Sound-propagation gap in fluid mixtures

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.Comment: Published; withdrawn since ordering in archive gives misleading impression of new publicatio

Dynamic structure factors of a dense mixture

We compute the dynamic structure factors of a dense binary liquid mixture. These describe dynamics on molecular length scales, where structural relaxation is important. We find that the presence of a few large particles in a dense fluid of small particles slows down the dynamics considerably. We also observe a deep narrowing of the spectrum for a disordered mixture composed of a nearly equal packing of the two species. In contrast, a few small particles diffuse easily in the background of a dense fluid of large particles. We expect our results to describe neutron scattering from a dense mixture

Veronesean representations of projective spaces over quadratic associative division algebras

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Proximal aortic stiffening in Turner patients may be present before dilation can be detected : a segmental functional MRI study

Background: To study segmental structural and functional aortic properties in Turner syndrome (TS) patients. Aortic abnormalities contribute to increased morbidity and mortality of women with Turner syndrome. Cardiovascular magnetic resonance (CMR) allows segmental study of aortic elastic properties. Method: We performed Pulse Wave Velocity (PWV) and distensibility measurements using CMR of the thoracic and abdominal aorta in 55 TS-patients, aged 13-59y, and in a control population (n = 38; 12-58y). We investigated the contribution of TS on aortic stiffness in our entire cohort, in bicuspid (BAV) versus tricuspid (TAV) aortic valve-morphology subgroups, and in the younger and older subgroups. Results: Differences in aortic properties were only seen at the most proximal aortic level. BAV Turner patients had significantly higher PWV, compared to TAV Turner (p = 0.014), who in turn had significantly higher PWV compared to controls (p = 0.010). BAV Turner patients had significantly larger ascending aortic (AA) luminal area and lower AA distensibility compared to both controls (all p < 0.01) and TAV Turner patients. TAV Turner had similar AA luminal areas and AA distensibility compared to Controls. Functional changes are present in younger and older Turner subjects, whereas ascending aortic dilation is prominent in older Turner patients. Clinically relevant dilatation (TAV and BAV) was associated with reduced distensibility. Conclusion: Aortic stiffening and dilation in TS affects the proximal aorta, and is more pronounced, although not exclusively, in BAV TS patients. Functional abnormalities are present at an early age, suggesting an aortic wall disease inherent to the TS. Whether this increased stiffness at young age can predict later dilatation needs to be studied longitudinally

Introductory clifford analysis

In this chapter an introduction is given to Clifford analysis and the underlying Clifford algebras. The functions under consideration are defined on Euclidean space and take values in the universal real or complex Clifford algebra, the structure and properties of which are also recalled in detail. The function theory is centered around the notion of a monogenic function, which is a null solution of a generalized Cauchy–Riemann operator, which is rotation invariant and factorizes the Laplace operator. In this way, Clifford analysis may be considered as both a generalization to higher dimension of the theory of holomorphic functions in the complex plane and a refinement of classical harmonic analysis. A notion of monogenicity may also be associated with the vectorial part of the Cauchy–Riemann operator, which is called the Dirac operator; some attention is paid to the intimate relation between both notions. Since a product of monogenic functions is, in general, no longer monogenic, it is crucial to possess some tools for generating monogenic functions: such tools are provided by Fueter’s theorem on one hand and the Cauchy–Kovalevskaya extension theorem on the other hand. A corner stone in this function theory is the Cauchy integral formula for representation of a monogenic function in the interior of its domain of monogenicity. Starting from this representation formula and related integral formulae, it is possible to consider integral transforms such as Cauchy, Hilbert, and Radon transforms, which are important both within the theoretical framework and in view of possible applications

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

Short-wavelength collective modes in a binary hard-sphere mixture

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive gives misleading impression of new publicatio

Decay-assisted collinear resonance ionization spectroscopy: Application to neutron-deficient francium

This paper reports on the hyperfine-structure and radioactive-decay studies of the neutron-deficient francium isotopes $^{202-206}$Fr performed with the Collinear Resonance Ionization Spectroscopy (CRIS) experiment at the ISOLDE facility, CERN. The high resolution innate to collinear laser spectroscopy is combined with the high efficiency of ion detection to provide a highly-sensitive technique to probe the hyperfine structure of exotic isotopes. The technique of decay-assisted laser spectroscopy is presented, whereby the isomeric ion beam is deflected to a decay spectroscopy station for alpha-decay tagging of the hyperfine components. Here, we present the first hyperfine-structure measurements of the neutron-deficient francium isotopes $^{202-206}$Fr, in addition to the identification of the low-lying states of $^{202,204}$Fr performed at the CRIS experiment.Comment: Accepted for publication with Physical Review

On a chain of harmonic and monogenic potentials in Euclidean half-space

In the framework of Clifford analysis, a chain of harmonic and monogenic potentials is constructed in the upper half of Euclidean space R^(m+1), including a higher dimensional generalization of the complex logarithmic function. Their distributional limits at the boundary R^(m) turn out to be well-known distributions such as the Dirac distribution, the Hilbert kernel, the fundamental solution of the Laplace and Dirac operators, the square root of the negative Laplace operator, and the like. It is shown how each of those potentials may be recovered from an adjacent kernel in the chain by an appropriate convolution with such a distributional limit