Sticky Limit Research Articles

Temporal variation in the soil properties and rice yield of organic rice farming in the tropical monsoon region, Indonesia

One of the organic farming goals is improving soil properties to support sustainable rice production. This study investigated the soil properties and rice yields under temporal variation of organic rice fields. Soil sampling was conducted in organic rice fields with three temporal variations, namely 0, 4, 7, and 10 years in a tropical monsoon region in Central Java, Indonesia. Variables observed included soil organic carbon, soil carbon stock, soil microbes population, dissolved organic carbon, soil liquid limit, soil sticky limit, soil plasticity limit, soil color changing limit, soil friability, soil porosity, soil total nitrogen, soil total phosphorus, soil available sulfur, exchangeable calcium, cation exchange capacity, total potassium, bulk density, base saturation, exchangeable sodium, exchangeable potassium, and rice yield. This study confirms that soil organic carbon increased by 51.63% within 10 years (from 1.84% to 2.79%). Organic farming also improved all the physical, chemical, and biological soil properties, by the increase of soil organic carbon. However, soil organic carbon is mostly determined by soil cation exchange capacity, soil total phosphorus, and soil porosity. The mechanism of rice yield increase in organic rice farming is not affected by soil organic carbon directly but through the synergic increase in soil total nitrogen. The 1% increase of soil organic carbon increases 0.065% of soil total nitrogen hence rice yield increases by 1.66 tons ha<sup>-1</sup>. This study supports sustainable agriculture by providing evidence of improved soil properties under organic farming.

A multi-linear approach to strength and plasticity states between the Atterberg limits

The separate plasticity or consistency states between the liquid and plastic limits originally introduced by Atterberg and Terzaghi have long been disregarded, with just one state, plastic, currently acknowledged. The semi-logarithmic relationship between undrained shear strength and liquidity index often considered as a unique straight line is shown to be more realistically represented by a multi-linear approach with much better correlation compared to the single line usually adopted. This approach produces more accurate shear strength values at the liquid and plastic limits compared to those obtained from a single line. The trilinear interpretation of liquidity index against undrained shear strength (fall cone and lab vane) delineates very soft and soft transitions. The stiff transition and a tentative measure of the sticky or adhesion limit have been derived from the author's toughness tests. The plastic range can then be separated, as originally suggested, into consistency regions marked by very soft, soft and stiff transitions and adhesive and non-adhesive states distinguished by the adhesion limit. The adhesion limit deserves further investigation as it represents a significant change of state.

Research Spotlights

Tensors, or multiway arrays, are often used for storage of high-dimensional data. In order to have compression, completion, or interpretation of such data, the data tensor is factored according to a proposed model consistent with some belief about the data. The first Research Spotlights article, “Generalized Canonical Polyadic Tensor Decomposition," by David Hong, Tamara G. Kolda, and Jed A. Duersch, treats the problem of finding a low-rank tensor decomposition that minimizes a cost functional defined from a componentwise loss function. The difference between the proposed generalized canonical polyadic (GCP) decomposition and the well-known CP decomposition is the flexibility in the choice of loss function, which can be tailored to reflect the appropriate statistical likelihood of a model given the data: low rankness of the tensor is enforced as a constraint. The main result of the paper is in Theorem 3, which addresses the computation of the gradients of a cost function defined in terms of any loss function that is continuously differentiable with respect to its second argument. Their result reveals an elegant expression for the gradients that enables the use of existing kernels for finding CP decompositions to be employed in their algorithm to compute the GCP. The authors use extensive numerical testing, highlighting the flexibility of their algorithm and its ability to efficiently handle missing data while simultaneously illustrating the potential gain to the data analyst in choosing loss functions more consistent with the data. A variety of applications are considered, including analysis of a chat network and explaining factors for mouse neural activity. A “sticky” diffusion process, as defined in the second Research Spotlights article, “Sticky Brownian Motion and Its Numerical Solution," refers to solutions to stochastic differential equations (SDEs) that can spend finite time on a lower-dimensional boundary. Materials like concrete, paint, and toothpaste have something in common: in the limit, the dynamics of the collection of mesoscale particles of which each is comprised approaches a sticky diffusion process. Sticky Brownian motion (SBM), the simplest example of a sticky diffusion process, is the primary focus of the present work. The goals of authors Nawaf Bou-Rabee and Miranda C. Holmes-Cerfon are to call the attention of the greater applied mathematics community to the topic of sticky diffusions as well as to offer a numerical method to allow for simulation of a sticky diffusion with a relatively large time step. These goals are evident in the presentation of material. The mathematical setup of an SBM is given in section 2. Beginning with the Brownian dynamics equations and assumptions on the potential energy function, the dynamics of the probability density are discussed, including asymptotic behavior in the “sticky limit." The authors discuss how to find the generator of the SBM and give some examples. The generator is the basis for the numerical method they develop in section 3, which the authors claim is orders of magnitude faster than alternative methods to simulate a sticky Brownian motion. The authors complement their presentation with a mathematical literature review of some additional methods for characterizing SBM. The final section serves as a well-considered road map for the reader interested in extending this work to a higher-dimensional setting.

