اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDisorder Perturbation Expansion for Athermal Crystals
431
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We introduce a perturbation expansion for athermal systems that allows an exact determination of displacement fields away from the crystalline state as a response to disorder. We show that the displacement fields in energy minimized configurations of particles interacting through central potentials with microscopic disorder, can be obtained as a series expansion in the strength of the disorder. We introduce a hierarchy of force balance equations that allows an order-by-order determination of the displacement fields, with the solutions at lower orders providing sources for the higher order solutions. This allows the simultaneous force balance equations to be solved, within a hierarchical perturbation expansion to arbitrary accuracy. We present exact results for an isotropic defect introduced into the crystalline ground state at linear order and second order in our expansion. We show that the displacement fields produced by the defect display interesting self-similar properties at every order. We derive a $|delta r| sim 1/r$ and $|delta f| sim 1/r^2$ decay for the displacement fields and excess forces at large distances $r$ away from the defect. Finally we derive non-linear corrections introduced by the interactions between defects at second order in our expansion. We verify our exact results with displacement fields obtained from energy minimized configurations of soft disks.
قيم البحث
اقرأ أيضاً
We analyze the fluctuations in particle positions and inter-particle forces in disordered jammed crystals in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characteri
zed by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order. We show that constrained fluctuations result as a consequence of local force balance conditions, and are characterized by non-Gaussian distributions which we derive exactly. We analytically predict several properties of such systems, including the scaling of the average coordination with polydispersity and packing fraction, which we verify with numerical simulations using soft disks with one-sided harmonic interactions.
We derive exact results for displacement fields that develop as a response to external pinning forces in two dimensional athermal networks. For a triangular lattice arrangement of particles interacting through soft potentials, we develop a Greens fun
ction formalism which we use to derive exact results for displacement fields produced by localized external forces. We show that in the continuum limit the displacement fields decay as $1/r$ at large distances $r$ away from a force dipole. Finally, we extend our formulation to study correlations in the displacement fields produced by the external pinning forces. We show that uncorrelated pinned forces at each vertex give rise to long-range correlations in displacements in athermal systems, with a non-trivial system size dependence. We verify our predictions with numerical simulations of athermal networks in two dimensions.
We develop an elasto-plastic description for the transient dynamics prior to steady flow of athermally yielding materials. Our mean-field model not only reproduces the experimentally observed non-linear time dependence of the shear-rate response to a
n external shear-stress, but also allows for the determination of the different physical processes involved in the onset of the re-acceleration phase after the initial critical slowing down and a distinct well defined fluidization phase. The evidenced power-law dependence of the fluidization time on the distance of the applied to an age dependent static yield stress is not universal but strongly dependent on initial conditions.
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We show that t
his formulation compares advantageously to the currently standard techniques due to its high efficiency, simplicity, and broad range of applicability. Our formalism permits to easily complement perturbation theory with non-perturbative information, which we illustrate by implementing expansions renormalized by the addition of a gap or the inclusion of Dynamical Mean-Field Theory. As a result, we present numerically-exact results for the square-lattice Fermi-Hubbard model in the low temperature non-Fermi-liquid regime and show the momentum-dependent suppression of fermionic excitations in the antinodal region.
We combine computer simulations and analytical theory to investigate the glassy dynamics in dense assemblies of athermal particles evolving under the sole influence of self-propulsion. The simulations reveal that when the persistence time of the self
-propelled particles is increased, the local structure becomes more pronounced whereas the long-time dynamics first accelerates and then slows down. These seemingly contradictory evolutions are explained by constructing a nonequilibrium mode-coupling-like theory for interacting self-propelled particles. To predict the collective dynamics the theory needs the steady state structure factor and the steady state correlations of the local velocities. It yields nontrivial predictions for the glassy dynamics of self-propelled particles in qualitative agreement with the simulations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
