arXiv subjects

Hans J. Herrmann

Publications and source records attributed to Hans J. Herrmann.

At least 37 records · Page 2Linked to original sources

arXiv2019

Collapse of orthotropic spherical shells

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy.

cond-mat.soft↗

arXiv2019

A universal approach for drainage basins

Drainage basins are essential to Geohydrology and Biodiversity. Defining those regions in a simple, robust and efficient way is a constant challenge in Earth Science. Here, we introduce a model to delineate multiple drainage basins through an extension of the Invasion Percolation-Based Algorithm (IPBA). In order to prove the potential of our approach, we apply it to real and artificial datasets. We observe that the perimeter and area distributions of basins and anti-basins display long tails extending over several orders of magnitude and following approximately power-law behaviors. Moreover, the exponents of these power laws depend on spatial correlations and are invariant under the landscape orientation, not only for terrestrial, but lunar and martian landscapes. The terrestrial and martian results are statistically identical, which suggests that a hypothetical martian river would present similarity to the terrestrial rivers. Finally, we propose a theoretical value for the Hack's exponent based on the fractal dimension of watersheds, $γ=D/2$. We measure $γ=0.54 \pm 0.01$ for Earth, which is close to our estimation of $γ\approx 0.55$. Our study suggests that Hack's law can have its origin purely in the maximum and minimum lines of the landscapes.

physics.comp-ph↗

arXiv2019

Sequential disruption of the shortest path in critical percolation

We investigate the effect of sequentiallydisrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two paths. The sequential approach allows to study spatial correlations. We find the lengths of the segments of successively constant differences in length to be uncorrelated. Simultaneously, we study the distance between red bonds. We find the probability distributions for the enclosed areas A, the differences in length $Δl$, and the lengths between the redbonds $l_r$ to follow power law distributions. Using maximum likelihood estimation and extrapolation we find the exponents $β$ = 1.38 $\pm$ 0.03 for $Δl$, $α$ = 1.186 $\pm$ 0.008 for A and $δ$ = 1.64 $\pm$ 0.025 for thedistribution of $l_r$.

cond-mat.stat-mech↗

arXiv2019

Quantized alternate current on curved graphene

Based on the numerical solution of the quantum lattice Boltzmann method in curved space, we predict the onset of a quantized alternating current on curved graphene sheets. Such numerical prediction is verified analytically via a set of semi-classical equations relating the Berry curvature to real space curvature. The proposed quantised oscillating current on curved graphene could form the basis for the implementation of quantum information processing algorithms.

cond-mat.mes-hall↗

arXiv2019

CFD simulation of the wind field over a terrain with sand fences: Critical spacing for the protected soil area

Sand fences are often erected to reduce wind speed, prevent aeolian soil erosion, and induce sand deposition and dune formation in areas affected by sand encroachment and desertification. However, the search for the most efficient array of fences by means of field experiments alone poses a challenging task given that field experiments are affected by weather conditions. Here we apply Computational Fluid Dynamic simulations to investigate the three-dimensional structure of the turbulent wind field over an array of fences of different sizes, porosity and spacing. Our goal is to perform a quantitative analysis of this structure in the absence of saltation or suspension transport, as first step toward the development of a continuum simulation of the aeolian soil in presence of the fences. We find that the area of soil protected against direct aerodynamic entrainment has two regimes, depending on the spacing $L_x$ between the fences. When $L_x$ is smaller than a critical value $L_{xc}$, the wake zones associated with each fence are inter-connected (regime A), while these wake zones appear separated from each other (regime B) when $L_x$ exceeds this critical value of spacing. The system undergoes a second order phase transition at $L_x = L_{xc}$, with the cross-wind width of the protected zone scaling with $\left[{1-{L}_x}/{L}_{xc}\right]^β$ in regime A, with $β\approx 0.32$. Our findings have implication for a better understanding of aeolian transport in the presence of sand fences, as well as to develop optimization strategies for measures to protect soils from wind erosion.

physics.flu-dyn↗

arXiv2019

Landau levels in wrinkled and rippled graphene sheets

We study the discrete energy spectrum of curved graphene sheets in the presence of a magnetic field. The shifting of the Landau levels is determined for complex and realistic geometries of curved graphene sheets. The energy levels follow a similar square root dependence on the energy quantum number as for rippled and flat graphene sheets. The Landau levels are shifted towards lower energies proportionally to the average deformation and the effect is larger compared to a simple uni-axially rippled geometry. Furthermore, the resistivity of wrinkled graphene sheets is calculated for different average space curvatures and shown to obey a linear relation. The study is carried out with a quantum lattice Boltzmann method, solving the Dirac equation on curved manifolds.

