Constraints on scalar diffusion anomaly in three-dimensional flows having bounded velocity gradients

This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d/dt$ of the scalar variance $$ is found to be bounded in terms of controlled physical parameters. Furthermore, in the zero diffusivity limit, $\kappa\to0$, this rate vanishes as $\kappa^{\alpha_0}$ if there exists an $\alpha_0\in(0,1]$ independent of $\kappa$ such that $<\infty$ for $\alpha\le\alpha_0$. This condition is satisfied if in the limit $\kappa\to0$, the variance spectrum $\Theta(k)$ remains steeper than $k^{-1}$ for large wave numbers $k$. When no such positive $\alpha_0$ exists, the scalar field may be said to become virtually singular. A plausible scenario consistent with Batchelor's theory is that $\Theta(k)$ becomes increasingly shallower for smaller $\kappa$, approaching the Batchelor scaling $k^{-1}$ in the limit $\kappa\to0$. For this classical case, the decay rate also vanishes, albeit more slowly -- like $(\ln P_r)^{-1}$, where $P_r$ is the Prandtl or Schmidt number. Hence, diffusion anomaly is ruled out for a broad range of scalar distribution, including power-law spectra no shallower than $k^{-1}$. The implication is that in order to have a $\kappa$-independent and non-vanishing decay rate, the variance at small scales must necessarily be greater than that allowed by the Batchelor spectrum. These results are discussed in the light of existing literature on the asymptotic exponential decay $\sim e^{-\gamma t}$, where $\gamma>0$ is independent of $\kappa$.Comment: 6-7 journal pages, no figures. accepted for publication by Phys. Fluid

The turing model comes of molecular age

Molecular analysis of hair follicle formation provide evidence to support the most well-known mathematical model for biological pattern formation

Reptile scale paradigm: Evo-Devo, pattern formation and regeneration

The purpose of this perspective is to highlight the merit of the reptile integument as an experimental model. Reptiles represent the first amniotes. From stem reptiles, extant reptiles, birds and mammals have evolved. Mammal hairs and feathers evolved from Therapsid and Sauropsid reptiles, respectively. The early reptilian integument had to adapt to the challenges of terrestrial life, developing a multi-layered stratum corneum capable of barrier function and ultraviolet protection. For better mechanical protection, diverse reptilian scale types have evolved. The evolution of endothermy has driven the convergent evolution of hair and feather follicles: both form multiple localized growth units with stem cells and transient amplifying cells protected in the proximal follicle. This topological arrangement allows them to elongate, molt and regenerate without structural constraints. Another unique feature of reptile skin is the exquisite arrangement of scales and pigment patterns, making them testable models for mechanisms of pattern formation. Since they face the constant threat of damage on land, different strategies were developed to accommodate skin homeostasis and regeneration. Temporally, they can be under continuous renewal or sloughing cycles. Spatially, they can be diffuse or form discrete localized growth units (follicles). To understand how gene regulatory networks evolved to produce increasingly complex ectodermal organs, we have to study how prototypic scale-forming pathways in reptiles are modulated to produce appendage novelties. Despite the fact that there are numerous studies of reptile scales, molecular analyses have lagged behind. Here, we underscore how further development of this novel experimental model will be valuable in filling the gaps of our understanding of the Evo-Devo of amniote integuments

Distinct mechanisms underlie pattern formation in the skin and skin appendages

Patterns form with the break of homogeneity and lead to the emergence of new structure or arrangement. There are different physiological and pathological mechanisms that lead to the formation of patterns. Here, we first introduce the basics of pattern formation and their possible biological basis. We then discuss different categories of skin patterns and their potential underlying molecular mechanisms. Some patterns, such as the lines of Blaschko and Naevus, are based on cell lineage and genetic mosaicism. Other patterns, such as regionally specific skin appendages, can be set by distinct combinatorial molecular codes, which in turn may be set by morphogenetic gradients. There are also some patterns, such as the arrangement of hair follicles (hair whorls) and fingerprints, which involve genetics as well as stochastic epigenetic events based on physiochemical principles. Many appendage primordia are laid out in developmental waves. In the adult, some patterns, such as those involving cycling hair follicles, may appear as traveling waves in mice. Since skin appendages can renew themselves in regeneration, their size and shape can still change in the adult via regulation by hormones and the environment. Some lesion patterns are based on pathological changes involving the above processes and can be used as diagnostic criteria in medicine. Understanding the different mechanisms that lead to patterns in the skin will help us appreciate their full significance in morphogenesis and medical research. Much remains to be learned about complex pattern formation, if we are to bridge the gap between molecular biology and organism phenotypes. Birth Defects Research (Part C) 78:280-291, 2006. © 2006 Wiley-Liss, Inc

Self-organizing & stochastic behaviors during the regeneration of hair stem cells