Financial Calendar

Resummed thermodynamic perturbation theory for central force associating potential is extended and applied to study the properties of shielded attractive shell model of polymerizing hard spheres of different sizes. The model is represented by the two-component mixture of hard spheres with additional square-well interaction treated in the sticky limit and located inside the hard-core region and acting only between particles of different species. The theory self-consistently takes into account the changes in the excluded volume of the system due to bonding of the particles. Theoretical predictions for the pressure and fraction of the particles in different bonding states at different temperatures and densities are compared against computer simulation predictions. The theory appears to be very accurate in description of the dimerizing and trimerizing versions of the model. For the model, which allows chain polymerization the theory is slightly less accurate, in particular for low temperatures and high densities.

Sticky-Sphere Clusters

Nano- and microscale particles, such as colloids, commonly interact over ranges much shorter than their diameters, so it is natural to treat them as “sticky,” interacting only when they touch exactly. The lowest-energy states, free energies, and dynamics of a collection of n particles can be calculated in the sticky limit of a deep, narrow interaction potential. This article surveys the theory of the sticky limit, explains the correspondence between theory and experiments on colloidal clusters, and outlines areas where the sticky limit may bring new insight.

Free energy of singular sticky-sphere clusters.

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential and complex fluids near jamming, to self-assembled lattices and various metamaterials. Under small thermal fluctuations the vibrational entropy of a ground state is given by the harmonic approximation if it has no zero-frequency vibrational modes, yet such singular modes are at the epicenter of many interesting behaviors in the systems above. We consider a system of N spherical particles, and directly account for the singularities that arise in the sticky limit where the pairwise interaction is strong and short ranged. Although the contribution to the partition function from singular clusters diverges in the limit, its asymptotic value can be calculated and depends on only two parameters, characterizing the depth and range of the potential. The result holds for systems that are second-order rigid, a geometric characterization that describes all known ground-state (rigid) sticky clusters. To illustrate the applications of our theory we address the question of emergence: how does crystalline order arise in large systems when it is strongly disfavored in small ones? We calculate the partition functions of all known rigid clusters up to N≤21 and show the cluster landscape is dominated by hyperstatic clusters (those with more than 3N-6 contacts); singular and isostatic clusters are far less frequent, despite their extra vibrational and configurational entropies. Since the most hyperstatic clusters are close to fragments of a close-packed lattice, this underlies the emergence of order in sticky-sphere systems, even those as small as N=10.

