Klystron stabilisé en phase

Summary In an earlier communication on High Resolution Microwave Spectroscopy²⁷) we described a spectrograph using a phase-stabilized klystron oscillator as a local oscillator in the detection system. The stabilizing system has a holding range of several megacycles which permits the sweeping of the reference crystal oscillator.     

A combined phase I—phase II scaled potential algorithm for linear programming

We develop an extension of the affinely scaled potential reduction algorithm which simultaneously obtains feasibility and optimality in a standard form linear program, without the addition of any M terms. The method, and its lower-bounding procedure, are particularly simple compared with previous interior algorithms not requiring feasibility.This paper was written while the author was a research fellow at the Center for Operations Reasearch and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, Belgium.     

On Julia sets concerning phase transitions

The sets of the points corresponding to the phase transitions of the Potts model on the diamond hierarchical lattice for antiferromagnetic coupling are studied. These sets are the Julia sets of a family of rational mappings. It is shown that they may be disconnected sets. Furthermore, the topological structures of these sets are described completely.     

Does Boris-SDC conserve phase space volume?

In this paper we investigate the conservation of phase space volume of the Boris-SDC algorithm. This method provides a generic way to extend the standard, second-order accurate Lorentz force integrator commonly used for charged particles in an electric and magnetic field to a high-order method using spectral deferred corrections. For a single particle in a Penning trap and different frequencies of the electric and magnetic fields, we assess the conservation properties of the method by computing the update matrix of one step of Boris-SDC as well as its determinant. We compare the results to the convergence regions and relate them to energy conservation properties of the method. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spline filter for optimum phase demodulation †

An optimum nonlinear filter is realized by sequentially updating the spline coefficients of the relevant conditional distribution. The nonlinear filtering problem considered is that of phase demodulation with a two-dimensional phase process model. Speed and accuracy comparison of spline realization with other realizations, such as Fourier filter and point mass, will be provided     

Hysteresis loops for para–ferromagnetic phase transitions

In this paper, by an extension of the Ginzburg–Landau theory, we propose a mathematical model describing hard magnets within which we are able to explore the para–ferromagnetic transition and by using the Landau–Lifshitz–Gilbert equation, to study the 3D evolution of magnetic field. Finally, the hysteresis loops are obtained and represented by numerical implementations.     

Hysteresis loops for para–ferromagnetic phase transitions

In this paper, by an extension of the Ginzburg–Landau theory, we propose a mathematical model describing hard magnets within which we are able to explore the para–ferromagnetic transition and by using the Landau–Lifshitz–Gilbert equation, to study the 3D evolution of magnetic field. Finally, the hysteresis loops are obtained and represented by numerical implementations.     

The minimal measurement number for generalized conjugate phase retrieval

The generalized conjugate phase retrieval problem aims to reconstruct a complex signal x ∈ Cⁿ from quadratic measurements x*A₁x,...,x*A_mx,where A₁,...,A_m∈R^n×n are real symmetric matrices.The equivalent formulation for generalized conjugate phase retrieval along with the minimal measurement number required for accurate retrieval(up to a global phase factor as well as conjugacy) is derived in this paper.We present a set of nine vectors in R⁴ and prove that it is conjugate phase retrievable on C⁴.This result implies the measurement number bound 4n-6 is not optimal for some n,which confirms a conjecture in the article by Evans and Lai(2019).     

Gaussian distributions and phase space Weyl–Heisenberg frames

Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation formulas for the expansion of a general Gaussian symbol in terms of elementary Gaussian functions. For this purpose we introduce the notion of a “phase space frame” associated with a Weyl–Heisenberg frame. Our results give explicit formulas for approximating general Gaussian symbols in phase space by phase space shifted standard Gaussians as well as explicit error estimates and the asymptotic behavior of the approximation.     

Absorbing-state phase transition for driven-dissipative stochastic dynamics on ℤ

We study the long-time behavior of conservative interacting particle systems in ℤ: the activated random walk model for reaction-diffusion systems and the stochastic sandpile. We prove that both systems undergo an absorbing-state phase transition.     

Oscillatory integrals for phase functions having certain degenerate critical points

The paper is concerned with oscillatory integrals for phase functions having certain de- generate critical points. Under a finite type condition of phase functions we show the estimate of oscillatory integrals of the first kind. The decay of the oscillatory integral depends on indices of the finite type, the spatial dimension and the symbol.     

Model investigation of non-thermal phase transition in high energy collisions

The non-thermal phase transition in high energy collisions is studied in detail in the framework of random cascade model. The relation between the characteristic parameter A_p, of phase transition and the rank q of moment is obtained using Monte Carlo simulation, and the existence of two phases in self-similar cascading multiparticle systems is shown. The relation between the critical point qc of phase transition on the fluctuation parameter a is obtained and compared with the experimental results from NA22. The same study is carried out also by analytical calculation under central limit approximation. The range of validity of the central limit approximation is discussed.     

Multiplication de fréquence et stabilité en phase

Summary A frequency multiplying system which delivers an exact multiple of the frequency of a 100 kc/s standard in the microwave region has been developed. High spectral purity of the signal has been obtained by servo-controlling the phase of a high frequency quartz crystal oscillator through an integrating filter with long time-constant.     

A one-dimensional coagulation–fragmentation process with a dynamical phase transition

We introduce a reversible Markovian coagulation–fragmentation process on the set of partitions of {1,…,L}$\{1,\dots ,L\}$ into disjoint intervals. Each interval can either split or merge with one of its two neighbors. The invariant measure can be seen as the Gibbs measure for a homogeneous pinning model (Giacomin (2007) [10]). Depending on a parameter λ$\lambda$, the typical configuration can be either dominated by a single big interval (delocalized phase), or composed of many intervals of order 1$1$ (localized phase), or the interval length can have a power law distribution (critical regime). In the three cases, the time required to approach equilibrium (in total variation) scales very differently with L$L$. In the localized phase, when the initial condition is a single interval of size L$L$, the equilibration mechanism is due to the propagation of two “fragmentation fronts” which start from the two boundaries and proceed by power-law jumps.     

Fractional amplitude and phase dynamics in super-diffusive reaction–diffusion systems

Study of weakly non-linear dynamics of a reaction–super-diffusion system near a Hopf bifurcation by means of fractional analogues of complex Ginzburg-Landau and Kuramoto-Sivashinsky equations is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Low-dimensional chaos in high-dimensional phase space: how does it occur?

A fundamental observation in nonlinear dynamics is that the asymptotic chaotic invariant sets in many high-dimensional systems are low-dimensional. We argue that such a behavior is typically associated with chaos synchronism. Numerical support using coupled chaotic systems including a class derived from a nonlinear partial differential equation is provided.     

Fourier phase retrieval with a single mask by Douglas–Rachford algorithms

The Fourier-domain Douglas–Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded.For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns without oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.     

A Ginzburg–Landau model for the phase transition in Helium II

The paper deals with the second-order phase transition in Helium II by a Ginzburg–Landau model, in which any particle has simultaneously a normal and superfluid velocity. This pattern is able to describe the classical effects of Helium II as the phase diagram, the vortices, the second sound and the thermomechanical effect. Finally, the vorticities and turbulence are described by an extension of the model in which the material time derivative is used.