Similarity solutions of Fokker-Planck equation with time-dependent coefficients

In this work, we consider the solvability of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients by means of the similarity method. By the introduction of the similarity variable, the Fokker-Planck equation is reduced to an ordinary differential equation. Adopting the natural requirement that the probability current density vanishes at the boundary, the resulted ordinary differential equation turns out to be integrable, and the probability density function can be given in closed form. New examples of exactly solvable Fokker-Planck equations are presented, and their properties analyzed.Comment: 13 pages, 8 figures. Version to appear in Ann. Phys. Presentation improved. Discussions and figures of easy examples remove

Systematic derivation of a rotationally covariant extension of the 2-dimensional Newell-Whitehead-Segel equation

An extension of the Newell-Whitehead-Segel amplitude equation covariant under abritrary rotations is derived systematically by the renormalization group method.Comment: 8 pages, to appear in Phys. Rev. Letters, March 18, 199

Emergence of Order in Textured Patterns

A characterization of textured patterns, referred to as the disorder function \bar\delta(\beta), is used to study properties of patterns generated in the Swift-Hohenberg equation (SHE). It is shown to be an intensive, configuration-independent measure. The evolution of random initial states under the SHE exhibits two stages of relaxation. The initial phase, where local striped domains emerge from a noisy background, is quantified by a power law decay \bar\delta(\beta) \sim t^{-{1/2} \beta}. Beyond a sharp transition a slower power law decay of \bar\delta(\beta), which corresponds to the coarsening of striped domains, is observed. The transition between the phases advances as the system is driven further from the onset of patterns, and suitable scaling of time and \bar\delta(\beta) leads to the collapse of distinct curves. The decay of $\bar\delta(\beta)$ during the initial phase remains unchanged when nonvariational terms are added to the underlying equations, suggesting the possibility of observing it in experimental systems. In contrast, the rate of relaxation during domain coarsening increases with the coefficient of the nonvariational term.Comment: 9 Pages, 8 Postscript Figures, 3 gif Figure

Using Nonlinear Response to Estimate the Strength of an Elastic Network

Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a network to static and periodic strain can be used to estimate its ultimate (or breaking) stress. Since bone fracture in older adults results from the weakening of porous bone, we discuss the possibility of using $\Gamma$ as a non-invasive diagnostic of osteoporotic bone.Comment: 4 pages, 4 figure

Ronin Governs Early Heart Development by Controlling Core Gene Expression Programs.

Ronin (THAP11), a DNA-binding protein that evolved from a primordial DNA transposon by molecular domestication, recognizes a hyperconserved promoter sequence to control developmentally and metabolically essential genes in pluripotent stem cells. However, it remains unclear whether Ronin or related THAP proteins perform similar functions in development. Here, we present evidence that Ronin functions within the nascent heart as it arises from the mesoderm and forms a four-chambered organ. We show that Ronin is vital for cardiogenesis during midgestation by controlling a set of critical genes. The activity of Ronin coincided with the recruitment of its cofactor, Hcf-1, and the elevation of H3K4me3 levels at specific target genes, suggesting the involvement of an epigenetic mechanism. On the strength of these findings, we propose that Ronin activity during cardiogenesis offers a template to understand how important gene programs are sustained across different cell types within a developing organ such as the heart

Physiological responses to basic tastes for sensory evaluation of chocolate using biometric techniques

Facial expressions are in reaction to basic tastes by the response to receptor stimulation. The objective of this study was to assess the autonomic nervous system responses to basic tastes in chocolates and to identify relationships between conscious and unconscious responses from participants. Panelists (n = 45) tasted five chocolates with either salt, citric acid, sugar, or monosodium glutamate, which generated four distinctive basic tastes plus bitter, using dark chocolate. An integrated camera system, coupled with the Bio-Sensory application, was used to capture infrared thermal images, videos, and sensory responses. Outputs were used to assess skin temperature (ST), facial expressions, and heart rate (HR) as physiological responses. Sensory responses and emotions elicited during the chocolate tasting were evaluated using the application. Results showed that the most liked was sweet chocolate (9.01), while the least liked was salty chocolate (3.61). There were significant differences for overall liking (p < 0.05) but none for HR (p = 0.75) and ST (p = 0.27). Sweet chocolate was inversely associated with angry, and salty chocolate positively associated with sad. Positive emotion-terms were associated with sweet samples and liking in self-reported responses. Findings of this study may be used to assess novel tastes of chocolate in the industry based on conscious and emotional responses more objectively

Influence of Fluorination on the Solubilities of Carbon Dioxide, Ethane, and Nitrogen in 1‑n‑Fluoro-alkyl-3-methylimidazolium Bis(n‑fluoroalkylsulfonyl)amide Ionic Liquids

