Deterministic version of Wigner's semicircle law for the distribution of matrix eigenvalues

It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let A_n=(a_ij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ⁽ⁿ⁾}_1?k?n its eigenvalues, and {u_k⁽ⁿ⁾}_1?k?n the corresponding (orthonormalized column) eigenvectors. Let $\text{v}{}^1{}_{\mathrm{n}}\text{=(a}{}_{\mathrm{n1}}\text{,a}{}_{\mathrm{n2}}\text{,?,a}{}_{\mathrm{n,n?1}}\text{)}$, put

$\text{X}{}_{\mathrm{n}}\text{(t)=[n(n-1)]}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}\text{∑}\text{k=1}\text{[(n-1)t]}\text{|v}{}_{\mathrm{n}}{}^1\text{u}{}_{\mathrm{f}}{}^{\mathrm{(n-1)}}\text{|}{}^2\text{,}\text{0?t?1}$

(bookeeping function for the length of the projections of the new row v¹_n of A_n onto the eigenvectors of the preceding matrix A_n?1), and let finally

$\text{F}{}_{\mathrm{n}}\text{(x)=n}{}^{-1}\text{(}\text{number of}\text{λ}{}_{\mathrm{k}}{}^{\mathrm{(n)}}\text{?x}\text{n}\text{,1?k?n)}$

(empirical distribution function of the eigenvalues of $\text{A}{}_{\mathrm{n}}\text{n}$. Suppose (i) $\text{lim}{}_{\mathrm{n}}\text{a}{}_{\mathrm{nn}}\text{n}\text{=0}$, (ii) lim_nX_n(t)=Ct(0<C<∞,0?t?1). Then

$\text{F}{}_{\mathrm{n}}\text{?W(·,C)}\text{(n→∞)}$

,where W is absolutely continuous with (semicircle) density

$\text{w(x,C)=}\text{(2Cπ)}{}^{-1}\text{(4C-x}{}^2{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{for}\text{|x|?2}\text{C}\text{0}\text{for}\text{|x|?2}\text{C}$

     

Kinetic energy spectrum and polarization of neutrons from the reaction 12C(p,n)X at 590 MeV

Abstact: The kinetic energy spectrum and the polarization of the PSI neutron beam produced in the reaction ¹²C(p,n)X at 0° with 590 MeV polarized protons were investigated. A strong energy dependence of the neutron beam polarization is observed which was not expected at the time the neutron beam was built. Received: 3 April 1998     

Utilizing Experiment and Theory to Evaluate Rhodamine B ethylenediamine as a Fluorescent Sensor for G-type Nerve Agents

Nerve gas mimic binding with Rhodamine B ethylenediamine (1) was studied in organic media. Binding of the nerve gas mimic, diethyl chlorophosphate (DCP), with the probe generated a non-fluorescent intermediate and a fluorescent product. Fluorescent and non-fluorescent products generated were identified using mass spectrometry and X-ray crystallography. Time-dependent density functional theory calculations were also used to investigate the electronic structure of the fluorescent probe in the ground and lowest lying π?→?π* singlet excited state. Though good agreement between theory and experiment can be obtained for the intense peak in the experimental spectrum using non-hybrid functionals, care must be taken when modelling these complexes due to the appearance of an n?→?π* transition that is too low in energy and appears to fall in the shoulders of the π?→?π* transitions.

     

Turbulent vortex rings in weakly turbulent and in turbulent ambient flow

Turbulent vortex rings were investigated in weakly turbulent flow and in three different grid generated turbulent flows to clarify the reciprocal action of the vortex ring with defined external turbulence. Assuming self-similarity and turbulent viscosity as proportional to V₀D₀ the equations for the ring diameter D(t) and the velocity of propagation V(t) were derived. The time difference Δt between the virtual origins of 1/V(t) respectively D²(t) led to an invariant term. The equation of momentum is fulfilled. – Position and diameter of the vortex rings were determined till their decay by means of an optical system, which did not disturb the vortex rings. The experimental results in weakly turbulent ambient flow obtained by the author and by others confirm the theory very well. The ambient turbulence was nearly constant in the measuring region; its effect could be described by simply adding its viscosity to the vortex ring’s internal turbulent viscosity. The results could be represented in unified non-dimensional diagrams. Moreover, an explanation was found as to why the mean internal turbulent viscosity is constant.     