Shielded attractive shell model of polymerizing hard spheres of different size. Resummed thermodynamic perturbation theory and computer simulation

Abstract Resummed thermodynamic perturbation theory for central force associating potential is extended and applied to study the properties of shielded attractive shell model of polymerizing hard spheres of different sizes. The model is represented by the two-component mixture of hard spheres with additional square-well interaction treated in the sticky limit and located inside the hard-core region and acting only between particles of different species. The theory self-consistently takes into account the changes in the excluded volume of the system due to bonding of the particles. Theoretical predictions for the pressure and fraction of the particles in different bonding states at different temperatures and densities are compared against computer simulation predictions. The theory appears to be very accurate in description of the dimerizing and trimerizing versions of the model. For the model, which allows chain polymerization the theory is slightly less accurate, in particular for low temperatures and high densities.

Mechanical Bowel Preparation Versus no Preparation in Elective Colorectal Surgery: A Prospective Randomised Study

Resummed thermodynamic perturbation theory for central force associating potential is extended and applied to study the properties of shielded attractive shell model of polymerizing hard spheres of different sizes. The model is represented by the two-component mixture of hard spheres with additional square-well interaction treated in the sticky limit and located inside the hard-core region and acting only between particles of different species. The theory self-consistently takes into account the changes in the excluded volume of the system due to bonding of the particles. Theoretical predictions for the pressure and fraction of the particles in different bonding states at different temperatures and densities are compared against computer simulation predictions. The theory appears to be very accurate in description of the dimerizing and trimerizing versions of the model. For the model, which allows chain polymerization the theory is slightly less accurate, in particular for low temperatures and high densities.

Implications of variability in soil structures and physio-mechanical properties of soil after different failure patterns

Soil may fail in a number of ways during tilling, depending on soil conditions and the type of implement. The present paper investigates soil structures and several soil physical and mechanical properties associated with different failure patterns in two agricultural soils (upland and paddy). The dry bulk density, soil cohesion, internal friction angle, and cone index decreased remarkably after brittle failure, while chip-forming and bending failure proved less adequate at modifying these parameters. In addition, the highest soil fractal dimensions and specific surface areas were found after brittle failure in both soils, while the lowest were found after bending failure. However, the Dm and Aspecific of paddy soil were higher than that of upland soil after brittle failure and chip-forming failure patterns, whereas the opposite occurred after bending failure. This study suggests that brittle failure is the most desirable type of soil failure pattern to achieve appropriate tilth, which can be found at the sticky limit of soil.

Sticky central limit theorems at isolated hyperbolic planar singularities

We derive the limiting distribution of the barycenter $b_n$ of an i.i.d. sample of $n$ random points on a planar cone with angular spread larger than $2\pi$. There are three mutually exclusive possibilities: (i) (fully sticky case) after a finite random time the barycenter is almost surely at the origin; (ii) (partly sticky case) the limiting distribution of $\sqrt{n} b_n$ comprises a point mass at the origin, an open sector of a Gaussian, and the projection of a Gaussian to the sector's bounding rays; or (iii) (nonsticky case) the barycenter stays away from the origin and the renormalized fluctuations have a fully supported limit distribution-usually Gaussian but not always. We conclude with an alternative, topological definition of stickiness that generalizes readily to measures on general metric spaces.

Les complications des microgreffes de cheveux

Resummed thermodynamic perturbation theory for central force associating potential is extended and applied to study the properties of shielded attractive shell model of polymerizing hard spheres of different sizes. The model is represented by the two-component mixture of hard spheres with additional square-well interaction treated in the sticky limit and located inside the hard-core region and acting only between particles of different species. The theory self-consistently takes into account the changes in the excluded volume of the system due to bonding of the particles. Theoretical predictions for the pressure and fraction of the particles in different bonding states at different temperatures and densities are compared against computer simulation predictions. The theory appears to be very accurate in description of the dimerizing and trimerizing versions of the model. For the model, which allows chain polymerization the theory is slightly less accurate, in particular for low temperatures and high densities.

Phonon contribution to the entropy of hard-sphere crystals.

