, we analyze its shortest path, backbone, red sites, and conductivity. Finally, bridge site growth is also considered. We propose expressions for the functional dependence of the critical exponents on $H$.

cond-mat.stat-mech↗

arXiv2013

Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation

We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and non-relativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wavefunction) propagates in space-time as a classical statistical process (Boltzmann distribution).

quant-ph↗

arXiv2013

Avoiding a Spanning Cluster in Percolation Models

When dynamics in a system proceeds under suppressive external bias, the system can undergo an abrupt phase transition, as it occurs for example in the epidemic spreading. Recently, an explosive percolation (EP) model was introduced in line with such phenomena. The order of the EP transition has not been clarified in a unified framework covering low dimensional systems and the mean-field limit. We introduce a stochastic model, in which a rule for dynamics is designed to avoid the formation of a spanning cluster through competitive selection in Euclidean space. We show by heuristic arguments that, in the thermodynamic limit and depending on a control parameter, the EP transition can be either continuous or discontinuous if $d < d_c$ and is always continuous if $d \geq d_c$, where $d$ is the spatial dimension and $d_c$ the upper critical dimension.

cond-mat.stat-mech↗

arXiv2013

Smart Rewiring for Network Robustness

While new forms of attacks are developed every day to compromise essential infrastructures, service providers are also expected to develop strategies to mitigate the risk of extreme failures. In this context, tools of Network Science have been used to evaluate network robustness and propose resilient topologies against attacks. We present here a new rewiring method to modify the network topology improving its robustness, based on the evolution of the network largest component during a sequence of targeted attacks. In comparison to previous strategies, our method lowers by several orders of magnitude the computational effort necessary to improve robustness. Our rewiring also drives the formation of layers of nodes with similar degree while keeping a highly modular structure. This "modular onion-like structure" is a particular class of the onion-like structure previously described in the literature. We apply our rewiring strategy to an unweighted representation of the World Air Transportation network and show that an improvement of 30% in its overall robustness can be achieved through smart swaps of around 9% of its links.

physics.soc-ph↗

arXiv2013

Relativistic effects on the Richtmyer-Meshkov instability

Theoretical and numerical analysis of the relativistic effects on the Richtmyer-Meshkov (RM) instability reveals new and potentially very useful effects. We find that, in contrast with the non- relativistic case, the growth rate of the RM instability depends strongly on the equation of state of the fluid, opening up the possibility to infer equations of state from experimental observations of the RM instability. As opposed to the non-relativistic case, we also discover that, above a critical value of the fluid velocity, the growth rate of the instability counter-intuitively decreases due to the Lorentz's factor, and vanishes in the ultrarelativistic limit, as the speed of the particles approaches the speed of light. Both effects might prove very useful for leading-edge applications, such as the study of the equation of state of quark-gluon matter, and the design of fast ignition inertial confinement fusion (ICF) schemes. We perform a linear stability analysis to characterize the instability, for an arbitrary equation of state, and implement numerical simulations to study the instability in the non-linear regime, using the equation of state of an ideal gas. Furthermore, based on the numerical results, we propose a general expression that characterizes the long term evolution of the instability.

astro-ph.HE↗

arXiv2013

Kinetic Formulation of the Kohn-Sham Equations for ab initio Electronic Structure Calculations

We introduce a new approach to density functional theory based on kinetic theory, showing that the Kohn-Sham equations can be derived as a macroscopic limit of a suitable Boltzmann kinetic equation in the limit of small mean free path versus the typical scale of density gradients (Chapman-Enskog expansion). To derive the approach, we first write the Schrödinger equation as a special case of a Boltzmann equation for a gas of quasi-particles, with the potential playing the role of an external source that generates and destroys particles, so as to drive the system towards the ground state. The ions are treated as classical particles, using the Born-Oppenheimer dynamics, or by imposing concurrent evolution with the electronic orbitals. In order to provide quantitative support to our approach, we implement a discrete (lattice) model and compute, the exchange and correlation energies of simple atoms, and the geometrical configuration of the methane molecule. Excellent agreement with values in the literature is found.

physics.chem-ph↗

arXiv2013

Gaussian Quadrature and Lattice Discretization of the Fermi-Dirac Distribution for Graphene

We construct a lattice kinetic scheme to study electronic flow in graphene. For this purpose, we first derive a basis of orthogonal polynomials, using as weight function the ultrarelativistic Fermi-Dirac distribution at rest. Later, we use these polynomials to expand the respective distribution in a moving frame, for both cases, undoped and doped graphene. In order to discretize the Boltzmann equation and make feasible the numerical implementation, we reduce the number of discrete points in momentum space to 18 by applying a Gaussian quadrature, finding that the family of representative wave (2+1)-vectors, that satisfies the quadrature, reconstructs a honeycomb lattice. The procedure and discrete model are validated by solving the Riemann problem, finding excellent agreement with other numerical models. In addition, we have extended the Riemann problem to the case of different dopings, finding that by increasing the chemical potential, the electronic fluid behaves as if it increases its effective viscosity.

