A two-dimensional X-ray scattering system for in-situ time-resolving studies of polymer structures subjected to controlled deformations

A two-dimensional X-ray scattering system developed around a CCD-based area detector is presented, both in terms of hardware employed and software designed and developed. An essential feature is the integration of hardware and software, detection and sample environment control which enables time-resolving in-situ wide-angle X-ray scattering measurements of global structural and orientational parameters of polymeric systems subjected to a variety of controlled external fields. The development and operation of a number of rheometers purpose-built for the application of such fields are described. Examples of the use of this system in monitoring degrees of shear-induced orientation in liquid-crystalline systems and crystallization of linear polymers subsequent to shear flow are presented.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Crooks' fluctuation theorem for a process on a two dimensional fluid field

We investigate the behavior of a two-dimensional inviscid and incompressible flow when pushed out of dynamical equilibrium. We use the two-dimensional vorticity equation with spectral truncation on a rectangular domain. For a sufficiently large number of degrees of freedom, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. We interpret this as doing work to the system. Evolving along a forward and its corresponding backward process, we find numerical evidence that the distributions of the work performed satisfy the Crooks relation. We confirm our results by proving the Crooks relation for this system rigorously.

Stress-induced changes in the Schizosaccharomyces pombe proteome using two-dimensional difference gel electrophoresis, mass spectrometry and a novel integrated robotics platform

Robotic and manual methods have been used to obtain identification of significantly changing proteins regulated when Schizosaccharomyces pombe is exposed to oxidative stress. Differently treated S. pombe cells were lysed, labelled with CyDye and analysed by two-dimensional difference gel electrophoresis. Gel images analysed off-line, using the DeCyder image analysis software [GE Healthcare, Amersham, UK] allowed selection of significantly regulated proteins. Proteins displaying differential expression were excised robotically for manual digestion and identified by matrix-assisted laser desorption/ionisation - mass spectrometry (MALDI-MS). Additionally the same set of proteins displaying differential expression were automatically cut and digested using a prototype robotic platform. Automated MALDI-MS, peak label assignment and database searching were utilised to identify as many proteins as possible. The results achieved by the robotic system were compared to manual methods. The identification of all significantly altered proteins provides an annotated peroxide stress-related proteome that can be used as a base resource against which other stress-induced proteomic changes can be compared.

Stress-induced changes in the Schizosaccharomyces pombe proteome using two-dimensional difference gel electrophoresis, mass spectrometry and a novel integrated robotics platform

Robotic and manual methods have been used to obtain identification of significantly changing proteins regulated when Schizosaccharomyces pombe is exposed to oxidative stress. Differently treated S. pombe cells were lysed, labelled with CyDye (TM) and analysed by two-dimensional difference gel. electrophoresis. Gel images analysed off-line, using the DeCyder (TM) image analysis software [GE Healthcare, Amersham, UK] allowed selection of significantly regulated proteins. Proteins displaying differential expression were excised robotically for manual digestion and identified by matrix-assisted laser desorption/ionisation - mass spectrometry (MALDI-MS). Additionally the same set of proteins displaying differential expression were automatically cut and digested using a prototype robotic platform. Automated MALDI-MS, peak label assignment and database searching were utilised to identify as many proteins as possible. The results achieved by the robotic system were compared to manual methods. The identification of all significantly altered proteins provides an annotated peroxide stress-related proteome that can be used as a base resource against which other stress-induced proteomic changes can be compared.

Towards dynamical system models of language-related brain potentials

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system's phase space.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Extensivity of two-dimensional turbulence

This study is concerned with how the attractor dimension of the two-dimensional Navier–Stokes equations depends on characteristic length scales, including the system integral length scale, the forcing length scale, and the dissipation length scale. Upper bounds on the attractor dimension derived by Constantin, Foias and Temam are analysed. It is shown that the optimal attractor-dimension estimate grows linearly with the domain area (suggestive of extensive chaos), for a sufficiently large domain, if the kinematic viscosity and the amplitude and length scale of the forcing are held fixed. For sufficiently small domain area, a slightly “super-extensive” estimate becomes optimal. In the extensive regime, the attractor-dimension estimate is given by the ratio of the domain area to the square of the dissipation length scale defined, on physical grounds, in terms of the average rate of shear. This dissipation length scale (which is not necessarily the scale at which the energy or enstrophy dissipation takes place) can be identified with the dimension correlation length scale, the square of which is interpreted, according to the concept of extensive chaos, as the area of a subsystem with one degree of freedom. Furthermore, these length scales can be identified with a “minimum length scale” of the flow, which is rigorously deduced from the concept of determining nodes.

Wave-breaking characteristics of Northern Hemisphere winter blocking: a two-dimensional approach

This paper generalises and applies recently developed blocking diagnostics in a two- dimensional latitude-longitude context, which takes into consideration both mid- and high-latitude blocking. These diagnostics identify characteristics of the associated wave-breaking as seen in the potential temperature (θ) on the dynamical tropopause, in particular the cyclonic or anticyclonic Direction of wave-Breaking (DB index), and the Relative Intensity (RI index) of the air masses that contribute to blocking formation. The methodology is extended to a 2-D domain and a cluster technique is deployed to classify mid- and high-latitude blocking according to the wave-breaking characteristics. Mid-latitude blocking is observed over Europe and Asia, where the meridional gradient of θ is generally weak, whereas high-latitude blocking is mainly present over the oceans, to the north of the jet-stream, where the meridional gradient of θ is much stronger. They occur respectively on the equatorward and poleward flank of the jet- stream, where the horizontal shear ∂u/∂y is positive in the first case and negative in the second case. A regional analysis is also conducted. It is found that cold-anticyclonic and cyclonic blocking divert the storm-track respectively to the south and to the north over the East Atlantic and western Europe. Furthermore, warm-cyclonic blocking over the Pacific and cold-anticyclonic blocking over Europe are identified as the most persistent types and are associated with large amplitude anomalies in temperature and precipitation. Finally, the high-latitude, cyclonic events seem to correlate well with low- frequency modes of variability over the Pacific and Atlantic Ocean.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

Theory of enhanced magnetic anisotropy induced by Pt adatoms on two-dimensional Co clusters supported on a Pt(111) substrate

Calculations are reported of the magnetic anisotropy energy of two-dimensional (2D) Co nanostructures on a Pt(111) substrate. The perpendicular magnetic anisotropy (PMA) of the 2D Co clusters strongly depends on their size and shape, and rapidly decreases with increasing cluster size. The PMA calculated is in reasonable agreement with experimental results. The sensitivity of the results to the Co-Pt spacing at the interface is also investigated and, in particular, for a complete Co monolayer we note that the value of the spacing at the interface determines whether PMA or in-plane anisotropy occurs. We find that the PMA can be greatly enhanced by the addition of Pt adatoms to the top surface of the 2D Co clusters. A single Pt atom can induce in excess of 5 meV to the anisotropy energy of a cluster. In the absence of the Pt adatoms the PMA of the Co clusters falls below 1 meV/Co atom for clusters of about 10 atoms whereas, with Pt atoms added to the surface of the clusters, a PMA of 1 meV/Co atom can be maintained for clusters as large as about 40 atoms. The effect of placing Os atoms on the top of the Co clusters is also considered. The addition of 5d atoms and clusters on the top of ferromagnetic nanoparticles may provide an approach to tune the magnetic anisotropy and moment separately.