In cosmology numerical simulations of structure formation are now of central importance, as they are the sole instrument for providing detailed predictions of current cosmological models for a whole class of important constraining observations. These simulations are essentially molecular dynamics simulations of N (≫ 1, now up to of order several billion) particles interacting through their self...

It has been shown by H. Bethe more than 70 years ago that the number of excited states of a Fermi gas grows, at high excitation energies Q, like the exponential of the square root of Q. This result takes into account only the average density of single particle (SP) levels near the Fermi energy. It ignores two important effects, namely the discreteness of the SP spectrum, and its fluctuations. W...

In classical general relativity, the generic approach to the initial singularity is usually understood in terms of the BKL scenario. In this scenario, along with the Bianchi IX model, the exact, singular, Kasner solution of vacuum Bianchi I model also plays a pivotal role. Using an effective classical Hamiltonian obtained from loop quantization of vacuum Bianchi I model, exact solution is obtai...

Current-voltage ( I V ) characteristics of linear and annular discrete arrays of underdamped small Josephson junctions with different values of single loop inductances are calculated numerically and compared with those obtained for continuum long Josephson junctions. The resonances between the moving fluxon and the linear waves caused by the array discreteness induce steps on t h e / V c u r v ...

An actuator array performs distributed manipulation where an object being transported and manipulated rests on a large number of stationary supporting actuators. The authors have developed a macroscopic actuator array consisting of many motorized wheels. As opposed to a MEMS array, the analysis requires the explicit modeling of the discreteness in the system, including the set of supports, dist...

The product of speech perception is contrast between discrete units of meaning, words, which are contrasted by features. While traditional approaches argued that discreteness is imposed by mechanisms like categorical perception that discard within-category detail, recent research suggests that fine-grained detail is preserved throughout processing. We develop an alternative that argues that dis...

Surprising things happen when we take the discreteness of molecule number seriously, abandoning the notion that chemical concentrations may be treated as continuous variables. Here we will show how ideas of discreteness force us into dealing with issues of noise and randomness. We will arrive at a probabilistic description of reaction kinetics which, in the limit of large numbers, will reproduc...

We establish necessary and sufficient conditions for the discreteness of spectrum and strict positivity of magnetic Schrödinger operators with a positive scalar potential. They are expressed in terms of Wiener capacity and local energy of the magnetic field. These conditions depend on two functional parameters. One of them is a decreasing function of one variable whose argument is the normalize...

We generalize a result of Sury [Sur92] and prove that uniform discreteness cocompact lattices in higher rank semisimple Lie groups (first conjectured by Margulis [Mar91]) is equivalent to weak form Lehmer’s conjecture. include short survey related results conjectures.