Scale separation in granular packings: stress plateaus and fluctuations

It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective' definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small' ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.Comment: 4 pages, 4 figures, RevTeX 4, Minor corrections to match the published versio

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

New method to study stochastic growth equations: a cellular automata perspective

We introduce a new method based on cellular automata dynamics to study stochastic growth equations. The method defines an interface growth process which depends on height differences between neighbors. The growth rule assigns a probability $p_{i}(t)=\rho$ exp$[\kappa \Gamma_{i}(t)]$ for a site $i$ to receive one particle at a time $t$ and all the sites are updated simultaneously. Here $\rho$ and $\kappa$ are two parameters and $\Gamma_{i}(t)$ is a function which depends on height of the site $i$ and its neighbors. Its functional form is specified through discretization of the deterministic part of the growth equation associated to a given deposition process. In particular, we apply this method to study two linear equations - the Edwards-Wilkinson (EW) equation and the Mullins-Herring (MH) equation - and a non-linear one - the Kardar-Parisi-Zhang (KPZ) equation. Through simulations and statistical analysis of the height distributions of the profiles, we recover the values for roughening exponents, which confirm that the processes generated by the method are indeed in the universality classes of the original growth equations. In addition, a crossover from Random Deposition to the associated correlated regime is observed when the parameter $\kappa$ is varied.Comment: 6 pages, 7 figure

Tricritical directed percolation

We consider a modification of the contact process incorporating higher-order reaction terms. The original contact process exhibits a non-equilibrium phase transition belonging to the universality class of directed percolation. The incorporated higher-order reaction terms lead to a non-trivial phase diagram. In particular, a line of continuous phase transitions is separated by a tricritical point from a line of discontinuous phase transitions. The corresponding tricritical scaling behavior is analyzed in detail, i.e., we determine the critical exponents, various universal scaling functions as well as universal amplitude combinations

Effects of Friction and Disorder on the Quasi-Static Response of Granular Solids to a Localized Force

The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].Comment: 21 pages (PDFLaTeX), 24 figures (some of them bitmapped to save space); submitted to Phys. Rev.

Universal scaling behavior of non-equilibrium phase transitions

One of the most impressive features of continuous phase transitions is the concept of universality, that allows to group the great variety of different critical phenomena into a small number of universality classes. All systems belonging to a given universality class have the same critical exponents, and certain scaling functions become identical near the critical point. It is the aim of this work to demonstrate the usefulness of universal scaling functions for the analysis of non-equilibrium phase transitions. In order to limit the coverage of this article, we focus on a particular class of non-equilibrium critical phenomena, the so-called absorbing phase transitions. These phase transitions arise from a competition of opposing processes, usually creation and annihilation processes. The transition point separates an active phase and an absorbing phase in which the dynamics is frozen. A systematic analysis of universal scaling functions of absorbing phase transitions is presented, including static, dynamical, and finite-size scaling measurements. As a result a picture gallery of universal scaling functions is presented which allows to identify and to distinguish universality classes.Comment: review article, 160 pages, 60 figures include

ANALISIS TINGKAT PENJUALAN PENGUSAHA KULINER DENGAN ADANYA PROMOSI DAN DISTRIBUSI MELALUI GRAB FOOD

The purpose of this study was to determine the effect of promotion and distribution on grab food services on increasing sales of culinary entrepreneurs registered at PT. Grab Sumbawa Besar. This type of this research is associative. The data used in this study is quantitative obtained from primary sources. Primary data in this study is data obtained directly from respondents through distributing questionnaires. The number of samples as respondents in this study was as many as 38 people. All data that has been collected will be processed using the SPSS program to be studied using techniques which include multiple linear regression analysis, partial hypothesis testing (t test), simultaneous hypothesis testing (F test), and determination coefficient test (R2). The results of this study indicate that promotion and distribution have a positive and significant effect on the sales level of culinary entrepreneurs registered at PT. Grab Sumbawa Besar, either partially or simultaneously. The degree of influence of promotion and distribution on the sales level of culinary entrepreneurs registered at PT. Grab Sumbawa Besar is 62.1%, while the remaining 37.9% is influenced by other variables not examined in this study, such as product quality, product selling price, and selling price of competitors' products

Objective activity tracking in spine surgery: a prospective feasibility study with a low-cost consumer grade wearable accelerometer

Patient-reported outcome measures (PROMs) are commonly used to estimate disability of patients with spinal degenerative disease. Emerging technological advances present an opportunity to provide objective measurements of activity. In a prospective, observational study we utilized a low-cost consumer grade wearable accelerometer (LCA) to determine patient activity (steps per day) preoperatively (baseline) and up to one year (Y1) after cervical and lumbar spine surgery. We studied 30 patients (46.7% male; mean age 57 years; 70% Caucasian) with a baseline activity level of 5624 steps per day. The activity level decreased by 71% in the 1$^{st}$ postoperative week (p < 0.001) and remained 37% lower in the 2$^{nd}$ (p < 0.001) and 23% lower in the 4$^{th}$ week (p = 0.015). At no time point until Y1 did patients increase their activity level, compared to baseline. Activity was greater in patients with cervical, as compared to patients with lumbar spine disease. Age, sex, ethnic group, anesthesia risk score and fusion were variables associated with activity. There was no correlation between activity and PROMs, but a strong correlation with depression. Determining activity using LCAs provides real-time and longitudinal information about patient mobility and return of function. Recovery took place over the first eight postoperative weeks, with subtle improvement afterwards

Postoperative Complication Burden, Revision Risk, and Health Care Use in Obese Patients Undergoing Primary Adult Thoracolumbar Deformity Surgery

Study Design: This is a retrospective cohort study using a nationally representative administrative database. Objective: To identify the impact of obesity on postoperative outcomes in patients undergoing thoracolumbar adult spinal deformity (ASD) surgery. Background: The obesity rate in the United States remains staggering, with approximately one-third of all Americans being overweight or obese. However, the impact of elevated body mass index on spine surgery outcomes remains unclear. Methods: We queried the MarketScan database to identify patients who were diagnosed with a spinal deformity and underwent ASD surgery from 2007 to 2016. Patients were then stratified by whether or not they were diagnosed as obese at index surgical admission. Propensity score matching (PSM) was then utilized to mitigate intergroup differences between obese and nonobese patients. Patients <18 years and those with any prior history of trauma or tumor were excluded from this study. Baseline demographics and comorbidities, postoperative complication rates, and short- and long-term reoperation rates were determined. Results: A total of 7423 patients met the inclusion criteria of this study, of whom 597 (8.0%) were obese. Initially, patients with obesity had a higher 90-day postoperative complication rate than nonobese patients (46.1% vs 40.8%, P < .05); however, this difference did not remain after PSM. Revision surgery rates after 2 years were similar across the 2 groups following primary surgery (obese, 21.4%, vs nonobese, 22.0%; P = .7588). Health care use occurred at a higher rate among obese patients through 2 years of long-term follow-up (obese, $152 930, vs nonobese,$140 550; P < .05). Conclusion: Patients diagnosed with obesity who underwent ASD surgery did not demonstrate increased rates of complications, reoperations, or readmissions. However, overall health care use through 2 years of follow-up after index surgery was higher in the obesity cohort