An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.Comment: arXiv admin note: text overlap with arXiv:1505.0544

Reversion of late progeny in mutants with reduced fertility in Caenorhabditis elegans.

The detailed study of fertility is an eminent objective due to its involvement in the human population. Interestingly, research in relation to dietary restriction in different species have related this circumstance to an increase in longevity and delay in fertility. The evolutionarily conserved insulin / insulin-like growth factor-1 pathway is directly related to this phenomenon. Caenorhabditis elegans is an animal model widely used for the study of, for which, and in relation to this pathway, the transcription factor DAF-16 (homologous to human FOXO) plays an especially important role. Mutants for the insulin pathway, which in some extent mimic a dietary restriction situation, have also shown to have reduced fertility. Based on this, previous studies corroborated that suppression by interfering RNA (iRNA) of DAF-16 in mutants with impaired fertility reverses this phenotype.The phenomenon of late progeny is that individuals appear to have offspring later in life than wild-type ones, not being described solidly in the literature; that is why the purposes of this project consist of its evaluation and the verification of a possible reversion. Two thermosensitive mutants of C. elegans have been selected for study, for which a reduction in fertility was observed: mutant daf-2 (e1370), receptor tyrosine kinase, and mutant age-1 (mg305), subunit of the PI3 Kinase. There is not much data regarding this second mutant.First, it has been necessary to establish a parameter to discern between what will be considered late progeny or not. To carry it out, its laying behavior has been observed after being incubated at different temperatures in its fertile period. The obtained results corroborate that the late progeny is a real and measurable phenomenon, reflecting a significant difference of the mutants with respect to the wild ones at a temperature of 22.5ºC; having established the fifth day of the fertile period as a margin to differentiate its existence. Subsequently, experiments are planned to observe a possible reversal of the condition through the administration of 4-5 iRNA for specific genes that have been previously identified through genetic screening, and that seem to intervene in some way in this route by suppressing the reduced fertility phenotype. If this is the case, these genes would be described as being involved in the phenomenon of late progeny, establishing a mechanical correlation between reduction of fertility and the phenomenon of late progeny

Global Orbit Patterns for Dynamical Systems On Finite Sets

In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed formulas, the number of gop of the set of all the function from $X$ to itself. We also explore, using the brute force of computers, some subsets of locally rigid functions on $X$, for which interesting patterns of periodic orbits are found.Comment: 29 pages, 3 figures. to appear in Proceedings of the International Conference On Modeling of Engineering & Technological Problems (ICMETP), Agra (India), 2009. Published by the American Institute of Physics, U.S.

Identification of bioactive compounds in diabetes and infertility models of C. elegans

Polycystic ovary syndrome (POS) is a complex and heterogeneous endocrine disease characterized by hyperandrogenism, oligo-anovulation and metabolic disorders, including insulin resistance, obesity and type II diabetes. Additionally, POS causes infertility in childbearing age women, making of great interest the search of new treatments and compounds for the improvement of the symptoms of this chronic disease. Despite the definitive pathological mechanism of POS is still unknown, as mentioned before there is a strong relation between the syndrome and different alterations in the insulin signaling pathway. This pathway is evolutionary conserved and it has a homologue pathway in the organism Caenorhabditis elegans. Mutations in the insulin receptor homologue daf-2 gene or in the phosphatidylinositol 3-kinase (PI3K) homologue age-1, result in reduction of fertility, being the decrease in progeny sharper in the allele age-1(mg305) mutant, in addition to a less pleiotropic effect. We consider this mutant of C. elegans a good model to study the insulin pathway, and specifically POS, due to the high degree of conservation of the pathway and the similarities between the phenotype caused by the mutation and the human symptoms

Three examples concerning the interaction of dry friction and oscillations

We discuss recent work concerning the interaction of dry friction, which is a rate independent effect, and temporal oscillations. First, we consider the temporal averaging of highly oscillatory friction coefficients. Here the effective dry friction is obtained as an infimal convolution. Second, we show that simple models with state-dependent friction may induce a Hopf bifurcation, where constant shear rates give rise to periodic behavior where sticking phases alternate with sliding motion. The essential feature here is the dependence of the friction coefficient on the internal state, which has an internal relaxation time. Finally, we present a simple model for rocking toy animal where walking is made possible by a periodic motion of the body that unloads the legs to be moved

