We consider a system of p species bosons, each which consists N1, N2, …, Np particles. The bosons are in three dimensions with interactions via an interaction potential V such that ≤ D(1 − Δ), includes the Coulomb interaction. set initial condition to describe mixture condensate, i.e., tensor product factorized states. show difference between many-body Schrödinger evolution mean-field regime an...

In this study, nanoscale zero-valent copper (nZVC) as catalyst activated persulfate (PS) was used for the degradation of p-chlorophenol (p-CP) under ultrasonic (US) irradiation in aqueous solution. The effect of different operational parameters such as solution pH (3.5-10.5), PS concentration (1-7.5 mm/L), nZVC dosage (5-35 mg/L) and initial p-CP concentration (10-100 mg/L) were evaluated at di...

We show that solutions to Smoluchowski’s equation with a constant coagulation kernel and an initial datum with some regularity and exponentially decaying tail converge exponentially fast to a selfsimilar profile. This convergence holds in a weighted Sobolev norm which implies the L2 convergence of derivatives up to a certain order k depending on the regularity of the initial condition. We prove...

This paper describes progress on the TLM modelling of the Laplace equation, in particular, how the rate of convergence is influenced by the choice of scattering parameter for a particular discretisation. The hypothesis that optimum convergence is achieved when the real and imaginary parts for the lowest harmonic in a Fourier solution cancel appears to be upheld. The Fourier solution for the pro...

This paper focuses on the stability analysis of systems having a continuum of equilibria. Two notions that are of particular relevance to such systems are convergence and semistability. Convergence is the property whereby every solution converges to a limit point that may depend on the initial condition. Semistability is the additional requirement that all solutions converge to limit points tha...

Motivated by a phenomenon of phase transition in a model of alignment of selfpropelled particles, we obtain a kinetic mean-field equation which is nothing more than the Smoluchowski equation on the sphere with dipolar potential. In this self-contained article, using only basic tools, we analyze the dynamics of this equation in any dimension. We first prove global wellposedness of this equation,...

We consider Ricci flow invariant cones C in the space of curvature operators lying between nonnegative Ricci curvature and nonnegative curvature operator. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to Ricci flow has its curvature operator which satsisfies R+ε I ∈ C at the initial time, then it satisfies R+Kε I ∈ C on some time interval depen...

We revisit the extremum seeking scheme whose local stability properties were analyzed in (Krstić and Wang, 2000) and propose its simplified version that still achieves extremum seeking. We show under slightly stronger conditions that this simplified scheme achieves extremum seeking from arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted...