Multiple orifice throttle valve Patent

Throttle valve for regulating fluid flow volum

Multiple-orifice throttle valve

Multiple-orifice throttle valve is not subject to cold welding in a vacuum environment and is compatible with strong oxidizing fluid. The valve is of all metal construction using simple components that do not slide or rotate and excludes static or dynamic seals

Piecewise contractions defined by iterated function systems

Let $\phi_1,\ldots,\phi_n:[0,1]\to (0,1)$ be Lipschitz contractions. Let $I=[0,1)$, $x_0=0$ and $x_n=1$. We prove that for Lebesgue almost every $(x_1,...,x_{n-1})$ satisfying $0<x_1<\cdots <x_{n-1}<1$, the piecewise contraction $f:I\to I$ defined by $x\in [x_{i-1},x_i)\mapsto \phi_i(x)$ is asymptotically periodic. More precisely, $f$ has at least one and at most $n$ periodic orbits and the $\omega$-limit set $\omega_f(x)$ is a periodic orbit of $f$ for every $x\in I$.Comment: 16 pages, two figure

Field induced multiple order-by-disorder state selection in antiferromagnetic honeycomb bilayer lattice

In this paper we present a detailed study of the antiferromagnetic classical Heisenberg model on a bilayer honeycomb lattice in a highly frustrated regime in presence of a magnetic field. This study shows strong evidence of entropic order-by-disorder selection in different sectors of the magnetization curve. For antiferromagnetic couplings $J_1=J_x=J_p/3$, we find that at low temperatures there are two different regions in the magnetization curve selected by this mechanism with different number of soft and zero modes. These regions present broken $Z_2$ symmetry and are separated by a not fully collinear classical plateau at $M=1/2$. At higher temperatures, there is a crossover from the conventional paramagnet to a cooperative magnet. Finally, we also discuss the low temperature behavior of the system for a less frustrated region, $J_1=J_x<J_p/3$.Comment: revised version - accepted for publication in Physical Review B - 12 pages, 11 figure

Asymptotically periodic piecewise contractions of the interval

We consider the iterates of a generic injective piecewise contraction of the interval defined by a finite family of contractions. Let $\phi_i:[0,1]\to (0,1)$, $1\le i\le n$, be $C^2$-diffeomorphisms with $\sup_{x\in (0,1)} \vert D\phi_i(x)\vert<1$ whose images $\phi_1([0,1]), \ldots, \phi_n([0,1])$ are pairwise disjoint. Let $0<x_1<\cdots<x_{n-1}<1$ and let $I_1,\ldots, I_n$ be a partition of the interval $[0,1)$ into subintervals $I_i$ having interior $(x_{i-1},x_i)$, where $x_0=0$ and $x_n=1$. Let $f_{x_1,\ldots,x_{n-1}}$ be the map given by $x\mapsto \phi_i(x)$ if $x\in I_i$, for $1\le i\le n$. Among other results we prove that for Lebesgue almost every $(x_1,\ldots,x_{n-1})$, the piecewise contraction $f_{x_1,\ldots,x_{n-1}}$ is asymptotically periodic.Comment: 8 page

Reparametrization Invariance and the Schr\"odinger Equation

In the present work we consider a time-dependent Schr\"odinger equation for systems invariant under the reparametrization of time. We develop the two-stage procedure of construction such systems from a given initial ones, which is not invariant under the time reparametrization. One of the first-class constraints of the systems in such description becomes the time-dependent Schr\"odinger equation. The procedure is applicable in the supersymmetric theories as well. The $n=2$ supersymmetric quantum mechanics is coupled to world-line supergravity, and the local supersymmetric action is constructed leading to the square root representation of the time-dependent Schr\"odinger equation.Comment: RevTeX,25 page

Affine semigroups having a unique Betti element

We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.Comment: 8 pages, 1 figure. To appear in Journal of Algebra and its Application

Two repelling random walks on Z\mathbb Z

We consider two interacting random walks on $\mathbb{Z}$ such that the transition probability of one walk in one direction decreases exponentially with the number of transitions of the other walk in that direction. The joint process may thus be seen as two random walks reinforced to repel each other. The strength of the repulsion is further modulated in our model by a parameter $\beta \geq 0$. When $\beta = 0$ both processes are independent symmetric random walks on $\mathbb{Z}$, and hence recurrent. We show that both random walks are further recurrent if $\beta \in (0,1]$. We also show that these processes are transient and diverge in opposite directions if $\beta > 2$. The case $\beta \in (1,2]$ remains widely open. Our results are obtained by considering the dynamical system approach to stochastic approximations.Comment: 17 pages. Added references and corrected typos. Revised the argument for the convergence to equilibria of the vector field. Improved the proof for the recurrence when beta belongs to (0,1); leading to the removal of a previous conjectur