Stem cells cycle through active and quiescent states. Large populations of stem cells in an organ may cycle randomly or in a coordinated manner. Although stem cell cycling within single hair follicles has been studied, less is known about regenerative behavior in a hair follicle population. By combining predictive mathematical modeling with in vivo studies in mice and rabbits, we show that a follicle progresses through cycling stages by continuous integration of inputs from intrinsic follicular and extrinsic environmental signals based on universal patterning principles. Signaling from the WNT/bone morphogenetic protein activator/inhibitor pair is coopted to mediate interactions among follicles in the population. This regenerative strategy is robust and versatile because relative activator/inhibitor strengths can be modulated easily, adapting the organism to different physiological and evolutionary needs

Localization of tenascin in human skin wounds

A total of 56 surgically treated human skin wounds with a wound age between 8h and 7 months were investigated. Tenascin was visualized by immunohistochemistry and appeared first in the wound area pericellularly around fibroblastic cells approximately 2 days after wounding. A network-like interstitial positive staining pattern was first detectable in 3-day-old skin wounds. In all wounds with an age of 5 days or more, intensive reactivity for tenascin could be observed in the lesional area (dermal-epidermal junction, wound edge, areas of bleeding). In wounds with an age of more than approximately 1.5 months no positive staining occurred in the scar tissue. In conclusion, for forensic purposes, positive staining for tenascin restricted to the pericellular area of fibroblastic cells indicates a wound age of at least 2 days. Network-like structures appear after approximately 3 days or more. Since tenascin seems to be regularly detectable in skin wounds older than 5 days, the lack of a positive reaction in a sufficient number of specimens indicates a wound age of less than 5 days. The lack of a positive reaction in the granulation tissue of wounds with advanced wound age indicates a survival time of more than about 1.5 months, but a positive staining in older wounds cannot be excluded

Real-Time Simulation for Verification and Validation of Diagnostic and Prognostic Algorithms

To verify that a health management system (HMS) performs as expected, a virtual system simulation capability, including interaction with the associated platform or vehicle, very likely will need to be developed. The rationale for developing this capability is discussed and includes the limited capability to seed faults into the actual target system due to the risk of potential damage to high value hardware. The capability envisioned would accurately reproduce the propagation of a fault or failure as observed by sensors located at strategic locations on and around the target system and would also accurately reproduce the control system and vehicle response. In this way, HMS operation can be exercised over a broad range of conditions to verify that it meets requirements for accurate, timely response to actual faults with adequate margin against false and missed detections. An overview is also presented of a real-time rocket propulsion health management system laboratory which is available for future rocket engine programs. The health management elements and approaches of this lab are directly applicable for future space systems. In this paper the various components are discussed and the general fault detection, diagnosis, isolation and the response (FDIR) concept is presented. Additionally, the complexities of V&V (Verification and Validation) for advanced algorithms and the simulation capabilities required to meet the changing state-of-the-art in HMS are discussed

Prevalence and risks of fascioliasis among adult cohorts in Binh Dinh and Quang Ngai provinces-central Viet Nam

Fascioliasis (liver fluke disease) has raised significant public health concerns in the 15 regional provinces of Central Vietnam, accounting for 93% of the national incidence of the disease. No control measures to date have proven effective. Annual reports show increasing incidence of fascioliasis but they are incomplete. This cross-sectional study was conducted to identify the prevalence of fascioliasis and to describe its associated risks in three communes in Central Vietnam. 500 human blood samples were examined (ELISA); and a survey of knowledge, attitude and practice (KAP) was conducted for 600 randomly selected adults per commune. The findings suggest that overall seroprevalence was 7.75% (95% CI 6.54-9.16%). Among the infected cases, people aged from 18-59 years (85.6%) and farmers (68.0%) accounted for majority of infection. Less than half of participants in all three communes (24.6% - 46.0%) knew the causes of fascioliasis; and considerable proportions ate improperly boiled vegetables (28.2-33.8%), drank unboiled water (23.5-42.5%), and did not own a household toilet (14.2-20.5%). Relatively high prevalence and risks of fascioliasis were found in Central Vietnam, supporting the need for comprehensive intervention measures including selective treatment, health education, and multisectoral approaches to reduce the morbidity associated with fascioliasis and thus improve the health status of the people

Magneto-transport properties of monolayer borophene in perpendicular magnetic field: influence of electron-phonon interaction

The magneto-transport properties of a borophene monolayer in a perpendicular magnetic field B are studied via calculating the conductivity tensor and resistance under electron-optical phonon interaction by using the linear response theory. Numerical results are obtained and discussed for some specific parameters. The magnetic field-dependent longitudinal conductivity shows the magneto-phonon resonance effect that describes the transition of electrons between Landau levels by absorbing/emitting an optical phonon. The Hall conductivity increases first and then decreases with the magnetic field strength. Also, the longitudinal resistance increases significantly with increasing temperature, which shows the metal behaviour of the material. Practically, the observed magneto-phonon resonance can be applied to experimentally determine some material parameters, such as the distance between Landau levels and the optical phonon energy