cond-mat.stat-mech↗

arXiv2013

Geometrical and transport properties of sequential adsorption clusters

We investigate transport properties of percolating clusters generated by irreversible cooperative sequential adsorption (CSA) on square lattices with Arrhenius rates given by ki= q^(ni), where ni is the number of occupied neighbors of the site i, and q a controlling parameter. Our results show a dependence of the prefactors on q and a strong finite size effect for small values of this parameter, both impacting the size of the backbone and the global conductance of the system. These results might be pertinent to practical applications in processes involving adsorption of particles.

cond-mat.stat-mech↗

arXiv2013

Stacked triangular lattice: Percolation properties

The stacked triangular lattice has the shape of a triangular prism. In spite of being considered frequently in solid state physics and materials science, its percolation properties have received few attention. We investigate several non-universal percolation properties on this lattice using Monte Carlo simulation. We show that the percolation threshold is $p_c^\text{bond}=0.186\;02\pm0.000\;02$ for bonds and $p_c^\text{site}=0.262\;40\pm0.000\;05$ for sites. The number of clusters at the threshold per site is $n_c^\text{bond}=0.284\;58\pm0.000\;05$ and $n_c^\text{site}=0.039\;98\pm0.000\;05$. The stacked triangular lattice is a convenient choice to study the RGB model [Sci. Rep. {\bf 2}, 751 (2012)]. We present results on this model and its scaling behavior at the percolation threshold.

cond-mat.stat-mech↗

arXiv2013

Exact evaluation of the cutting path length in a percolation model on a hierarchical network

This work presents an approach to evaluate the exact value of the fractal dimension of the cutting path $d^{CP}_f$ on hierarchical structures with finite order of ramification. This represents the first renormalization group treatment of the universality class of watersheds. By making use of the self-similar property, we show that $d^{CP}_f$ depends only on the average cutting path (CP) of the first generation of the structure. For the simplest Wheastone hierarchical lattice (WHL), we present a mathematical proof. For a larger WHL structure, the exact value of $d^{CP}_f$ is derived based on an computer algorithm that identifies the length of all possible CP's of the first generation.

cond-mat.stat-mech↗

arXiv2013

Lattice Boltzmann model for ultra-relativistic flows

We develop a relativistic lattice Boltzmann model capable of describing relativistic fluid dynamics at ultra-high velocities, with Lorentz factors up to $γ\sim 10$. To this purpose, we first build a new lattice kinetic scheme by expanding the Maxwell-Jüttner distribution function in an orthogonal basis of polynomials and applying an appropriate quadrature, providing the discrete versions of the relativistic Boltzmann equation and the equilibrium distribution. To achieve ultra-high velocities, we include a flux limiter scheme, and introduce the bulk viscosity by a suitable extension of the discrete relativistic Boltzmann equation. The model is validated by performing simulations of shock waves in viscous quark-gluon plasmas and comparing with existing models, finding very good agreement. To the best of our knowledge, we for the first time successfully simulate viscous shock waves in the highly relativistic regime. Moreover, we show that our model can also be used for near-inviscid flows even at very high velocities. Finally, as an astrophysical application, we simulate a relativistic shock wave, generated by, say, a supernova explosion, colliding with a massive interstellar cloud, e.g. molecular gas.

astro-ph.HE↗

arXiv2013

Optimal synchronizability of bearings

Bearings are mechanical dissipative systems that, when perturbed, relax toward a synchronized (bearing) state. Here we find that bearings can be perceived as physical realizations of complex networks of oscillators with asymmetrically weighted couplings. Accordingly, these networks can exhibit optimal synchronization properties through fine tuning of the local interaction strength as a function of node degree [Motter, Zhou, and Kurths, Phys. Rev. E 71, 016116 (2005)]. We show that, in analogy, the synchronizability of bearings can be maximized by counterbalancing the number of contacts and the inertia of their constituting rotor disks through the mass-radius relation, $m\sim r^α$, with an optimal exponent $α=α_{\times}$ which converges to unity for a large number of rotors. Under this condition, and regardless of the presence of a long-tailed distribution of disk radii composing the mechanical system, the average participation per disk is maximized and the energy dissipation rate is homogeneously distributed among elementary rotors.

cond-mat.stat-mech↗

arXiv2013

Hydrodynamic Model for Conductivity in Graphene

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and the existence of a minimum conductivity. The model treats impurities as submerged rigid obstacles, forming a disordered medium through which graphene electrons flow, in close analogy with classical fluid dynamics. To describe the minimum conductivity, we take into account the additional carrier density induced by the impurities in the sample. The model, which predicts the conductivity as a function of the impurity fraction of the sample, is supported by extensive simulations for different values of ${\cal E}$, the dimensionless strength of the electric field, and provides excellent agreement with experimental data.