cond-mat.mes-hall↗

arXiv2019

A Boundary-Spheropolygon Element Method for Stress Determination and Breakage Modelling of Particles

We present a boundary-spheropolygon element method (BSEM), that combines the boundary integral method (BIM) and the spheropolygon-based discrete element method (SEM). The interaction between particles is simulated via the SEM, and the sub-particle stress (stress inside the grains) is calculated by BIM. The framework of BSEM is presented. Then the accuracy and efficiency of the method are analysed by comparison with both analytical solutions and a well-established finite element method (ABAQUS). The results demonstrate that BSEM could efficiently provide instant sub-particle stress for irregular particles with an optimized compromise between computational time and accuracy. The effect of particles aspect ratio, coordination number and heterogeneity on the sub-particle stress are discussed through parametric studies. Key conclusions on particle breakage are derived based on the analysis of the distribution of the sub-particle tensile stress. The simulation results suggest that BSEM could overcome most of the disadvantages of existing numerical methods and must be used for advanced simulations of particle breakage

cond-mat.soft↗

arXiv2019

Behavior of confined granular beds under cyclic thermal loading

We investigate the mechanical behavior of a confined granular packing of irregular polyhedral particles under repeated heating and cooling cycles by means of numerical simulations with the Non-Smooth Contact Dynamics method. Assuming a homogeneous temperature distribution as well as constant temperature rate, we study the effect of the container shape, and coefficients of thermal expansions on the pressure buildup at the confining walls and the density evolution. We observe that small changes in the opening angle of the confinement can lead to a drastic peak pressure reduction. Furthermore, the displacement fields over several thermal cycles are obtained and we discover the formation of convection cells inside the granular material having the shape of a torus. The root mean square of the vorticity is then calculated from the displacement fields and a quadratic dependency on the ratio of thermal expansion coefficients is established.

cond-mat.soft↗

arXiv2019

Evolution of fragment size distributions from the crushing of granular materials

We study the fragment size distributions after crushing of single and many particles under uniaxial compression inside a cylindrical container by means of numerical simulations. Under the assumption that breaking goes through the bulk of the particle we obtain the size distributions of fragments for both cases after large displacements. For the single particle crushing, this fragmentation mechanism produces a log-normal size distribution, which deviates from the power-law distribution of fragment sizes for the packed bed. We show that as the breaking process evolves, a power-law dependency on the displacement is present for the single grain, while for the many grains system, the distribution converges to a steady state. We further investigate the force networks and the average coordination number as a function of the particle size, which gives inside about the origin of the power-law distributions for the granular assembly under uniaxial compression.

cond-mat.soft↗

arXiv2018

Avalanche Dynamics and Correlations in Neural Systems

The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression of a system acting close to a critical point. This chapter focuses on temporal correlations and avalanche dynamics in the spontaneous activity of cortex slice cultures and in the resting fMRI BOLD signal. Long-range correlations are investigated by means of the scaling of power spectra and of Detrended Fluctuations Analysis. The existence of 1/f decay in the power spectrum, as well as of power-law scaling in the root mean square fluctuations function for the appropriate balance of excitation and inhibition suggests that long-range temporal correlations are distinctive of "healthy brains". The corresponding temporal organization of neuronal avalanches can be dissected by analyzing the distribution of inter-event times between successive events. In rat cortex slice cultures this distribution exhibits a non-monotonic behavior, not usually found in other natural processes. Numerical simulations provide evidences that this behavior is a consequence of the alternation between states of high and low activity, leading to a dynamic balance between excitation and inhibition that tunes the system at criticality. In this scenario, inter-times show a peculiar relation with avalanche sizes, resulting in a hierarchical structure of avalanche sequences. Large avalanches correspond to low-frequency oscillations, and trigger cascades of smaller avalanches that are part of higher frequency rhythms. The self-regulated balance of excitation and inhibition observed in cultures is confirmed at larger scales, i.e. on fMRI data from resting brain activity, and appears to be closely related to critical features of avalanche activity.

cond-mat.stat-mech↗

arXiv2018

Percolation on Isotropically Directed Lattice

We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We derive exact results for the percolation threshold on planar lattices, and present a conjecture for the value the percolation-threshold for in any lattice. We also identify presumably universal critical exponents, including a fractal dimension, associated with the strongly-connected components both for planar and cubic lattices. These critical exponents are different from those associated either with standard percolation or with directed percolation.

cond-mat.dis-nn↗

arXiv2018

Confining massless Dirac particles in two-dimensional curved space

Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.

