A large class of evolutionary processes can bemodeled by a rule that involves self-replication of some physical quantity with a nonlocal rescaling. We show that a class of such models is exactly solvable in the discrete as well as the continuum limit and can represent several physical situations, as varied as from the formation of galaxies in some cosmological models to growth of bacterial cult...

We study the spin-1/2 chain with nearest neighbor (κ1) and next-nearest neighbor (κ2) interactions in the regime κ2 ≫ κ1, which is equivalent to two chains with a ‘zig-zag’ interaction. In the continuum limit, this system is described in term of two coupled level-1 WZW field theories. We illustrate its equivalence with four off-critical Ising models (Majorana fermions). This description is used...

We combine experiments, large scale simulations and continuum models to study the emergence of coherent structures in a suspension of magnetically driven microrollers sedimented near a floor. Collective hydrodynamic effects are predominant in this system, leading to strong density-velocity coupling. We characterize a uniform suspension and show that density waves propagate freely in all directi...

In this talk, I will give an overview of the theoretical status of staggered Lattice QCD with the “fourth-root trick.” In this regularization of QCD, a separate staggered quark field is used for each physical flavor, and the inherent four-fold multiplicity that comes with the use of staggered fermions is removed by taking the fourth root of the staggered determinant for each flavor. At nonzero ...

Self-consistent Hamiltonian formulation of scalar theory on the null plane is constructed following Dirac method. The theory contains also constraint equations. They would give, if solved, to a nonlinear and nonlocal Hamiltonian. The constraints lead us in the continuum to a different description of spontaneous symmetry breaking since, the symmetry generators now annihilate the vacuum. In two e...

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...

Abstract. Using the theory of Lp-graphons [C. Borgs et al., preprint, arXiv:1401.2906, 2014; C. Borgs et al., preprint, arXiv:1408.0744, 2014], we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specifically, we show that the solutions of the initial value problems for the discrete models can be approximated by those of an appropr...

The elastic moduli of vortex crystals in anisotropic superconductors are frequently involved in the investigation of their phase diagram and transport properties. We provide a detailed analysis of the harmonic eigenvalues ~normal modes! of the vortex lattice for general values of the magnetic field strength, going beyond the elastic continuum regime. The detailed behavior of these wave-vector-d...

Scheduling problems are NP – Hard combinatorial optimization problems, since many algorithms have been developed which offers new promising insights for solving resource allocation problems. Considering the problems faced in automobile repair shops, who sets the customer due dates of the car based on processing time, jobs already waiting for processing and mechanic available time. Also the work...

This report is a detailed review of the current data on the mechanic and gravitational sensitivity of osteoblasts and osteogenic precursor cells in vitro. It summarizes the numerous responses of cells with an osteoblastic phenotype and osteogenic precursor cells and especially their responses to the alteration of their mechanic or gravitational surroundings. The review also discusses the osteog...