Mesoscopic time scale

In this review we consider large-scale polymer motions which naturally occur on mesoscopic time scales. In order to access such times by neutron scattering a very high resolution technique is needed in order to obtain times of several tens of nanoseconds. Such a technique is neutron spin echo (NSE), which can directly measure energy changes in the neutron during scattering [32,33]. 

We can summarize that the great advantage of NSE spectroscopy lies in investigations of aperiodic relaxation dynamics. On mesoscopic time scales well separated from atomic time scales, these processes show broad quasi-elastic features in frequency space, but a featureless decaying structure in the time domain. 

The algorithmic description of MPC dynamics given earlier outlined its essential elements and properties and provided a basis for implementations of the dynamics. However, a more formal specification of the evolution is required in order to make a link between the mesoscopic description and macroscopic laws that govern the system on long distance and time scales. This link will also provide us with expressions for the transport coefficients that enter the... 

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

TDFRS allows for experiments on a micro- to mesoscopic length scale with short subsecond diffusion time constants, which eliminate almost all convection problems. There is no permanent bleaching of the dye as in related forced Rayleigh scattering experiments with photochromic markers [29, 30] and no chemical modification of the polymer. Furthermore, the perturbations are extremely weak, and the solution stays close to thermal equilibrium. 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

The set of dynamical variables of interest is enlarged via inclusion of a few additional variables (usually termed auxiliary or virtual). This serves the twofold purpose of providing a simplified picture of the real thermal bath and recovering a distinct time-scale separation between relevant and irrelevant parts. In other words, the system of interest plus the set of virtual variables behaves like a mesoscopic system—a system with a time scale intermediate between the microscopic and the macroscopic. The first well-known example at the mesoscopic level is the Brownian particle of Einstein theory. ... 

Recently a new field, mesoscopic physics, has emerged. It is interesting to understand the physical properties of systems that are not as small as a single atom, but small enough that the properties can be dramatically different from those in a larger assembly. All these new mesoscopic phenomena can easily be observed in the dielectric properties of colloid systems. Their properties strictly depend on the dimensional scale and the time scale of observation. Self-assembling systems such as micellar surfactant solutions, micro emulsions, emulsions, aqueous solutions of biopolymers, and cell and lidposome suspensions all to-... 

This relation between the relaxation time t of the flux and the time scale l/F (p) of the reaction appears to be a purely mathematical requirement. The following mesoscopic approach will shed light on the foundational problems of the reaction-Cattaneo system (2.17) and (2.18) and the reaction-telegraph equation (2.19) hinted at by points (i) and (ii). 

The term macroscopic description refers to the long-time and large-scale limit, t -> oo and x -> oo, of mesoscopic equations where the details of the microscopic movement are irrelevant. In particular, it refers to the diffusive limit where balance equations such as (3.13), (3.41), and (3.74) are approximated by the diffusion equation (2.1). The standard derivation of the diffusion equation involves the assumption that the typical microscopic jumps and times are small compared to the characteristic macroscopic space and time scales. Let us illustrate this using the mesoscopic transport equation (3.74). If the jump density w(z) is a rapidly decaying function for large z, one can expand p(x - z, t) in z and truncate the Taylor series at the second moment ... 

---