Critical scaling in linear response of frictionless granular packings near jamming

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly non-affine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.Comment: 4 pages, 3 figures. v2: Added new results; removed part of discussion; changed Fig.

Non-affine response: jammed packings versus spring networks

We compare the elastic response of spring networks whose contact geometry is derived from real packings of frictionless discs, to networks obtained by randomly cutting bonds in a highly connected network derived from a well-compressed packing. We find that the shear response of packing-derived networks, and both the shear and compression response of randomly cut networks, are all similar: the elastic moduli vanish linearly near jamming, and distributions characterizing the local geometry of the response scale with distance to jamming. Compression of packing-derived networks is exceptional: the elastic modulus remains constant and the geometrical distributions do not exhibit simple scaling. We conclude that the compression response of jammed packings is anomalous, rather than the shear response.Comment: 6 pages, 6 figures, submitted to ep

Exact mean field inference in asymmetric kinetic Ising systems

We develop an elementary mean field approach for fully asymmetric kinetic Ising models, which can be applied to a single instance of the problem. In the case of the asymmetric SK model this method gives the exact values of the local magnetizations and the exact relation between equal-time and time-delayed correlations. It can also be used to solve efficiently the inverse problem, i.e. determine the couplings and local fields from a set of patterns, also in cases where the fields and couplings are time-dependent. This approach generalizes some recent attempts to solve this dynamical inference problem, which were valid in the limit of weak coupling. It provides the exact solution to the problem also in strongly coupled problems. This mean field inference can also be used as an efficient approximate method to infer the couplings and fields in problems which are not infinite range, for instance in diluted asymmetric spin glasses.Comment: 10 pages, 7 figure

Scaling of phononic transport with connectivity in amorphous solids

The effect of coordination on transport is investigated theoretically using random networks of springs as model systems. An effective medium approximation is made to compute the density of states of the vibrational modes, their energy diffusivity (a spectral measure of transport) and their spatial correlations as the network coordination $z$ is varied. Critical behaviors are obtained as $z\to z_c$ where these networks lose rigidity. A sharp cross-over from a regime where modes are plane-wave-like toward a regime of extended but strongly-scattered modes occurs at some frequency $\omega^*\sim z-z_c$, which does not correspond to the Ioffe-Regel criterion. Above $\omega^*$ both the density of states and the diffusivity are nearly constant. These results agree remarkably with recent numerical observations of repulsive particles near the jamming threshold \cite{ning}. The analysis further predicts that the length scale characterizing the correlation of displacements of the scattered modes decays as $1/\sqrt{\omega}$ with frequency, whereas for $\omega<<\omega^*$ Rayleigh scattering is found with a scattering length $l_s\sim (z-z_c)^3/\omega^4$. It is argued that this description applies to silica glass where it compares well with thermal conductivity data, and to transverse ultrasound propagation in granular matter

Bounds on the shear load of cohesionless granular matter

We characterize the force state of shear-loaded granular matter by relating the macroscopic stress to statistical properties of the force network. The purely repulsive nature of the interaction between grains naturally provides an upper bound for the sustainable shear stress, which we analyze using an optimization procedure inspired by the so-called force network ensemble. We establish a relation between the maximum possible shear resistance and the friction coefficient between individual grains, and find that anisotropies of the contact network (or the fabric tensor) only have a subdominant effect. These results can be considered the hyperstatic limit of the force network ensemble and we discuss possible implications for real systems. Finally, we argue how force anisotropies can be related quantitatively to experimental measurements of the effective elastic constants.Comment: 17 pages, 6 figures. v2: slightly rearranged, introduction and discussion rewritte

Ensemble Theory for Force Networks in Hyperstatic Granular Matter

An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a-priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution $P(f)$. For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a non-invertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting $P(f)$'s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a new perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.Comment: 17 pages, 17 figure