Superparamagnetic iron oxide (SPIO) enhancement in the cirrhotic liver: a comparison of two doses of ferumoxides in patients with advanced disease

The aim of this study was to establish whether enhancement of the liver by the MRI contrast agent ferumoxides could be effectively achieved at a reduced dose of 7.5 micromol/kg in patients with advanced liver cirrhosis. Forty-two liver transplant candidates with end-stage cirrhosis underwent SPIO-enhanced MRI at 1.5T, using either 15 micromol/kg or 7.5 micromol/kg ferumoxides. The lower dose of ferumoxides was also used in 21 non-cirrhotic patients with colorectal liver metastases who acted as a control group. The percentage signal intensity loss (PSIL) after SPIO was measured in all patients, and in those patients with tumors the post-SPIO contrast-to-noise ratio (CNR) was measured. The median PSIL after SPIO in the high dose cirrhotic (HDLC), low dose non-cirrhotic (LDNC) and low dose cirrhotic (LDLC) patients was 86.3%, 74.6%, and 64.2% respectively. These differences were significant using the Mann-Whitney U test. Tumors were found in 8 patients in the high dose cirrhotic group, 9 in the low dose cirrhotic group, and all 21 of the control group. No significant differences were found between the CNR values after SPIO in the 3 groups (median values HDLC 15.1, LDNC 23.7, LDLC 19.5). In patients with late-stage cirrhosis the PSIL after SPIO was significantly less at 7.5 micromol/kg than at 15 micromol/kg, but both doses produced a substantial loss of signal. Lesion to liver CNR was not adversely affected by using the lower dose, so when imaging at 1.5T the authors would recommend using 7.5 micromol/kg in patients with liver cirrhosis.     

Quantification of Secondary Fe-Phases Formed During Sorption Experiments on Chlorites

Hyperfine Interactions - During batch sorption experiments of heavy metals on chlorite not only sorption reactions take place, but also reactions of chemical weathering leading to mineral...     

Measurements of motionally averaged heteronuclear dipolar couplings in MAS NMR using R-type recoupling

A novel MAS NMR approach is presented for the determination of heteronuclear dipolar couplings in unoriented materials. The technique is based on the proton-detected local field (PDLF) protocol, and achieves dipolar recoupling by R-type radio-frequency irradiation. The experiment, which is called R-PDLF spectroscopy, is demonstrated on solid and liquid-crystalline systems. For mobile systems, it is shown that the R-PDLF scheme provides better dipolar resolution as compared to techniques combining conventional separated local field (SLF) spectroscopy with R-type recoupling.     

Pressure enhancement of the giant magnetocaloric effect in Tb5Si2Ge2

Effects of temperature and pressure on magnetic, elastic, structural, and thermal properties of Tb5Si2Ge2 have been studied by means of macroscopic (thermal expansion and magnetization) and microscopic (neutron powder diffraction) techniques. We present evidence that the high-temperature second-order ferromagnetic transition can be coupled with the low-temperature first-order structural phase change into a single first-order magnetic-crystallographic transformation at and above a tricritical point in the vicinity of 8.6 kbar. This pressure-induced coupling has a remarkable effect on the magnetocaloric effect, transforming Tb5Si2Ge2 from an ordinary into a giant magnetocaloric effect material.     

Dynamics of the biopolymers in articular cartilage studied by magic angle spinning NMR

To understand the viscoelastic properties of cartilage tissue and for the development of tissue-engineered cartilage, we have studied the physicochemical properties of bovine nasal and pig articular cartilage by¹³C nuclear magnetic resonance (NMR) methods. The major macromolecular components of cartilage can be investigated individually by applying¹³C high-resolution (HR) NMR with scalar decoupling (for the polysaccharide component) and solid-state NMR with dipolar decoupling (for the collagen component). Partially resolved NMR spectra of the cartilage polysaccharides can be obtained by HR¹³C NMR indicating that these polysaccharides are highly mobile. Resonance lines have been assigned to chondroitin sulfate, the most mobile component of cartilage. To characterize time scales of molecular motions, we have measuredT ₁ andT ₂ relaxation times as a function of temperature and analyzed these data by means of a broad distribution of molecular correlation times. Typical correlation times for the large amplitude motions of chondroitin sulfate are of the order of 0.1–10 ns. For the detection and dynamical characterization of the cartilage collagen cross-polarization magic angle spinning (CP MAS) and high-power decoupling are indispensable.¹³C CP MAS spectra of cartilage are dominated by resonances from rigid collagen, while only low-intensity signals from the polysaccharides are observed. The good sensitivity at a magnetic field strength of 17.6 T allows the site-specific investigation of cartilage collagen dynamics by two-dimensional NMR methods. The cartilage collagen is essentially rigid with low-amplitude segmental motions on the fast time scale. Considering the high water content of cartilage and the almost isotropic mobility of the chondroitin sulfate molecules it is remarkable how little this affects the collagen dynamics. The dynamics of cartilage macromolecules is broadly distributed from almost completely rigid to highly mobile, which lends cartilage its mechanical strength and shock-absorbing properties.