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We present the Multi-Particle-Collision (MPC) dynamics approach to simulate properties of low-dimensional systems. In particular, we illustrate the method for a simple model: a one-dimensional gas of point particles interacting through…
We present a study of the spectral properties like the energy spectrum, the eigenmodes and density of states of a classical finite system of two-dimensional (2D) charged particles which are confined by a quadratic potential. Using the…
A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…
There have been some interesting recent advances in understanding the notion of mechanical disorder in structural glasses and the statistical mechanics of these systems' low-energy excitations. Here we contribute to these advances by…
We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
We investigate two one-dimensional tight-binding models with disorder that have extended states at zero energy. We use exact and partial diagonalisation of the Hamiltonian to obtain the eigenmodes and the associated participation ratios,…
We consider nematic liquid crystals in a bounded, convex polyhedron described by a director field n(r) subject to tangent boundary conditions. We derive lower bounds for the one-constant elastic energy in terms of topological invariants.…
The energetic properties of nuclear clusters inside a low-density, finite-temperature medium are studied with a Lattice Gas Model including isospin dependence and Coulomb forces. Important deviations are observed respect to the Fisher…
We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical…
We consider a hierarchical nested microstructure, which also contains a point of singularity (disclination) at the origin, observed in lead orthovanadate. We show how to exactly compute the energy cost and associated displacement field…
Astrophysical observations suggest that magnetic reconnection in relativistic plasmas plays an important role in the acceleration of energetic particles. Modeling this accurately requires numerical schemes capable of addressing large scales…
We consider the elastic energy of a hanging drape -- a thin elastic sheet, pulled down by the force of gravity, with fine-scale folding at the top that achieves approximately uniform confinement. This example of energy-driven pattern…
We develop a 1D model of twin branching in shape memory alloys. The free energy of the branched microstructure comprises the interfacial and elastic strain energy contributions, both expressed in terms of the average twin spacing treated as…
Two-dimensional (2D) nanomaterials exhibit unique properties that are promising for diverse applications, including those relevant to concentration-gradient-driven transport of electrolyte solutions through porous membranes made from these…
In this article, a compliance minimisation scheme for designing spatially varying orthotropic porous structures is proposed. With the utilisation of conformal mapping, the porous structures here can be generated by two controlling field…
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…
An outstanding challenge in chemical computation is the many-electron problem where computational methodologies scale prohibitively with system size. The energy of any molecule can be expressed as a weighted sum of the energies of…
In part I: We find a series physical scales such as 1) Planck scale, 2) Minimal approximate grand unification SU(5), 3) the mass scale of the see saw model right handed or Majorana neutrinoes, some invented scale with many scalar bosons,…
A method for solving the shell-model eigenproblem in a severely truncated space, spanned by properly selected correlated states obtained by partitioning the full configuration space, is proposed. The method describes in a practically exact…