Origin of Corrections to Mean-field at the Onset of Unjamming

We present a detailed analysis of the unjamming transition in 2D frictionless disk packings using a static correlation function that has been widely used to study disordered systems. We show that this point-to-set (PTS) correlation function exhibits a dominant length scale that diverges as the unjamming transition is approached through decompression. In addition, we identify deviations from meanfield predictions, and present detailed analysis of the origin of non-meanfield behavior. A mean-field bulk-surface argument is reviewed. Corrections to this argument are identified, which lead to a change in the functional form of the critical PTS boundary size. An entropic description of the origin of the correlations is presented, and simple rigidity assumptions are shown to predict the functional form of the critical PTS boundary size as a function of the pressure

The Melanin-Concentrating Hormone (MCH) System Modulates Behaviors Associated with Psychiatric Disorders

Deficits in sensorimotor gating measured by prepulse inhibition (PPI) of the startle have been known as characteristics of patients with schizophrenia and related neuropsychiatric disorders. PPI disruption is thought to rely on the activity of the mesocorticolimbic dopaminergic system and is inhibited by most antipsychotic drugs. These drugs however act also at the nigrostriatal dopaminergic pathway and exert adverse locomotor responses. Finding a way to inhibit the mesocorticolimbic- without affecting the nigrostriatal-dopaminergic pathway may thus be beneficial to antipsychotic therapies. The melanin-concentrating hormone (MCH) system has been shown to modulate dopamine-related responses. Its receptor (MCH1R) is expressed at high levels in the mesocorticolimbic and not in the nigrostriatal dopaminergic pathways. Interestingly a genomic linkage study revealed significant associations between schizophrenia and markers located in the MCH1R gene locus. We hypothesize that the MCH system can selectively modulate the behavior associated with the mesocorticolimbic dopamine pathway. Using mice, we found that central administration of MCH potentiates apomorphine-induced PPI deficits. Using congenic rat lines that differ in their responses to PPI, we found that the rats that are susceptible to apomorphine (APO-SUS rats) and exhibit PPI deficits display higher MCH mRNA expression in the lateral hypothalamic region and that blocking the MCH system reverses their PPI deficits. On the other hand, in mice and rats, activation or inactivation of the MCH system does not affect stereotyped behaviors, dopamine-related responses that depend on the activity of the nigrostriatal pathway. Furthermore MCH does not affect dizocilpine-induced PPI deficit, a glutamate related response. Thus, our data present the MCH system as a regulator of sensorimotor gating, and provide a new rationale to understand the etiologies of schizophrenia and related psychiatric disorders

Effect of apomorphine on cognitive performance and sensorimotor gating in humans

Contains fulltext : 88792.pdf (publisher's version ) (Closed access)INTRODUCTION: Dysfunction of brain dopamine systems is involved in various neuropsychiatric disorders. Challenge studies with dopamine receptor agonists have been performed to assess dopamine receptor functioning, classically using the release of growth hormone (GH) from the hindbrain as primary outcome measure. The objective of the current study was to assess dopamine receptor functioning at the forebrain level. METHODS: Fifteen healthy male volunteers received apomorphine sublingually (2 mg), subcutaneously (0.005 mg/kg), and placebo in a balanced, double-blind, cross-over design. Outcome measures were plasma GH levels, performance on an AX continuous performance test, and prepulse inhibition of the acoustic startle. The relation between central outcome measures and apomorphine levels observed in plasma and calculated in the brain was modeled using a two-compartmental pharmacokinetic-pharmacodynamic analysis. RESULTS: After administration of apomorphine, plasma GH increased and performance on the AX continuous performance test deteriorated, particularly in participants with low baseline performance. Apomorphine disrupted prepulse inhibition (PPI) on high-intensity (85 dB) prepulse trials and improved PPI on low intensity (75 dB) prepulse trials, particularly in participants with low baseline PPI. High cognitive performance at baseline was associated with reduced baseline sensorimotor gating. Neurophysiological measures correlated best with calculated brain apomorphine levels after subcutaneous administration. CONCLUSION: The apomorphine challenge test appears a useful tool to assess dopamine receptor functioning at the forebrain level. Modulation of the effect of apomorphine by baseline performance levels may be explained by an inverted U-shape relation between prefrontal dopamine functioning and cognitive performance, and mesolimbic dopamine functioning and sensorimotor gating. Future apomorphine challenge tests preferentially use multiple outcome measures, after subcutaneous administration of apomorphine.1 januari 201