Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

Safe and effective variability-a criterion for dose individualization.

BACKGROUND: : A primary goal of clinical pharmacology is to understand the factors that determine the dose-effect relationship and to use this knowledge to individualize drug dose. METHODS: : A principle-based criterion is proposed for deciding among alternative individualization methods. RESULTS: : Safe and effective variability defines the maximum acceptable population variability in drug concentration around the population average. CONCLUSIONS: : A decision on whether patient covariates alone are sufficient, or whether therapeutic drug monitoring in combination with target concentration intervention is needed, can be made by comparing the remaining population variability after a particular dosing method with the safe and effective variability.

Severe neurologic manifestations from cervical spine instability in spondylo-megaepiphyseal-metaphyseal dysplasia.

Spondylo-megaepiphyseal-metaphyseal dysplasia (SMMD; OMIM 613330) is a dysostosis/dysplasia caused by recessive mutations in the homeobox-containing gene, NKX3-2 (formerly known as BAPX1). Because of the rarity of the condition, its diagnostic features and natural course are not well known. We describe clinical and radiographic findings in six patients (five of which with homozygous mutations in the NKX3-2 gene) and highlight the unusual and severe changes in the cervical spine and the neurologic complications. In individuals with SMMD, the trunk and the neck are short, while the limbs, fingers and toes are disproportionately long. Radiographs show a severe ossification delay of the vertebral bodies with sagittal and coronal clefts, missing ossification of the pubic bones, large round "balloon-like" epiphyses of the long bones, and presence of multiple pseudoepiphyses at all metacarpals and phalanges. Reduced or absent ossification of the cervical vertebrae leads to cervical instability with anterior or posterior kinking of the cervical spine (swan neck-like deformity, kyknodysostosis). As a result of the cervical spine instability or deformation, five of six patients in our series suffered cervical cord injury that manifested clinically as limb spasticity. Although the number of individuals observed is small, the high incidence of cervical spine deformation in SMMD is unique among skeletal dysplasias. Early diagnosis of SMMD by recognition of the radiographic pattern might prevent of the neurologic complications via prophylactic cervical spine stabilization. © 2012 Wiley Periodicals, Inc.

Nonlinear Saffman-Taylor instability

We show, both theoretically and experimentally, that the interface between two viscous fluids in a Hele-Shaw cell can be nonlinearly unstable before the Saffman-Taylor linear instability point is reached. We identify the family of exact elastica solutions [Nye et al., Eur. J. Phys. 5, 73 (1984)] as the unstable branch of the corresponding subcritical bifurcation which ends up at a topological singularity defined by interface pinchoff. We devise an experimental procedure to prepare arbitrary initial conditions in a Hele-Shaw cell. This is used to test the proposed bifurcation scenario and quantitatively asses its practical relevance.

Model for curvature-driven pearling instability in membranes

A phase-field model for dealing with dynamic instabilities in membranes is presented. We use it to study curvature-driven pearling instability in vesicles induced by the anchorage of amphiphilic polymers on the membrane. Within this model, we obtain the morphological changes reported in recent experiments. The formation of a homogeneous pearled structure is achieved by consequent pearling of an initial cylindrical tube from the tip. For high enough concentration of anchors, we show theoretically that the homogeneous pearled shape is energetically less favorable than an inhomogeneous one, with a large sphere connected to an array of smaller spheres.

Interfacial instability induced by external fluctuations

The dynamics of an interface separating the two coexistent phases of a binary system in the presence of external fluctuations in temperature is studied. An interfacial instability is obtained for an interface that would be stable in the absence of fluctuations or in the presence of internal fluctuations. Analytical stability analysis and numerical simulations are in accordance with an explanation of these effects in terms of a quenchlike instability induced by fluctuations.

Lateral instability in normal viscous fingers

We study a low-amplitude, long-wavelength lateral instability of the Saffman-Taylor finger by means of a phase-field model. We observe such an instability in two situations in which small dynamic perturbations are overimposed to a constant pressure drop. We first study the case in which the perturbation consists of a single oscillatory mode and then a case in which the perturbation consists of temporal noise. In both cases the instability undergoes a process of selection.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.

Dynamics of sweeping through an instability: Passage-time statistics for colored noise

A calculation of passage-time statistics is reported for the laser switch-on problem, under the influence of colored noise, when the net gain is continuously swept from below to above threshold. Cases of fast and slow sweeping are considered. In the weak-noise limit, asymptotic results are given for small and large correlation times of the noise. The mean first passage time increases with the correlation time of the noise. This effect is more important for fast sweeping than for slow sweeping.

Growth and melting of the nematic phase: sample thickness dependence of the Mullins-Sekerka instability

In this article we report our systematic studies of the dependence on the sample thickness of the onset parameters of the instability of the nematic-isotropic interface during directional growth and melting, in homeotropic or planar anchoring.