Related papers: Falling Coupled Oscillators & Trigonometric Sums
We study statistical properties of a one dimensional infinite system of coalescing particles. Each particle moves with constant velocity $\pm v$ towards its closest neighbor and merges with it upon collision. We propose a mean-field theory…
Collective phenomena arise from interactions within complex systems, leading to behaviors absent in individual components. Observing quantum collective phenomena with macroscopic mechanical oscillators has been impeded by the stringent…
We consider a linear Hamiltonian system consisting of a classical particle and a scalar field describing by the wave or Klein-Gordon equations with variable coefficients. The initial data of the system are supposed to be a random function…
We study the symmetric outer product decomposition which decomposes a fully (partially) symmetric tensor into a sum of rank-one fully (partially) symmetric tensors. We present iterative algorithms for the third-order partially symmetric…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
We present a methodology for simulating dilute suspensions of particles settling under gravity, with the main purpose of overcoming limitations of triply periodic configurations, mainly the strong vertical correlation that hinders the study…
Measurements of single electron tunneling through a quantum dot using a quantum point contact as charge detector have been performed for very long time traces with very large event counts. This large statistical basis is used for a detailed…
This paper studies the particle motion when the tune is in the stable region close to the edge of linear sum resonance stopband. Results are found for the tune and the beta functions. Results are also found for the two solutions of the…
A method to calculate particle fluxes applicable in most of the spectroscopy techniques is described. Flux intensities of backscattered or absorbed electrons and emitted photons are calculated using a method of convergence to solve the…
In this paper, we study the dynamics of a system of $n$ coupled, self-propelled particles: $\ddot r_k = (\alpha-\beta |\dot r_k|^2)\dot r_k - \frac{\gamma}{n}\sum_{m=1}^n(r_k-r_m)$, $r_k\in \mathbb R^2.$ Numerical experiments indicate that,…
The gravitational radiation originating from a compact binary system in circular orbit is usually expressed as an infinite sum over radiative multipole moments. In a slow-motion approximation, each multipole moment is then expressed as a…
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
Photons carrying non-zero orbital angular momentum (twisted photons) are well-known in optics. Recently, it was suggested to use Compton backscattering to boost optical twisted photons to high energies. Twisted electrons in the intermediate…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
We investigate the critical dynamics of O(N)-symmetric scalar field theories to determine the critical exponents of transport coefficients as a second-order phase transition is approached from the symmetric phase. A set of stochastic…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
Coupled oscillators are among the simplest composite quantum systems in which the interplay of entanglement and interaction may be explored. We examine the effects of coupling on fluctuations of the coordinates and momenta of the…
The collective motion of a finite nuclear system is investigated by numerical simulation and by linear response theory. Using a pseudo-particle simulation technique we analyze the giant resonances with a multipole decomposition scheme. We…
We analyze the frictionless motion of a point-like particle that slides under gravity on an inverted conical surface. This motion is studied for arbitrary initial conditions and a general relation, valid within 13%, between the periods of…