اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدChaotic Geodesics
401
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
When a shallow layer of inviscid fluid flows over a substrate, the fluid particle trajectories are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. Since the two-dimensional geodesic equation is a two degree-of-freedom autonomous Hamiltonian system, it can exhibit chaos, depending on the shape of the substrate. We find chaotic behaviour for a range of substrates.
قيم البحث
اقرأ أيضاً
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the region where
stable fixed points exist are calculated on the parameter space of the system. It is shown that the transitions to robust chaos in these systems occur either through the routes of type-I or type-III intermittency and the critical boundaries for each type of transition have been determined on the phase diagram of the system. The simplicity of these singular maps and the robustness of their chaotic dynamics make them useful ingredients in the construction of models and in applications that require reliable operation under chaos.
Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting as a therm
al bath. The second is the same except for the shape of the particles, which is now square. The basic difference of these two systems lies in the interaction: hard core elastic collisions make the dynamics of the disks chaotic whereas that of squares is not. Remarkably, this difference is not reflected in the transport properties of the two systems: simulations show that the diffusion coefficients, velocity correlations and response functions of the heavy impurity are in agreement with kinetic theory for both the chaotic and the non-chaotic model. The relaxation to equilibrium, however, is very sensitive to the kind of interaction. These observations are used to reconsider and discuss some issues connected to chaos, statistical mechanics and diffusion.
This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applic
ations with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a m
inimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.
Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparativel
y small dimension and the positive largest Lyapunov exponent
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
