Computing the Price of Anarchy in Processor Load Balancing Game with Linear Delays

This paper considers a generalization of the processor load balancing game also known as KP-model. A linear delay of a processor may depend on not only its load but on loads of other processors. Players choose processors of different speeds to run their jobs striving to minimize job's delay, i.e., the job completion time on a chosen processor. The social cost is the maximum delay over all processors. We propose a computing algorithm of the exact PoA value which can be applied to estimate the POA visually if its exact analytical expression is not obtained yet or it is rather complicated to figure out its formula.

Exact quasi-relativistic wavefunctions of Hydrogen-like atoms

Exact solutions of a novel quasi-relativistic quantum mechanical wave equation are found for Hydrogen-like atoms. This includes both, an exact analytical expression for the energies of the bound states, and exact analytical expressions for the wavefunctions, which successfully describe quantum particles with mass and spin-0 up to energies comparable to the energy associated to the mass of the particle. These quasi-relativistic atomic orbitals may be used for improving ab-initio software packages dedicated to numerical simulations in physical-chemistry and atomic and solid-state physics.

Effective Angle of Synchrotron Radiation

An exact analytical expression for the effective angle is determined for an arbitrary energy value of a radiating particle. An effective angle of instantaneous power is defined for synchrotron radiation in the framework of classical electrodynamics. This definition explicitly contains the most symmetric distribution of half the total of the instantaneous power of synchrotron radiation. Two exact analytical expressions for the effective angle are considered for the arbitrary energy values of a radiating particle, and the second expression brings to light the exact asymptotics of the effective angle in the ultrarelativistic limit.

Электрическая площадь поля в вакууме с движущимися зарядами

An exact analytical expression is presented for the electric field area generated by the motion of charged particles with constant acceleration. An approximate form of the spatial distribution of the electric area in the vicinity of the point of instantaneous stopping of charges is given. The possibility of generating quasi-unipolar pulses of electromagnetic radiation with a significant electric area is shown.

Inverse Brillouin Function and Demonstration of Its Application

The Brillouin function arises in the quantum theory of paramagnetic materials, where it describes the dependence of the magnetization on the externally applied magnetic field and on the temperature of the system. There is no closed form exact analytical expression for the inverse Brillouin function, however, there have been several approximations proposed. In this work, we first compare relative errors and simplicity of several approximations for the inverse Brillouin function. Next, we demonstrate the application of the inverse Brillouin function by determining the Hamiltonian of the system using the simulation data of the magnetization dependence on the temperature. Then we compare the Hamiltonian that was used to set up the simulation with the Hamiltonian determined from the magnetization temperature dependence and an approximation to the inverse Brillouin function. We found that some of the approximations for the inverse Brillouin function can be used to accurately predict the Hamiltonian of the system given the magnetization dependence on temperature.

Time-dependent versus time-independent probabilities of transmission and reflection of a quantum particle incident upon a step potential and a square potential well

We investigate the transmission and reflection of a quantum particle incident upon a step potential decrease and a square well. The probabilities of transmission and reflection using the time-independent Schrödinger equation and also the time-dependent Schrödinger equation are in excellent agreement. We explain why the probabilities agree so well. In doing so, we make use of an exact analytical expression for the square well for time-dependent transmission and reflection, which reveals additional interesting and unexpected results. One such result is that transmission of a wave packet can occur with the probability of transmission depending weakly on the initial spread of the packet. The explanations and the additional results will be of interest to instructors of and students in upper year undergraduate quantum mechanics courses.

Evolution arrests invasions of cooperative populations

Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from inevitable. In cooperative populations, mutations reducing dispersal have a competitive advantage. Such mutations then steadily accumulate at the expansion front bringing invasion to a halt. Our findings are a rare example of evolution driving the population into an unfavorable state and could lead to new strategies to combat unwelcome invaders. In addition, we obtain an exact analytical expression for the fitness advantage of mutants with different dispersal rates.