اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUnderstanding Degeneracy of Two-Point Correlation Functions via Debye Random Media
106
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
It is well-known that the degeneracy of two-phase microstructures with the same volume fraction and two-point correlation function $S_2(mathbf{r})$ is generally infinite. To elucidate the degeneracy problem explicitly, we examine Debye random media, which are entirely defined by a purely exponentially decaying two-point correlation function $S_2(r)$. In this work, we consider three different classes of Debye random media. First, we generate the most probable class using the Yeong-Torquato construction algorithm. A second class of Debye random media is obtained by demonstrating that the corresponding two-point correlation functions are effectively realized in the first three space dimensions by certain models of overlapping, polydisperse spheres. A third class is obtained by using the Yeong-Torquato algorithm to construct Debye random media that are constrained to have an unusual prescribed pore-size probability density function. We structurally discriminate these three classes of Debye random media from one another by ascertaining their other statistical descriptors, including the pore-size, surface correlation, chord-length probability density, and lineal-path functions. We also compare and contrast the percolation thresholds as well as the diffusion and fluid transport properties of these degenerate Debye random media. We find that these three classes of Debye random media are generally distinguished by the aforementioned descriptors and their microstructures are also visually distinct from one another. Our work further confirms the well-known fact that scattering information is insufficient to determine the effective physical properties of two-phase media. Additionally, our findings demonstrate the importance of the other two-point descriptors considered here in the design of materials with a spectrum of physical properties.
قيم البحث
اقرأ أيضاً
We show that smectic liquid crystals confined in_anisotropic_ porous structures such as e.g.,_strained_ aerogel or aerosil exhibit two new glassy phases. The strain both ensures the stability of these phases and determines their nature. One type of s
train induces an ``XY Bragg glass, while the other creates a novel, triaxially anisotropic ``m=1 Bragg glass. The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase diagram for the system, and numerous other experimental observables.
We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a vari
ety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $gamma$-ensemble for which analytic results are not yet available.
Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble their bulk
counterparts. For instance, the electrostatic potential of a point charge at an air-water interface falls off as $r^{-3}$, where $r$ is the distance from the charge, exhibiting a dipolar behaviour. This behaviour is often assumed to be generic, and is widely referred to when interpreting experimental results. Here we explicitly calculate the in-plane potential of a point charge at an interface between two electrolyte solutions with different dielectric permittivities and Debye screening lengths. We show that the asymptotic behaviour of this potential is neither a dipole, which characterises the potential at air-water interfaces, nor a screened monopole, which describes the bulk behaviour in a single electrolyte solution. By considering the same problem in arbitrary dimensions, we find that the physics behind this difference can be traced to the asymmetric propagation of the interaction in the two media. Our results are relevant, for instance, to understand the physics of charged colloidal particles trapped at oil-water interfaces.
Evolving structure and rheology across Kuhn scale interfaces in entangled polymer fluids under flow play a prominent role in processing of manufactured plastics, and have numerous other applications. Quantitative tracking of chain conformation statis
tics on the Kuhn scale is essential for developing computational models of such phenomena. For this purpose, we formulate here a two-scale/two-mode model of entangled polymer chains under flow. Each chain is partitioned by successive entanglements into strands that are in one of two modes: entangled or dangling. On the strand scale, conformation statistics of ideal (non-interacting) strands follows a differential evolution equation for the second moment of its end-to-end distance. The latter regulates persistent random walks sampling conformation statistics of ideal entangled strands on the Kuhn scale, as follows from a generalized Green-Kubo relation and the Maximum Entropy Principle. We test it numerically for a range of deformation rates at the start-up of simple elongational and shear flows. A self-consistent potential, representing segmental interactions, modifies strand conformation statistics on the Kuhn scale, as it renormalizes the parameters controlling the persistent random walk. The generalized Green-Kubo relation is then inverted to determine how the second moment of the strand end-to-end distance is changed by the self-consistent potential. This allows us to devise a two-scale propagation scheme for the statistical weights of subchains of the entangled chain. The latter is used to calculate local volume fractions for each chemical type of Kuhn segments in entangled chains, thus determining the self-consistent potential.
In their seminal paper on scattering by an inhomogeneous solid, Debye and coworkers proposed a simple exponentially decaying function for the two-point correlation function of an idealized class of two-phase random media. Such {it Debye random media}
, which have been shown to be realizable, are singularly distinct from all other models of two-phase media in that they are entirely defined by their one- and two-point correlation functions. To our knowledge, there has been no determination of other microstructural descriptors of Debye random media. In this paper, we generate Debye random media in two dimensions using an accelerated Yeong-Torquato construction algorithm. We then ascertain microstructural descriptors of the constructed media, including their surface correlation functions, pore-size distributions, lineal-path function, and chord-length probability density function. Accurate semi-analytic and empirical formulas for these descriptors are devised. We compare our results for Debye random media to those of other popular models (overlapping disks and equilibrium hard disks), and find that the former model possesses a wider spectrum of hole sizes, including a substantial fraction of large holes. Our algorithm can be applied to generate other models defined by their two-point correlation functions, and their other microstructural descriptors can be determined and analyzed by the procedures laid out here.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
