Related papers: Hooke and Coulomn Energy of Tripod Spiders
The mutual influence of two layers with strongly loclized electrons is exercised through the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage…
We study pullback from a topological viewpoint with emphasis on pullback of covering maps. We generalize a triad of Quillen on properties of the pullback functor.
When superimposing the potentials of external fields on the Coulomb potential of the hydrogen atom a saddle point appears, which is called the Stark saddle point. For energies slightly above the saddle point energy one can find classical…
This paper presents a convexity analysis for the dynamic snake model based on the Potential Energy functional and the Hamiltonian formulation of the classical mechanics. First we see the snake model as a dynamical system whose singular…
We analytically examine the pair interaction for parallel, discrete helices of charge. Symmetry arguments allow for the energy to be decomposed into a sum of terms, each of which has an intuitive geometric interpretation. Truncated Fourier…
A key test for any quasi-local energy in general relativity is that it be nonnegative and satisfy a rigidity property; if it vanishes, the region enclosed is flat. We show that the Hawking energy, when evaluated on its natural…
Adaptive structures are equipped with sensors and actuators to actively counteract external loads such as wind. This can significantly reduce resource consumption and emissions during the life cycle compared to conventional structures. A…
This paper deals with the old and classical problem of determining necessary conditions for the overconstrained mobility of some mechanical device. In particular, we show that the mobility of pentapods/hexapods implies either a collinearity…
Low energy effective actions arising from string theory typically contain many scalar fields, some with a very complicated potential and others with no potential at all. The evolution of these scalars is of great interest. Their late time…
We analyzed the Hartree-Fock approximation for an electron system. The interaction between particles is modeled by a non-Coulombian potential. We analyzed both the three-dimensional and two-dimensional systems. We obtained accurate…
Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is…
We implement the rotationally-invariant formulation of the two-dimensional Hubbard model, with nearest-neighbors hopping $t$, which allows for the analytical study of the system in the low-energy limit. Both U(1) and SU(2) gauge…
Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community…
The method of Morse theory is used to analyze the distributions of unit charges interacting through a repulsive force and constrained to move on the surface of a sphere -- the Thomson problem. We find that, due to topological reasons, the…
Any swimmer embedded on a inertialess fluid must perform a non-reciprocal motion to swim forward. The archetypal demonstration of this unique motion-constraint was introduced by Purcell with the so-called "scallop theorem". Scallop here is…
We consider static solutions of the sine-Gordon theory defined on a cylinder, which can be either periodic or quasi-periodic in space. They are described by the different modes of a simple pendulum moving in an inverted effective potential…
We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body,…
Electrons confined in semiconductor quantum dot arrays have both charge and spin degrees of freedom. The spin provides a well-controllable and long-lived qubit implementation. The charge configuration in the dot array is influenced by…
We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in…
It has been observed that certain classical chains admit topologically protected zero-energy modes that are localized on the boundaries. The static features of such localized modes are captured by linearized equations of motion, but the…