The human genome and gene expression profiling

The mapping and sequencing of the human genome has generated a large resource for answering questions about human disease. This achievement is akin in scientific importance to developing the periodic table of elements. Plastic surgery has always been at the frontier medical research. This resource will help us to improve our understanding on the many unknown physiological and pathogical conditions we deal with daily, such as wound heating keloid scar formation, Dupuytren's disease, rheumatoid arthritis, vascular malformation and carcinogenesis. We are primed in obtaining both disease and normal tissues to use this resource and applying it to clinical use. This review is about the human genome, the basis of gene expression profiling and how it will affect our clinical and research practices in the future and for those embarking on the use of this new technology as a research tool, we provide a brief insight on its limitations and pitfalls. (C) 2006 The British Association of Plastic Surgeons. Published by Elsevier Ltd. All rights reserved.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

Modulational Instability in Periodic Quadratic Nonlinear Materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Experimentally tracking unstable steady states by large periodic modulation

Experimental suppression of chaos has been achieved in an optically pumped far-infrared (NH3)-N-15 laser which displays Lorenz-like chaos. The method of control involves the application of a large amplitude slow (i.e., nonresonant) modulation of the pump power. This may be related to a delayed bifurcation to chaos observed when the pump power is ramped at a constant late.

Periodic orbit resonances in layered metals in tilted magnetic fields

The frequency dependence of the interlayer conductivity of a layered Fermi liquid in a magnetic field that is tilted away from the normal to the layers is considered. For both quasi-one- and quasi-two-dimensional systems resonances occur when the frequency is a harmonic of the frequency at which the magnetic field causes the electrons to oscillate on the Fermi surface within the layers. The intensity of the different harmonic resonances varies significantly with the direction of the field. The resonances occur for both coherent and weakly incoherent interlayer transport and so their observation does not imply the existence of a three-dimensional Fermi surface. [S0163-1829(99)51240-X].

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

Spring-neap tide-induced beach water table fluctuations in a sloping coastal aquifer

Predictions of water table fluctuations in coastal aquifers are needed for numerous coastal and water resources engineering problems. Most previous investigations have been based on the Boussinesq equation for the case of a vertical beach. In this note an analytical solution based on shallow water expansion for the spring- neap tide- induced water table fluctuations in a coastal aquifer is presented. Unlike most previous investigations, multitidal signals are considered with a sloping coastal aquifer. The new solution is verified by comparing with field observations from Ardeer, Scotland. On the basis of the analytical approximation the influences of higher- order components on water table elevation are examined first. Then, a parametric study has been performed to investigate the effects of the amplitude ratio (lambda), frequency ratio (omega), and phases (delta(1) and delta(2)) on the tide- induced water table fluctuations in a sloping sandy beach.

Periodic electric field enhanced transport through membranes

We examine the mean flux across a homogeneous membrane of a charged tracer subject to an alternating, symmetric voltage waveform. The analysis is based on the Nernst-Planck flux equation, with electric field subject to time dependence only. For low frequency electric fields the quasi steady-state flux can be approximated using the Goldman model, which has exact analytical solutions for tracer concentration and flux. No such closed form solutions can be found for arbitrary frequencies, however we find approximations for high frequency. An approximation formula for the average flux at all frequencies is also obtained from the two limiting approximations. Numerical integration of the governing equation is accomplished by use of the numerical method of lines and is performed for four different voltage waveforms. For the different voltage profiles, comparisons are made with the approximate analytical solutions which demonstrates their applicability. (c) 2005 Elsevier B.V. All rights reserved.

Numerical modelling of tide-induced beach water table fluctuations

Field studies have shown that the elevation of the beach groundwater table varies with the tide and such variations affect significantly beach erosion or accretion. In this paper, we present a BEM (Boundary Element Method) model for simulating the tidal fluctuation of the beach groundwater table. The model solves the two-dimensional flow equation subject to free and moving boundary conditions, including the seepage dynamics at the beach face. The simulated seepage faces were found to agree with the predictions of a simple model (Turner, 1993). The advantage of the present model is, however, that it can be used with little modification to simulate more complicated cases, e.g., surface recharge from rainfall and drainage in the aquifer may be included (the latter is related to beach dewatering technique). The model also simulated well the field data of Nielsen (1990). In particular, the model replicated three distinct features of local water table fluctuations: steep rising phase versus flat falling phase, amplitude attenuation and phase lagging.

Beach water table fluctuations due to wave run-up: Capillarity effects

High-frequency beach water table fluctuations due to wave run-up and rundown have been observed in the field [Waddell, 1976]. Such fluctuations affect the infiltration/exfiltration process across the beach face and the interstitial oxygenation process in the beach ecosystem. Accurate representation of high-frequency water table fluctuations is of importance in the modeling of (1) the interaction between seawater and groundwater, more important, the effects on swash sediment transport and (2) the biological activities in the beach ecosystem. Capillarity effects provide a mechanism for high-frequency water table fluctuations. Previous modeling approaches adopted the assumption of saturated flow only and failed to predict the propagation of high-frequency fluctuations in the aquifer. In this paper we develop a modified kinematic boundary condition (kbc) for the water table which incorporates capillarity effects. The application of this kbc in a boundary element model enables the simulation of high-frequency water table fluctuations due to wave run-up. Numerical tests were carried out for a rectangular domain with small-amplitude oscillations; the behavior of water table responses was found to be similar to that predicted by an analytical solution based on the one-dimensional Boussinesq equation. The model was also applied to simulate the water table response to wave run-up on a doping beach. The results showed similar features of water table fluctuations observed in the field. In particular, these fluctuations are standing wave-like with the amplitude becoming increasingly damped inland. We conclude that the modified kbc presented here is a reasonable approximation of capillarity effects on beach water table fluctuations. However, further model validation is necessary before the model can confidently be used to simulate high-frequency water table fluctuations due to wave run-up.

A continuum model for periodic two-dimensional block structures

A continuum model for regular block structures is derived by replacing the difference quotients of the discrete equations by corresponding differential quotients. The homogenization procedure leads to an anisotropic Cosserat Continuum. For elastic block interactions the dispersion relations of the discrete and the continuous models are derived and compared. Yield criteria for block tilting and sliding are formulated. An extension of the theory for large deformation is proposed. (C) 1997 by John Wiley & Sons, Ltd.

Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.