Galactosemia tipo III

Un gran número de enfermedades metabólicas pertenecen al grupo de enfermedades clasificadas como enfermedades raras. Las mutaciones en cada una de las tres enzimas encargadas del correcto metabolismo de la galactosa producen un tipo de enfermedad rara conocida como galactosemias, clasificadas como tipo I, II y III, según la enzima afectada. Dentro de las galactosemias, la deficiencia de galactosa-4-epimerasa (GALE) responsable de la galactosemia tipo III es la más rara, la de más difícil diagnóstico, con la aparición de signos clínicos más severos y no cuenta con un tratamiento definido. Las investigaciones sobre la galactosemia tipo III en células de mamíferos, levaduras, moscas y Caenorhabditis elegans que se están realizando pretenden comprender mejor los mecanismos de la enfermedad, buscar nuevos métodos diagnósticos y dianas para su tratamiento

Suppressing nano-scale stick-slip motion by feedback

When a micro cantilever with a nano-scale tip is manipulated on a substrate with atomic-scale roughness, the periodic lateral frictional force and stochastic fluctuations may induce stick-slip motion of the cantilever tip, which greatly decreases the precision of the nano manipulation. This unwanted motion cannot be reduced by open-loop control especially when there exist parameter uncertainties in the system model, and thus needs to introduce feedback control. However, real-time feedback cannot be realized by the existing virtual reality virtual feedback techniques based on the position sensing capacity of the atomic force microscopy (AFM). To solve this problem, we propose a new method to design real-time feedback control based on the force sensing approach to compensate for the disturbances and thus reduce the stick-slip motion of the cantilever tip. Theoretical analysis and numerical simulations show that the controlled motion of the cantilever tip tracks the desired trajectory with much higher precision. Further investigation shows that our proposal is robust under various parameter uncertainties. Our study opens up new perspectives of real-time nano manipulation.Comment: 8 pages, 10 figure

Desiccation and storage of Caenorhabditis elegans for use in aquaculture

Aquaculture is a thriving sector, although the main issues it faces at the moment is the feeding of fish at an early stage of development. The most utilised specie for that is Artemia. Nematodes could replace Artemia in larviculture thanks to its rapid development by self-fertilization and its ability to be produced in a massive way fed with bacteria. Therefore, it would reduce the price of the raw.The use of nematodes for feeding fish larvae in aquaculture has required an adaptation to different salt concentrations in liquid medium. There is also necessary to develop an efficient protocol for the desiccation and storage of nematodes at different larval stages, this would allow the product to be transported to fish farms worldwide.We are developing desecating protocols for different conditions such as time, temperature and relative humidity. In this way we will be able to determine which of them is the most effectiv

Functional Integration Approach to Hysteresis

A general formulation of scalar hysteresis is proposed. This formulation is based on two steps. First, a generating function g(x) is associated with an individual system, and a hysteresis evolution operator is defined by an appropriate envelope construction applied to g(x), inspired by the overdamped dynamics of systems evolving in multistable free energy landscapes. Second, the average hysteresis response of an ensemble of such systems is expressed as a functional integral over the space G of all admissible generating functions, under the assumption that an appropriate measure m has been introduced in G. The consequences of the formulation are analyzed in detail in the case where the measure m is generated by a continuous, Markovian stochastic process. The calculation of the hysteresis properties of the ensemble is reduced to the solution of the level-crossing problem for the stochastic process. In particular, it is shown that, when the process is translationally invariant (homogeneous), the ensuing hysteresis properties can be exactly described by the Preisach model of hysteresis, and the associated Preisach distribution is expressed in closed analytic form in terms of the drift and diffusion parameters of the Markovian process. Possible applications of the formulation are suggested, concerning the interpretation of magnetic hysteresis due to domain wall motion in quenched-in disorder, and the interpretation of critical state models of superconducting hysteresis.Comment: 36 pages, 9 figures, to be published on Phys. Rev.

On the Path of a Quasi-static Crack in Mode III

A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path