arXiv subjects

Daniel Hexner

Publications and source records attributed to Daniel Hexner.

26 records · Page 2Linked to original sources

arXiv2018

Two diverging length scales in the structure of jammed packings

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $ξ_{Z}$, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, $ξ_{f}$, is associated with contact-number fluctuations in subsystems of different sizes. On scales below $ξ_{f}$ the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of $ξ_{Z}$ and $ξ_{f}$ are different and appear to be different in two and three dimensions.

cond-mat.soft↗

arXiv2017

Role of local response in manipulating the elastic properties of disordered solids by bond removal

We explore the range over which the elasticity of disordered spring networks can be manipulated by the removal of selected bonds. By taking into account the local response of a bond, we demonstrate that the effectiveness of pruning can be improved so that auxetic (i.e., negative Poisson's ratio) materials can be designed without the formation of cracks even while maintaining the global isotropy of the network. The bulk, $B$, and shear, $G$, moduli scale with the number of bonds removed and we estimate the exponents characterizing these power laws. We also find that there are spatial correlation lengths in the change of $B$ and $G$ upon removing different bonds that diverge as the network approaches the isostatic limit where the excess coordination number $ΔZ\rightarrow0$.

cond-mat.soft↗

arXiv2017

Linking microscopic and macroscopic response in disordered solids

The modulus of a rigid network of harmonic springs depends on the sum of the energies in each of the bonds due to the applied distortion: compression in the case of the bulk modulus, $B$, or shear in the case of the shear modulus, $\mathcal{G}$. The distortion need not be global and we introduce a local modulus, $L_{i}$, associated with changing the equilibrium length of a single bond, $i$, in the network. We show that $L_{i}$ is useful for understanding many aspects of the mechanical response of the entire system. For example, it allows an understanding, and efficient computation, of how each bond in a network contributes to global properties such as $B$ and $\mathcal{G}$ and sheds light on how a particular bond's contribution to one modulus is, or is not, correlated with its contribution to another.

cond-mat.soft↗

arXiv2016

Noise, diffusion, and hyperuniformity

We consider driven many-particle models which have a phase transition between an active and an absorbing phase. Like previously studied models, we have particle conservation, but here we introduce an additional symmetry - when two particles interact, we give them stochastic kicks which conserve center of mass. We find that the density fluctuations in the active phase decay in the fastest manner possible for a disordered isotropic system, and we present arguments that the large scale fluctuations are determined by a competition between a noise term which generates fluctuations, and a deterministic term which reduces them. Our results may be relevant to shear experiments and may further the understanding of hyperuniformity which occurs at the critical point.

cond-mat.stat-mech↗

arXiv2014

Hyperuniformity of critical absorbing states

The properties of the absorbing states of non-equilibrium models belonging to the conserved directed percolation universality class are studied. We find that at the critical point the absorbing states are hyperuniform, exhibiting anomalously small density fluctuations. The exponent characterizing the fluctuations is measured numerically, a scaling relation to other known exponents is suggested, and a new correlation length relating to this ordering is proposed. These results may have relevance to photonic band-gap materials.

cond-mat.stat-mech↗

arXiv2014

Self Organization and Self Avoiding Limit Cycles

A simple periodically driven system displaying rich behavior is introduced and studied. The system self-organizes into a mosaic of static ordered regions with three possible patterns, which are threaded by one-dimensional paths on which a small number of mobile particles travel. These trajectories are self-avoiding and non-intersecting, and their relationship to self-avoiding random walks is explored. Near $ρ=0.5$ the distribution of path lengths becomes power-law like up to some cutoff length, suggesting a possible critical state.

cond-mat.stat-mech↗

arXiv2013

Entropic commensurate-incommensurate transition

The equilibrium properties of a minimal tiling model are investigated. The model has extensive ground state entropy, with each ground state having a quasiperiodic sequence of rows. It is found that the transition from the quasiperiodic ground state to the high temperature disordered phase proceeds through a sequence of periodic arrangements of rows, in analogy with the Frenkel-Kontorova model, but with temperature playing the role of the strength of the substrate potential.

cond-mat.stat-mech↗

arXiv2009

Tug-of-war in motility assay experiments

The dynamics of two groups of molecular motors pulling in opposite directions on a rigid filament is studied theoretically. To this end we first consider the behavior of one set of motors pulling in a single direction against an external force using a new mean-field approach. Based on these results we analyze a similar setup with two sets of motors pulling in opposite directions in a tug-of-war in the presence of an external force. In both cases we find that the interplay of fluid friction and protein friction leads to a complex phase diagram where the force-velocity relations can exhibit regions of bistability and spontaneous symmetry breaking. Finally, motivated by recent work, we turn to the case of motility assay experiments where motors bound to a surface push on a bundle of filaments. We find that, depending on the absence or the presence of a bistability in the force-velocity curve at zero force, the bundle exhibits anomalous or biased diffusion on long-time and large-length scales.

q-bio.SC↗