Flow-correlated dilution of a regular network leads to a percolating network during tumor induced angiogenesis

We study a simplified stochastic model for the vascularization of a growing tumor, incorporating the formation of new blood vessels at the tumor periphery as well as their regression in the tumor center. The resulting morphology of the tumor vasculature differs drastically from the original one. We demonstrate that the probabilistic vessel collapse has to be correlated with the blood shear force in order to yield percolating network structures. The resulting tumor vasculature displays fractal properties. Fractal dimension, microvascular density (MVD), blood flow and shear force has been computed for a wide range of parameters.Comment: 15 pages, 12 figure

Abrupt transitions in turbulent thermoacoustic systems

Abrupt transitions to the state of thermoacoustic instability (TAI) in gas turbine combustors are a significant challenge plaguing the development of next-generation low-emission aircraft and power generation engines. In this paper, we present the observation of abrupt transition in three disparate turbulent thermoacoustic systems: an annular combustor, a swirl-stabilized combustor, and a preheated bluff-body stabilized combustor. Using a low-order stochastic thermoacoustic model, we show that the reported abrupt transitions occur when an initially stable, supercritical limit cycle becomes unstable, leading to a secondary bifurcation to a large amplitude limit cycle solution. The states of combustion noise and intermittency observed in these turbulent combustors are well captured by the additive stochastic noise in the model. Through amplitude reduction, we analyze the underlying potential functions affecting the stability of the observed dynamical states. Finally, we make use of the Fokker-Planck equation, educing the effect of stochastic fluctuations on subcritical and secondary bifurcation. We conclude that a high enough intensity of stochastic fluctuations which transforms a subcritical bifurcation into an intermittency-facilitated continuous transition may have little effect on the abrupt nature of secondary bifurcation. Our findings imply the high likelihood of abrupt transitions in turbulent combustors possessing higher-order nonlinearities where turbulence intensities are disproportionate to the large amplitude limit cycle solution

New conditions for finite-time stability of impulsive dynamical systems via piecewise quadratic functions

In this paper, the use of time-varying piecewise quadratic functions is investigated to characterize the finite-time stability of state-dependent impulsive dynamical linear systems. Finite-time stability defines the behavior of a dynamic system over a bounded time interval. More precisely, a system is said to be finite-time stable if, given a set of initial conditions, its state vector does not exit a predefined domain for a certain finite interval of time. This paper presents new sufficient conditions for finite-time stability based on time-varying piecewise quadratic functions. These conditions can be reformulated as a set of Linear Matrix Inequalities that can be efficiently solved through convex optimization solvers. Dif ferent numerical analysis are included in order to prove that the presented conditions are able to improve the results presented so far in the literature

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.Comment: To appear in Scientific Report

On finite time stability with guaranteed cost control of uncertain linear systems

summary:This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example

Optimal Control of a Large Space Telescope Using an Annular Momentum Control Device

Application of a new development in the field of momentum storage devices, the Annular Momentum Control Device (AMCD), to the twin problems of large angle maneuvers and fine pointing control is considered. The basic concept of the AMCD consists of a spinning rim, with no central hub area, suspended by a minimum of three magnetic bearings, and driven by a noncontacting electromagnetic spin motor. The dissertation considers in detail the design of an optimal controller to achieve both large angle maneuvers and the fine pointing control of a Large Telescope (LST) with a single configuration, consisting of a single AMCD mounted in a single gimbal

Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate

When a system crosses a second-order phase transition on a finite timescale, spontaneous symmetry breaking can cause the development of domains with independent order parameters, which then grow and approach each other creating boundary defects. This is known as Kibble-Zurek mechanism. Originally introduced in cosmology, it applies both to classical and quantum phase transitions, in a wide variety of physical systems. Here we report on the spontaneous creation of solitons in Bose-Einstein condensates via the Kibble-Zurek mechanism. We measure the power-law dependence of defects number with the quench time, and provide a check of the Kibble-Zurek scaling with the sonic horizon. These results provide a promising test bed for the determination of critical exponents in Bose-Einstein condensates.Comment: 7 pages, 4 figure

Resilient Finite-Time Controller Design of a Class of Stochastic Nonlinear Systems

This paper deals with the problem of resilient finite-time control for a class of stochastic nonlinear systems. The notion of finite-time annular domain stability of stochastic nonlinear systems is first introduced. Then, some sufficient conditions are given for the existence of resilient state feedback finite-time annular domain stabilizing controller, which are expressed in terms of matrix inequalities. A double-parameter searching algorithm is proposed to solve these obtained matrix inequalities. Finally, an example is given to illustrate the effectiveness of the developed method