International audienceThe effect on gas solubilities of adding partially fluorinated alkyl side chains either on imidazolium-based cations or on bis(perfluoroalkylsulfonyl)amide anions was studied. The aim was to gain knowledge of the mechanisms of dissolution of gases in fluorinated ionic liquids and, if possible, to improve physical absorption of carbon dioxide in ionic liquids. We have determined experimentally, in the temperature range of 298–343 K and at pressures close to atmospheric pressure, the solubility and thermodynamics of solvation of carbon dioxide, ethane, and nitrogen in the ionic liquids 1-octyl-3-methylimidazolium bis[trifluoromethylsulfonyl]amide ([C8mim][NTf2]), 1-octyl-3-methylimidazolium bis[pentafluoroethylsulfonyl]amide ([C8mim][BETI]), 1-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluorooctyl)-3-methylimidazolium bis[trifluoromethylsulfonyl]amide ([C8H4F13mim][NTf2]), and 1-(3,3,4,4,5,5,6,6,7,7,8,8,8-tridecafluorooctyl)-3-methylimidazolium bis[pentafluoroethylsulfonyl]amide ([C8H4F13mim][BETI]). Ionic liquids with partial fluorination on the cation were found to exhibit higher carbon dioxide and nitrogen mole fraction solubilities but lower ethane solubilities, compared to those of their hydrogenated counterparts. Molecular simulation provided insights about the mechanisms of solvation of the different gases in the ionic liquids

Exploring how people with dementia can be best supported to manage long-term conditions: a qualitative study of stakeholder perspectives

OBJECTIVES: To explore how the self-management of comorbid long-term conditions is experienced and negotiated by people with dementia and their carers. DESIGN: Secondary thematic analysis of 82 semi-structured interviews. SETTING: Community settings across the United Kingdom. PARTICIPANTS: 11 people with dementia, 22 family carers, 19 health professionals and 30 homecare staff. RESULTS: We identified three overarching themes: (1) The process of substituting self-management: stakeholders balanced the wishes of people with dementia to retain autonomy with the risks of lower adherence to medical treatments. The task of helping a person with dementia to take medication was perceived as intermediate between a personal care and a medical activity; rules about which professionals could perform this activity sometimes caused conflict. (2) Communication in the care network: family carers often communicated with services and made decisions about how to implement medical advice. In situations where family carers or homecare workers were not substituting self-management, it could be challenging for general practitioners to identify changes in self-management and decide when to intervene. (3) Impact of physical health on and from dementia: healthcare professionals acknowledged the inter-relatedness of physical health and cognition to adapt care accordingly. Some treatments prescribed for long-term conditions were perceived as unhelpful when not adapted to the context of dementia. Healthcare professionals and homecare workers sometimes felt that family carers were unable to accept that available treatments may not be helpful to people with dementia and that this sometimes led to the continuation of treatments of questionable benefit. CONCLUSION: The process of substituting self-management evolves with advancement of dementia symptoms and relies on communication in the care network, while considering the impact on and from dementia to achieve holistic physical health management. Care decisions must consider people with dementia as a whole, and be based on realistic outcomes and best interests

Universal bifurcation property of two- or higher-dimensional dissipative systems in parameter space: Why does 1D symbolic dynamics work so well?

The universal bifurcation property of the H\'enon map in parameter space is studied with symbolic dynamics. The universal-$L$ region is defined to characterize the bifurcation universality. It is found that the universal-$L$ region for relative small $L$ is not restricted to very small $b$ values. These results show that it is also a universal phenomenon that universal sequences with short period can be found in many nonlinear dissipative systems.Comment: 10 pages, figures can be obtained from the author, will appeared in J. Phys.

Renormalization group approach to multiscale modelling in materials science

Dendritic growth, and the formation of material microstructure in general, necessarily involves a wide range of length scales from the atomic up to sample dimensions. The phase field approach of Langer, enhanced by optimal asymptotic methods and adaptive mesh refinement, copes with this range of scales, and provides an effective way to move phase boundaries. However, it fails to preserve memory of the underlying crystallographic anisotropy, and thus is ill-suited for problems involving defects or elasticity. The phase field crystal (PFC) equation-- a conserving analogue of the Hohenberg-Swift equation --is a phase field equation with periodic solutions that represent the atomic density. It can natively model elasticity, the formation of solid phases, and accurately reproduces the nonequilibrium dynamics of phase transitions in real materials. However, the PFC models matter at the atomic scale, rendering it unsuitable for coping with the range of length scales in problems of serious interest. Here, we show that a computationally-efficient multiscale approach to the PFC can be developed systematically by using the renormalization group or equivalent techniques to derive appropriate coarse-grained coupled phase and amplitude equations, which are suitable for solution by adaptive mesh refinement algorithms