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Stability of Branched Flow from a Quantum Point Contact  [PDF]
Bo Liu,Eric J. Heller
Physics , 2013, DOI: 10.1103/PhysRevLett.111.236804
Abstract: In classically chaotic systems, small differences in initial conditions are exponentially magnified over time. However, it was observed experimentally that the (necessarily quantum) "branched flow" pattern of electron flux from a quantum point contact (QPC) traveling over a random background potential in two-dimensional electron gases(2DEGs) remains substantially invariant to large changes in initial conditions. Since such a potential is classically chaotic and unstable to changes in initial conditions, it was conjectured that the origin of the observed stability is purely quantum mechanical, with no classical analog. In this paper, we show that the observed stability is a result of the physics of the QPC and the nature of the experiment. We show that the same stability can indeed be reproduced classically, or quantum mechanically. In addition, we explore the stability of the branched flow with regards to changes in the eigenmodes of quantum point contact.
Flow-injection of branched polymers inside nanopores  [PDF]
Takahiro Sakaue,Elie Rapha?l,Pierre-Gilles De Gennes,Fran?oise Brochard-Wyart
Physics , 2005, DOI: 10.1209/epl/i2005-10190-3
Abstract: Flexible chains (linear or branched) can be forced to enter into a narrow capillary by using a hydrodynamic flow. Here, we correct our earlier description of this problem by considering the progressive nature of the suction process. We find that the critical current for penetration, $J\_c$, is controlled by the entry of a single blob of the capillary size, and that its scaling structure is the same for branched and linear chains.
Branched RNA: A New Architecture for RNA Interference  [PDF]
Anna Avi?ó,Sandra M. Ocampo,José Carlos Perales,Ramon Eritja
Journal of Nucleic Acids , 2011, DOI: 10.4061/2011/586935
Abstract: Branched RNAs with two and four strands were synthesized. These structures were used to obtain branched siRNA. The branched siRNA duplexes had similar inhibitory capacity as those of unmodified siRNA duplexes, as deduced from gene silencing experiments of the TNF-α protein. Branched RNAs are considered novel structures for siRNA technology, and they provide an innovative tool for specific gene inhibition. As the method described here is compatible with most RNA modifications described to date, these compounds may be further functionalized to obtain more potent siRNA derivatives and can be attached to suitable delivery systems. 1. Introduction In recent years, siRNAs have generated tremendous interest in therapeutics [1]. Nevertheless, the transition of siRNAs from the laboratory to the clinical practice has encountered several obstacles. Briefly, siRNA duplexes are rapidly degraded in serum by exonucleases and endonucleases [2]. The polyanionic phosphodiester backbone of siRNA suffers from difficult cell uptake [3], and oligonucleotides may have off-target effects, either by stimulating the immune system [4] or by entering other endogenous gene regulation pathways [5]. Several chemical modifications have been proposed in the literature to address these drawbacks [2–4]. Most of these modifications are based on modified nucleosides and changes on backbone linkages [6, 7]. Thus, changes in sugar moiety influences sugar conformation, and, therefore, overall siRNA structure. Modifications of the 2′-OH by F or OMe as well as LNA [8, 9] are well tolerated and improve binding affinity and nuclease resistance. Base modifications that stabilize base pairs (5-bromouracil, 5-methylcytosine, 5-propynyluracil, and others) have also been proposed [7, 10]. Terminal conjugates, especially at the termini of the sense strand, have been modified with a large number of lipids to achieve improved cellular uptake [11]. In addition to these modifications, siRNA architecture is also crucial in the design of effective and specific siRNA. The architecture itself can be altered by chemical synthesis. In addition to the canonical siRNA architecture of 21-nt antiparallel, double-strand RNA with 2-nt 3′-overhangs [12], several forms of siRNA have been described. Blunt-ended siRNA [13], 25/27?mer Dicer-substrate or asymmetric siRNA [14] are among the siRNA structures formed by two strands. Moreover, functional siRNA can also be formed by one single RNA strand. This is the case in small hairpin RNA (shRNA), where the two strands are linked by a single loop [15], or RNA dumbbells [16],
Statistical stability for multidimensional piecewise expanding maps  [PDF]
Jose F. Alves,Antonio Pumarino,Enrique Vigil
Mathematics , 2014,
Abstract: We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional family of tent maps is statistically stable.
Unexpected features of branched flow through high-mobility two-dimensional electron gases  [PDF]
M. P. Jura,M. A. Topinka,L. Urban,A. Yazdani,H. Shtrikman,L. N. Pfeiffer,K. W. West,D. Goldhaber-Gordon
Physics , 2010, DOI: 10.1038/nphys756
Abstract: GaAs-based two-dimensional electron gases (2DEGs) show a wealth of remarkable electronic states, and serve as the basis for fast transistors, research on electrons in nanostructures, and prototypes of quantum-computing schemes. All these uses depend on the extremely low levels of disorder in GaAs 2DEGs, with low-temperature mean free paths ranging from microns to hundreds of microns. Here we study how disorder affects the spatial structure of electron transport by imaging electron flow in three different GaAs/AlGaAs 2DEGs, whose mobilities range over an order of magnitude. As expected, electrons flow along narrow branches that we find remain straight over a distance roughly proportional to the mean free path. We also observe two unanticipated phenomena in high-mobility samples. In our highest-mobility sample we observe an almost complete absence of sharp impurity or defect scattering, indicated by the complete suppression of quantum coherent interference fringes. Also, branched flow through the chaotic potential of a high-mobility sample remains stable to significant changes to the initial conditions of injected electrons.
Stability of piecewise-linear models of genetic regulatory networks

Lin Peng,Qin Kai-Yu,Wu Hai-Yan,

中国物理 B , 2011,
Abstract: This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero.
Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments
Minghui Song,M. Z. Liu
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/258329
Abstract: In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the -methods are obtained. Some examples are illustrated.
Second-order analysis of piecewise linear functions with applications to optimization and stability  [PDF]
Boris S. Mordukhovich,M. Ebrahim Sarabi
Mathematics , 2015,
Abstract: This paper is devoted to second-order variational analysis of a rather broad class of extended-real-valued piecewise liner functions and their applications to various issues of optimization and stability. Based on our recent explicit calculations of the second-order subdifferential for such functions, we establish relationships between nondegeneracy and second-order qualification for fully amenable compositions involving piecewise linear functions and obtain new applications of the developed second-order theory to full stability in composite optimization and constrained minimax problems, strong regularity of associate generalized equations and strong stability of stationary points in composition optimization, and Lipschitzian stability of parametric variational systems.
Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC
Morten Hovd,Sorin Olaru
Modeling, Identification and Control , 2010, DOI: 10.4173/mic.2010.2.1
Abstract: Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ) Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC). A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.
Robust stability of nonlinear piecewise deterministic systems under matching conditions
Boukas E. K.,Yang H.
Mathematical Problems in Engineering , 1997,
Abstract: This paper deals with the robustness of the class of nonlinear piecewise deterministic systems with unknown but bounded uncertainties. Under the assumption that all the modes of the markovian jump process (disturbance) communicate, the complete access to the system state and the boundedness of the uncertainties, a sufficient condition for stochastic stability of this class of systems is given. An example is presented to validate the proposed results.
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