اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
250
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with stiffness in the system of equations by handling systematically the statistical contributions of the fastest dynamics of the fluid and immersed structures over long time steps. An important feature of the numerical method is that time steps can be taken in which the degrees of freedom of the fluid are completely underresolved, partially resolved, or fully resolved while retaining a good level of accuracy. Error estimates in each of these regimes are given for the method. A number of theoretical and numerical checks are furthermore performed to assess its physical fidelity. For a conservative force, the method is found to simulate particles with the correct Boltzmann equilibrium statistics. It is shown in three dimensions that the diffusion of immersed particles simulated with the method has the correct scaling in the physical parameters. The method is also shown to reproduce a well-known hydrodynamic effect of a Brownian particle in which the velocity autocorrelation function exhibits an algebraic tau^(-3/2) decay for long times. A few preliminary results are presented for more complex systems which demonstrate some potential application areas of the method.
قيم البحث
اقرأ أيضاً
We study hydrodynamic fluctuations in a compressible and viscous fluid film confined between two rigid, no-slip, parallel plates, where one of the plates is kept fixed, while the other one is driven in small-amplitude, translational, displacements ar
ound its reference position. This jiggling motion is assumed to be driven by a stochastic, external, surface forcing of zero mean and finite variance. Thus, while the transverse (shear) and longitudinal (compressional) hydrodynamic stresses produced in the film vanish on average on either of the plates, these stresses exhibit fluctuations that can be quantified through their equal-time, two-point, correlation functions. For transverse stresses, we show that the correlation functions of the stresses acting on the same plate (self-correlators) as well as the correlation function of the stresses acting on different plates (cross-correlators) exhibit universal, decaying, power-law behaviors as functions of the inter-plate separation. At small separations, the exponents are given by -1, while at large separations, the exponents are found as -2 (self-correlator on the fixed plate), -4 (excess self-correlator on the mobile plate) and -3 (cross-correlator). For longitudinal stresses, we find much weaker power-law decays in the large separation regime, with exponents -3/2 (excess self-correlator on the mobile plate) and -1 (cross-correlator). The self-correlator on the fixed plate increases and levels off upon increasing the inter-plate separation, reflecting the non-decaying nature of the longitudinal forces acting on the fixed plate.
The dynamics of membrane undulations inside a viscous solvent is governed by distinctive, anomalous, power laws. Inside a viscoelastic continuous medium these universal behaviors are modified by the specific bulk viscoelastic spectrum. Yet, in struct
ured fluids the continuum limit is reached only beyond a characteristic correlation length. We study the crossover to this asymptotic bulk dynamics. The analysis relies on a recent generalization of the hydrodynamic interaction in structured fluids, which shows a slow spatial decay of the interaction toward the bulk limit. For membranes which are weakly coupled to the structured medium we find a wide crossover regime characterized by different, universal, dynamic power laws. We discuss various systems for which this behavior is relevant, and delineate the time regime over which it may be observed.
A computational approach is introduced for the study of the rheological properties of complex fluids and soft materials. The approach allows for a consistent treatment of microstructure elastic mechanics, hydrodynamic coupling, thermal fluctuations,
and externally driven shear flows. A mixed description in terms of Eulerian and Lagrangian reference frames is used for the physical system. Microstructure configurations are represented in a Lagrangian reference frame. Conserved quantities, such as momentum of the fluid and microstructures, are represented in an Eulerian reference frame. The mathematical formalism couples these different descriptions using general operators subject to consistency conditions. Thermal fluctuations are taken into account in the formalism by stochastic driving fields introduced in accordance with the principles of statistical mechanics. To study the rheological responses of materials subject to shear, generalized periodic boundary conditions are developed where periodic images are shifted relative to the unit cell to induce shear. Stochastic numerical methods are developed for the formalism. As a demonstration of the methods, results are presented for the shear responses of a polymeric fluid, lipid vesicle fluid, and a gel-like material.
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newtons equations of motion a
re often sufficient to solve for the motion of cylindrical particles with low density ratios, for more complex particles - such as a body with a protrusion - they become unstable. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. Similarly to previous work on this method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We show that our method achieves second-order accuracy in space and first-order in time (third-order for practical settings), only with a small additional computational cost to the original method. Our implicit coupling yields stable solution for density ratios as low as $10^{-4}$. We also consider the influence of fictitious fluid located inside the rigid bodies on the accuracy and stability of our method.
The morphology and the microscopic internal dynamics of a bidimensional gel formed by spontaneous aggregation of gold nanoparticles confined at the water surface are investigated by a suite of techniques, including grazing-incidence x-ray photon corr
elation spectroscopy (GI-XPCS). The range of concentrations studied spans across the percolation transition for the formation of the gel. The dynamical features observed by GI-XPCS are interpreted in view of the results of microscopical imaging; an intrinsic link between the mechanical modulus and internal dynamics is demonstrated for all the concentrations. Our work presents, to the best of our knowledge, the first example of a transition from stretched to compressed correlation function actively controlled by quasistatically varying the relevant thermodynamic variable. Moreover, by applying a model proposed time ago by Duri and Cipelletti [A. Duri and L. Cipelletti, Europhys. Lett. 76, 972 (2006)] we are able to build a novel master curve for the shape parameter, whose scaling factor allows us to quantify a long time displacement length. This characteristic length is shown to converge, as the concentration is increased, to the short time localization length determined by pseudo Debye-Waller analysis of the initial contrast. Finally, the intrinsic dynamics of the system are then compared with that induced by means of a delicate mechanical perturbation applied to the interface.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
