Search results for "singular"

Fluctuations and lack of self-averaging in the kinetics of domain growth

1986

The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t)d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeLd of the system. This lack of self-averaging is tested for both the Ising model and the φ4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt)x withx=1/2, although the φ4 model has “soft walls”. However, spurious results withx≷1/2 are obtained if “bad” pseudorandom numbers are used, and if the n…

Symmetry, winding number, and topological charge of vortex solitons in discrete-symmetry media

2009

[EN] We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrodinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance

Numerical study of the primitive equations in the small viscosity regime

2018

In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.

Singular behavior of a vortex layer in the zero thickness limit

2017

The aim of this paper is to study the Euler dynamics of a 2D periodic layer of non uniform vorticity. We consider the zero thickness limit and we compare the Euler solution with the vortex sheet evolution predicted by the Birkhoff-Rott equation. The well known process of singularity formation in shape of the vortex sheet correlates with the appearance of several complex singularities in the Euler solution with the vortex layer datum. These singularities approach the real axis and are responsible for the roll-up process in the layer motion.

Triangle singularity in the B−→K−π0X(3872) reaction and sensitivity to the X(3872) mass

2020

We have done a study of the ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}X(3872)$ reaction by means of a triangle mechanism via the chain of reactions: ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{D}^{*0}{\overline{D}}^{*0}$; ${D}^{*0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{D}^{0}$; ${D}^{0}{\overline{D}}^{*0}\ensuremath{\rightarrow}X(3872)$. We show that this mechanism generates a triangle singularity in the ${\ensuremath{\pi}}^{0}X(3872)$ invariant mass for a very narrow window of the $X(3872)$ mass, around the present measured values, and show that the peak positions and the shape of the mass distributions are sensitiv…

a1(1420) peak as the πf0(980) decay mode of the a1(1260)

2016

We study the decay mode of the ${a}_{1}(1260)$ into a ${\ensuremath{\pi}}^{+}$ in $p$ wave and the ${f}_{0}(980)$ that decays into ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in $s$ wave. The mechanism proceeds via a triangular mechanism where the ${a}_{1}(1260)$ decays into ${K}^{*}\overline{K}$, the ${K}^{*}$ decays to an external ${\ensuremath{\pi}}^{+}$ and an internal $K$ that fuses with the $\overline{K}$ producing the ${f}_{0}(980)$ resonance. The mechanism develops a singularity at a mass of the ${a}_{1}(1260)$ around 1420 MeV, producing a peak in the cross section of the $\ensuremath{\pi}p$ reaction, used to generate the mesonic final state, which provides a natural…

Role of a triangle singularity in the πN(1535) contribution to γp→pπ0η

2017

We have studied the $\ensuremath{\gamma}p\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ reaction paying attention to the two main mechanisms at low energies, the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\eta}\mathrm{\ensuremath{\Delta}}(1232)$ and the $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{\ensuremath{\Delta}}(1700)\ensuremath{\rightarrow}\ensuremath{\pi}N(1535)$. Both are driven by the photoexcitation of the $\mathrm{\ensuremath{\Delta}}(1700)$ and the second one involves a mechanism that leads to a triangle singularity. We are able to evaluate quantitatively the cross section for thi…

Triangle singularity in the J/ψ → K+K− f0(980) decay

2020

Scaling Regimes and the Singularity of Specific Heat in the 3D Ising Model

2013

AbstractThe singularity of specific heat CV of the three-dimensional Ising model is studied based on Monte Carlo data for lattice sizes L≤1536. Fits of two data sets, one corresponding to certain value of the Binder cumulant and the other — to the maximum of CV, provide consistent values of C0 in the ansatz CV(L)=C0+ALα/ν at large L, if α/ν=0.196(6). However, a direct estimation from our data suggests that α/ν, most probably, has a smaller value (e.g., α/ν= 0.113(30)). Thus, the conventional power-law scaling ansatz can be questioned because of this inconsistency. We have found that the data are well described by certain logarithmic ansatz.

Investigations of Superheavy Quasiatoms via Spectroscopy of δ Rays and Positrons

1984

There exists a long-standing and very interesting problem in atomic physics, namely, the question: What is the binding energy of an electron if the strength of the Coulomb potential exceeds Zα = 1? According to the Dirac-Sommerfeld fine-structure formula for a point charge $$E = {m_e}{c^2}{[1 - {(Z\alpha )^2}]^{1/2}}$$ (1) the total energy of the lowest bound Is-state becomes imaginary for Zα > 1. But even as early as 1945 it was realized(59) that this property of Eq. (1) is caused by the singularity of the Coulomb potential at the origin. Assuming a realistic charge distribution of the nucleus there is no restriction suc as Zα < 1 for the binding energy. Recent calculations show (cf., e.g.…