Comparing the entropies of hard spheres in the limit of close packing, for different stacking sequences of the hexagonal layers, has been a challenge because the differences are so small. Here we present a method based on a "sticky-sphere" model by which the system interpolates between hard spheres in one limit and a harmonic crystal in the other. For the fcc and hcp stackings we have calculated the entropy difference in the harmonic (sticky) limit, as well as the differences in the free energy change upon removing the stickiness in the model. The former, or phonon entropy, accounts for most of the entropy difference. Our value for the net entropy difference, Δs = 0.001164(8)k(B) per sphere, is in excellent agreement with the best previous estimate by Mau and Huse [Phys. Rev. E 59, 4396 (1999)].

Soil failure patterns and draft as influenced by consistency limits: An evaluation of the remolded soil cutting test

Soil failure patterns play an important role in obtaining a better understanding of the mechanical behavior of soils. Despite the large number of studies over the past few decades, a better understanding of soil failure patterns and its relation to soil and tool parameters for particular soils such as dry land and paddy has not been developed. This study investigated soil failure patterns and related draft at sticky, plastic and liquid consistency limits and the sticky point of dry land and paddy soils. A soil cutting test rig was developed to perform soil cutting at three consistency limits (sticky limit, plastic limit and liquid limit) and the sticky point of soil, three rake angles (15°, 30° and 45°), and three operating depths (30mm, 50mm and 70mm). A flat triangular shaped tool operating at a constant speed of 10mms−1 was used in all experiments. Soil failure patterns were observed and recorded using a digital camera, and draft per unit displacement was measured by load cells attached to the soil bin. A direct relationship between soil failure patterns or draft and the consistency limits of soil was found. Brittle failure was obtained at the sticky limit, chip forming failure was observed at 15° rake angle and 30mm depth, and bending failure with little strains of elements at 30° and 45° rake angles and 50mm and 70mm depths at plastic limit, while flow failure was linked to the liquid limit of the soil. At the sticky point, flow failure was observed at an operating depth of 30mm and 15° rake angle, while flow with considerable bending and no strains of elements occurred at 50mm and 70mm operating depths and 30° and 45° rake angles. However, bending was more prominent at 70mm depth and 45° rake angle. The draft at the sticky limit, plastic limit and sticky point was cyclic in nature, whereas at the liquid limit it was comparatively diverse and fading. The highest draft was found at the plastic limit, and the lowest at the liquid limit. Since the soil failure patterns may change with moisture content, soil type and particle size distribution within the same textural class, consistency limits can provide clearer and more accurate definitions of soil failure patterns than moisture content levels alone.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension $1$ and hence measure $0$) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine. We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky).

Phase behavior of the modified-Yukawa fluid and its sticky limit

Simple model systems with short-range attractive potentials have turned out to play a crucial role in determining theoretically the phase behavior of proteins or colloids. However, as pointed out by D. Gazzillo [J. Chem. Phys. 134, 124504 (2011)], one of these widely used model potentials, namely, the attractive hard-core Yukawa potential, shows an unphysical behavior when one approaches its sticky limit, since the second virial coefficient is diverging. However, it is exactly this second virial coefficient that is typically used to depict the experimental phase diagram for a large variety of complex fluids and that, in addition, plays an important role in the Noro-Frenkel scaling law [J. Chem. Phys. 113, 2941 (2000)], which is thus not applicable to the Yukawa fluid. To overcome this deficiency of the attractive Yukawa potential, D. Gazzillo has proposed the so-called modified hard-core attractive Yukawa fluid, which allows one to correctly obtain the second and third virial coefficients of adhesive hard-spheres starting from a system with an attractive logarithmic Yukawa-like interaction. In this work we present liquid-vapor coexistence curves for this system and investigate its behavior close to the sticky limit. Results have been obtained with the self-consistent Ornstein-Zernike approximation (SCOZA) for values of the reduced inverse screening length parameter up to 18. The accuracy of SCOZA has been assessed by comparison with Monte Carlo simulations.

