Christiansennunez9678

We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into edge-disjoint subgraphs and planting frustrated, elementary subproblems that share a common local ground state, which guarantees that the ground state of the entire problem is known a priori. Using population annealing Monte Carlo, we compare the typical hardness of problem classes over a large region of the multidimensional tuning parameter space. SB-297006 purchase Our results show that the problems have a wide range of tunable hardness. Moreover, we observe multiple transitions in the hardness phase space, which we further corroborate using simulated annealing and simulated quantum annealing. By investigating thermodynamic properties of these planted systems, we demonstrate that the harder samples undergo magnetic ordering transitions which are also ultimately responsible for the observed hardness transitions on changing the sample composition.In experiments on membrane protein polyhedral nanoparticles (MPPNs) [Basta et al., Proc. Natl. Acad. Sci. USA 111, 670 (2014)PNASA60027-842410.1073/pnas.1321936111], it has been observed that membrane proteins and lipids can self-assemble into closed lipid bilayer vesicles with a polyhedral arrangement of membrane proteins. In particular, MPPNs formed from the mechanosensitive channel of small conductance (MscS) were found to have the symmetry of the snub cube-a chiral, Archimedean solid-with one MscS protein located at each one of the 24 vertices of the snub cube. It is currently unknown whether MPPNs with heterogeneous protein composition maintain a high degree of symmetry. Inspired by previous work on viral capsid symmetry, we employ here computational modeling to study the symmetry of MPPNs with heterogeneous protein size. We focus on MPPNs formed from MscS proteins, which can exist in closed or open conformational states with distinct sizes. We find that, as an increasing number of closed-state MscS proteins transitions to the open conformational state of MscS, the minimum-energy MscS arrangement in MPPNs follows a strikingly regular pattern, with the dominant MPPN symmetry always being provided by the snub cube. Our results suggest that MPPNs with heterogeneous protein size can be highly symmetric, with a well-defined polyhedral ordering of membrane proteins of different sizes.Compressible lattice Boltzmann model on standard lattices [M. H. Saadat, F. Bösch, and I. V. Karlin, Phys. Rev. E 99, 013306 (2019).2470-004510.1103/PhysRevE.99.013306] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).2470-004510.1103/PhysRevE.95.023305] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.In part I of this two-stage exposition [Pandey, Kumar, and Puri, preceding paper, Phys. Rev. E 101, 022217 (2020)10.1103/PhysRevE.101.022217], we introduced finite-range Coulomb gas (FRCG) models, and developed an integral-equation framework for their study. We obtained exact analytical results for d=0,1,2, where d denotes the range of eigenvalue interaction. We found that the integral-equation framework was not analytically tractable for higher values of d. In this paper, we develop a Monte Carlo (MC) technique to study FRCG models. Our MC simulations provide a solution of FRCG models for arbitrary d. We show that, as d increases, there is a transition from Poisson to Wigner-Dyson classical random matrix statistics. Thus FRCG models provide a route for transition from Poisson to Wigner-Dyson statistics. The analytical formulation obtained in part I, and MC techniques developed in this paper, are used to study banded random matrices (BRMs) and quantum kicked rotors (QKRs). We demonstrate that, for a BRM of bandwidth b and a QKR of chaos parameter α, the appropriate FRCG model has range d=b^2/N=α^2/N, for N→∞. Here, N is the dimensionality of the matrix in the BRM, and the evolution operator matrix in the QKR.Laser wakefield acceleration relies on the excitation of a plasma wave due to the ponderomotive force of an intense laser pulse. However, plasma wave trains in the wake of the laser have scarcely been studied directly in experiments. Here we use few-cycle shadowgraphy in conjunction with interferometry to quantify plasma waves excited by the laser within the density range of GeV-scale accelerators, i.e., a few 10^18cm^-3. While analytical models suggest a clear dependency between the nonlinear plasma wavelength and the peak potential a_0, our study shows that the analytical models are only accurate for driver strength a_0≲1. Experimental data and systematic particle-in-cell simulations reveal that nonlinear lengthening of the plasma wave train depends not solely on the laser peak intensity but also on the waist of the focal spot.Modularity is a key organizing principle in real-world large-scale complex networks. Many real-world networks exhibit modular structures such as transportation infrastructures, communication networks, and social media. Having the knowledge of the shortest paths length distribution between random pairs of nodes in such networks is important for understanding many processes, including diffusion or flow. Here, we provide analytical methods which are in good agreement with simulations on large scale networks with an extreme modular structure. By extreme modular, we mean that two modules or communities may be connected by maximum one link. As a result of the modular structure of the network, we obtain a distribution showing many peaks that represent the number of modules a typical shortest path is passing through. We present theory and results for the case where interlinks are weighted, as well as cases in which the interlinks are spread randomly across nodes in the community or limited to a specific set of nodes.