cond-mat.mes-hall↗

arXiv2013

Ultrarelativistic Transport Coefficients in Two Dimensions

We compute the shear and bulk viscosities, as well as the thermal conductivity of an ultrarelativistic fluid obeying the relativistic Boltzmann equation in 2+1 space-time dimensions. The relativistic Boltzmann equation is taken in the single relaxation time approximation, based on two approaches, the first, due to Marle and using the Eckart decomposition, and the second, proposed by Anderson and Witting and using the Landau-Lifshitz decomposition. In both cases, the local equilibrium is given by a Maxwell-Juettner distribution. It is shown that, apart from slightly different numerical prefactors, the two models lead to a different dependence of the transport coefficients on the fluid temperature, quadratic and linear, for the case of Marle and Anderson-Witting, respectively. However, by modifying the Marle model according to the prescriptions given in Ref.[1], it is found that the temperature dependence becomes the same as for the Anderson-Witting model.

cond-mat.stat-mech↗

arXiv2013

Relativistic Lattice Boltzmann Model with Improved Dissipation

We develop a relativistic lattice Boltzmann (LB) model, providing a more accurate description of dissipative phenomena in relativistic hydrodynamics than previously available with existing LB schemes. The procedure applies to the ultra-relativistic regime, in which the kinetic energy (temperature) far exceeds the rest mass energy, although the extension to massive particles and/or low temperatures is conceptually straightforward. In order to improve the description of dissipative effects, the Maxwell-Juettner distribution is expanded in a basis of orthonormal polynomials, so as to correctly recover the third order moment of the distribution function. In addition, a time dilatation is also applied, in order to preserve the compatibility of the scheme with a cartesian cubic lattice. To the purpose of comparing the present LB model with previous ones, the time transformation is also applied to a lattice model which recovers terms up to second order, namely up to energy-momentum tensor. The approach is validated through quantitative comparison between the second and third order schemes with BAMPS (the solution of the full relativistic Boltzmann equation), for moderately high viscosity and velocities, and also with previous LB models in the literature. Excellent agreement with BAMPS and more accurate results than previous relativistic lattice Boltzmann models are reported.

physics.comp-ph↗

arXiv2012

Watersheds are Schramm-Loewner Evolution curves

We show that in the continuum limit watersheds dividing drainage basins are Schramm-Loewner Evolution (SLE) curves, being described by one single parameter $κ$. Several numerical evaluations are applied to ascertain this. All calculations are consistent with SLE$_κ$, with $κ=1.734\pm0.005$, being the only known physical example of an SLE with $κ<2$. This lies outside the well-known duality conjecture, bringing up new questions regarding the existence and reversibility of dual models. Furthermore it constitutes a strong indication for conformal invariance in random landscapes and suggests that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT) with central charge $c\approx-7/2$.

cond-mat.stat-mech↗

arXiv2012

How to suppress undesired synchronization

It is delightful to observe the emergence of synchronization in the blinking of fireflies to attract partners and preys. Other charming examples of synchronization can also be found in a wide range of phenomena such as, e.g., neurons firing, lasers cascades, chemical reactions, and opinion formation. However, in many situations the formation of a coherent state is not pleasant and should be mitigated. For example, the onset of synchronization can be the root of epileptic seizures, traffic congestion in communication networks, and the collapse of constructions. Here we propose the use of contrarians to suppress undesired synchronization. We perform a comparative study of different strategies, either requiring local or total knowledge of the system, and show that the most efficient one solely requires local information. Our results also reveal that, even when the distribution of neighboring interactions is narrow, significant improvement in mitigation is observed when contrarians sit at the highly connected elements. The same qualitative results are obtained for artificially generated networks as well as two real ones, namely, the Routers of the Internet and a neuronal network.

nlin.AO↗

arXiv2012

How to share underground reservoirs

Many resources, such as oil, gas, or water, are extracted from porous soils and their exploration is often shared among different companies or nations. We show that the effective shares can be obtained by invading the porous medium simultaneously with various fluids. Partitioning a volume in two parts requires one division surface while the simultaneous boundary between three parts consists of lines. We identify and characterize these lines, showing that they form a fractal set consisting of a single thread spanning the medium and a surrounding cloud of loops. While the spanning thread has fractal dimension ${1.55\pm0.03}$, the set of all lines has dimension ${1.69\pm0.02}$. The size distribution of the loops follows a power law and the evolution of the set of lines exhibits a tricritical point described by a crossover with a negative dimension at criticality.

cond-mat.stat-mech↗