An apparatus for the determination of the workability and plastic limit of clays

An apparatus is described that replicates Atterberg's procedure of rolling a thread of clay for the determination of the plastic limit of soils with minimal operator interference or judgement of the crumbling condition required. From nominal stresses applied during rolling and changes in diameter measured for each rolling traverse the toughness of the clay is determined from the stress–strain curves, as work/unit volume for a specified amount of deformation. Threads are tested at water contents ranging from near the sticky limit through the workable plastic region to the brittle state. An abrupt ductile–brittle or plastic–brittle transition is found allowing the plastic limit to be defined as the transition water content. A less abrupt but distinct stiffness transition is frequently obtained that separates the workable plastic region into a soft-plastic and a stiff-plastic region. Good relationships between toughness and water content are achieved from which the maximum toughness, Tmax, at the plastic limit is derived together with other new and useful properties such as the water content at the stiffness transition, wS and at zero toughness, the toughness limit, wT. Also derived are the gradients of the relationships, the toughness coefficients, TC, the range of water contents over which the clay is plastic and tough, the toughness index, IT and the water content in relation to the toughness index, the workability index, Iw. Each clay is found to have a closely correlated toughness–water content relationship depending mainly on the clay content and clay mineralogy demonstrating that control of the plasticity of the clay and its associated water contents are achievable.

Janus fluid with fixed patch orientations: Theory and simulations

We study thermophysical properties of a Janus fluid with constrained orientations, using analytical techniques and numerical simulations. The Janus character is modeled by means of a Kern-Frenkel potential where each sphere has one hemisphere of square-well and the other of hard-sphere character. The orientational constraint is enforced by assuming that each hemisphere can only point either North or South with equal probability. The analytical approach hinges on a mapping of the above Janus fluid onto a binary mixture interacting via a "quasi" isotropic potential. The anisotropic nature of the original Kern-Frenkel potential is reflected by the asymmetry in the interactions occurring between the unlike components of the mixture. A rational-function approximation extending the corresponding symmetric case is obtained in the sticky limit, where the square-well becomes infinitely narrow and deep, and allows a fully analytical approach. Notwithstanding the rather drastic approximations in the analytical theory, this is shown to provide a rather precise estimate of the structural and thermodynamical properties of the original Janus fluid.

Sticky central limit theorems on open books

Sticky central limit theorems on open books

An investigation of the SCOZA for narrow square-well potentials and in the sticky limit

We present a study of the self-consistent Ornstein–Zernike approximation (SCOZA) for square-well (SW) potentials of narrow width δ. The main purpose of this investigation is to elucidate whether, in the limit δ → 0, the SCOZA predicts a finite value for the second virial coefficient at the critical temperature B 2(T c), and whether this theory can lead to an improvement of the approximate Percus–Yevick solution of the sticky hard-sphere (SHS) model due to Baxter [J. Chem. Phys. 49, 2770 (1968)]. For the SW of non-vanishing δ, the difficulties due to the influence of the boundary condition at high density, already encountered in an earlier investigation by Schöll-Paschinger et al. [J. Chem. Phys. 123, 234513 (2005)], prevented us from obtaining reliable results for δ <0.1. In the sticky limit, this difficulty can be circumvented, but then the SCOZA fails to predict a liquid–vapor transition. The picture that emerges from this study is that, for δ → 0, the SCOZA does not fulfill the expected prediction of a constant B 2(T c) [J. Chem. Phys. 113, 2941 (2000)], and that, for thermodynamic consistency to be usefully exploited in this regime, one should probably go beyond the Ornstein–Zernike ansatz.

On the impossibility of defining adhesive hard spheres as sticky limit of a hard-sphere-Yukawa potential

For fluids of molecules with short-ranged hard-sphere-Yukawa (HSY) interactions, it is proven that the Noro-Frenkel "extended law of corresponding states" cannot be applied down to the vanishing attraction range, since the exact HSY second virial coefficient diverges in such a limit. It is also shown that, besides Baxter's original approach, a fully correct alternative definition of "adhesive hard spheres" can be obtained by taking the vanishing-range-limit (sticky limit) not of a Yukawa tail, as is commonly done, but of a slightly different potential with a logarithmic-Yukawa attraction.