cond-mat.mes-hall↗

arXiv2018

Perturbing the Shortest Path on a Critical Directed Square Lattice

We investigate the behaviour of the shortest path on a directed two-dimensional square lattice for bond percolation at the critical probability $p_c$ . We observe that flipping an edge lying on the shortest path has a non-local effect in the form of power-law distributions for both the differences in shortest path lengths and for the minimal enclosed areas. Using maximum likelihood estimation and extrapolation we find the exponents $α= 1.36 \pm 0.01$ for the path length differences and $β= 1.186 \pm 0.001$ for the enclosed areas.

cond-mat.stat-mech↗

arXiv2018

Clogging at Pore Scale and Pressure Induced Erosion

Introducing a model to study deposition and erosion of single particles at microscopic scale, we investigate the clogging and erosive processes in a pore. The particle diameter, concentration, and adhesive forces rule the way particles are deposited, and therefore, characterize the clogging process. We study the hydraulic pressure that induces erosive bursts and conclude that this pressure depends linearly on the deposited volume and inversely on the pores' diameter. While cohesion does not play an important role for erosive bursts, the adhesion is the main force initiating clogging and when overcome by the hydraulic pressure, erosive bursts are triggered. Finally, we show how the magnitude of erosive bursts depends on the pore length, particle diameter and pore size.

physics.flu-dyn↗

arXiv2018

Fully dissipative relativistic lattice Boltzmann method in two dimensions

In this paper, we develop and characterize the fully dissipative Lattice Boltzmann method for ultra-relativistic fluids in two dimensions using three equilibrium distribution functions: Maxwell-Jüttner, Fermi-Dirac and Bose-Einstein. Our results stem from the expansion of these distribution functions up to fifth order in relativistic polynomials. We also obtain new Gaussian quadratures for square lattices that preserve the spatial resolution. Our models are validated with the Riemann problem and the limitations of lower order expansions to calculate higher order moments are shown. The kinematic viscosity and the thermal conductivity are numerically obtained using the Taylor-Green vortex and the Fourier flow respectively and these transport coefficients are compared with the theoretical prediction from Grad's theory. In order to compare different expansion orders, we analyze the temperature and heat flux fields on the time evolution of a hot spot.

physics.flu-dyn↗

arXiv2018

Elastic backbone defines a new transition in the percolation model

The elastic backbone is the set of all shortest paths. We found a new phase transition at $p_{eb}$ above the classical percolation threshold at which the elastic backbone becomes dense. At this transition in $2d$ its fractal dimension is $1.750\pm 0.003$, and one obtains a novel set of critical exponents $β_{eb} = 0.50\pm 0.02$, $γ_{eb} = 1.97\pm 0.05$, and $ν_{eb} = 2.00\pm 0.02$ fulfilling consistent critical scaling laws. Interestingly, however, the hyperscaling relation is violated. Using Binder's cumulant, we determine, with high precision, the critical probabilities $p_{eb}$ for the triangular and tilted square lattice for site and bond percolation. This transition describes a sudden rigidification as a function of density when stretching a damaged tissue.

cond-mat.stat-mech↗

arXiv2018

Fluid structure interaction with curved space lattice Boltzmann

We present a novel method for fluid structure interaction (FSI) simulations where an original 2nd-order curved space lattice Boltzmann fluid solver (LBM) is coupled to a finite element method (FEM) for thin shells. The LBM can work independently on a standard lattice in curved coordinates without the need for interpolation, re-meshing or an immersed boundary. The LBM distribution functions are transformed dynamically under coordinate change. In addition, force and momentum can be calculated on the nodes exactly in any geometry. Furthermore, the FEM shell is a complete numerical tool with implementations such as growth, self-contact and strong external forces. We show resolution convergent error for standard tests under metric deformation. Mass and volume conservation, momentum transfer, boundary-slip and pressure maintenance are verified through specific examples. Additionally, a brief deformation stability analysis is carried out. Next, we study the interaction of a square fluid flow channel to a deformable shell. Finally, we simulate a flag at moderate Reynolds number, air flow channel. The scheme is limited to small deformations of O(10%) relative to domain size, by improving its stability the method can be naturally extended to multiple applications without further implementations.

physics.comp-ph↗

arXiv2018

Explicit size distributions of failure cascades redefine systemic risk on finite networks

How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain or changing parameters and missing information. In infinitely large networks, the average cascade size can often be well estimated by established approaches building on local tree approximations and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not even need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to $10^{7}$ and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.

physics.soc-ph↗