Related papers: Discrete knot energies
We present a simple discrete formula for the elastic energy of a bilayer. The formula is convenient for rapidly computing equilibrium configurations of actuated bilayers of general initial shapes. We use maps of principal curvatures and…
Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
This working paper presents a comprehensive study on the development and analysis of various electricity market models, focusing on continuous, discrete, and fractional-order approaches. The continuous model captures the ongoing…
We present a novel route to constructing cost-efficient semi-empirical approximations for the non-additive kinetic energy in subsystem density functional theory. The developed methodology is based on the use of Slater determinants composed…
We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on…
For renormalizable models a method is presented to unambiguously compute the energy that is carried by localized field configurations (solitons). A variational approach for the total energy is utilized to search for soliton configurations.…
The nuclear symmetry energy, which describes the energy difference of per proton and neutron in nuclear matter, has been extensively studied within the last two decades. Around saturation density, both the value and the slope of the nuclear…
We introduce the discrete distribution of a Wiener process range. Rather than finding some basic distributional properties including hazard rate function, moments, Stress-strength parameter and order statistics of this distribution, this…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
Motivated by the occurrence of "shattering" mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete--continuous fragmentation models.…
The problem of discretization of Darboux integrable equations is considered. Given a Darboux integrable continuous equation, one can obtain a Darboux integrable differential-discrete equation, using the integrals of the continuous equation.…
A microscopic framework of nuclear energy density functionals is reviewed, which establishes a direct relation between low-energy QCD and nuclear structure, synthesizing effective field theory methods and principles of density functional…
Discretization is a fundamental step in numerical analysis for the problems described by differential equations, and the difference between the continuous model and discrete model is one of the most important problems. In this paper, we…
We present an efficient second-order finite difference scheme for solving the 2D sine-Gordon equation, which can inherit the discrete energy conservation for the undamped model theoretically. Due to the semi-implicit treatment for the…
The quest for an approximate yet accurate kinetic energy density functional is central to the development of orbital-free density functional theory. While a recipe for closed-shell systems has been proposed earlier, we have shown that it…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
The rovibrational kinetic energy for an arbitrary number of rigid molecules is computed. The result has the same general form as the kinetic energy in the molecular rovibrational Hamiltonian, although certain quantities are augmented to…
This review on dark energy is intended for a wider audience, beginners as well as experts. It contains important notes on various aspects of dark energy and its alternatives. The section on Newtonian cosmology followed by heuristic…
The use of energy functionals based on density as the basic variable is advocated for ab initio molecular dynamics. It is demonstrated that the constraint of positivity of density can be incorporated easily by using square root density for…