Upon the formation of a train structure in the steady state, the following particle shows periodic oscillations on a two-dimensional (2D) limit cycle around its equilibrium position, whereas the leading particle exhibits 1D oscillation at a specific distance downstream. The 2D oscillatory motion of ...
Thus, if the matter Lagrangian does not contain the Lorentz connection then the dilaton model is equivalent to the two-dimensional gravity with torsion. In fact, we have proved that if the original variables eαa, ωα, pa, π, and X satisfy equations of motion (7)–(11), then the ...
We study the adiabatic asymptotics of reflection coefficients of a quantum electron moving in a two-dimensional waveguide. The direction of the waveguide axis can slowly change, whereas the cut-section is a periodic function slowly varying along the waveguide axis. The motion of an electron is ...
Given z and y in Rd, we can apply the one-dimensional Taylor's theorem with remainder to f (t) = φ(y + t (z − y)) to get Super-Brownian motion in two or more dimensions 335 d1 φ(z)−φ(y) = φi(y)(zi −yi)+ 2 φij (v)(zi −yi)(zj −yj ) (3.3) ...
The relative motion Hamiltonian (5b) is equivalent to the Hamiltonian of a single particle of mass μ confined in a two-dimensional harmonic trap imposed in the center by the additional rectangular convenience we express all potential V(|ξ|). quantities in the Our aim is to analyze all the...
To visualise the individual-level variation in these high-dimensional task profiles we used the LargeVis algorithm40 to reduce the task profiles to a two-dimensional ‘task space’. In this representation, each point represents a worker, and the distance between pairs points represents the ...
A Two-dimensional Mesh refers to a geometric structure used in computer graphics for modeling shapes and motion in a 2D space, such as on an image plane. It consists of interconnected nodes that define the geometry and motion information at a specific moment in time. ...
Along with the mean motion n, we will also consider the semi-major axis of the orbit a associated with n with Kepler's third law as an orbit parameter n=μa3. The change of variables in Eqs. (3.32) is done using the Keplerian motion formulas. These formulas are described in previous...
All of the following examples are particular cases of the general concept, i.e., use of a 1D or 2D array to capture 1-dimensional or 2-dimensional motion. Also described are a few new optical sensor configurations. There are a couple of basic ideas behind a speckle-based optical navigati...
On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem Two bounds on the noncommuting graph A new kind of the solution of degenerate parabolic equation with unbounded convection term A signature-based algorithm for computing Gröbner-Shirshov ...