Pion suppression in nuclear collisions

The pion multiplicity per participating nucleon in central nucleus–nucleus collisions at the energies 2–15 AGeV is significantly smaller than in nucleon–nucleon interactions at the same collision energy. This effect of pion suppression is argued to appear due to the evolution of the system produced at the early stage of heavy–ion collisions towards a local thermodynamic equilibrium and further isentropic expansion. Received: 21 July 1997 / Revised version: 12 November 1997 / Published online: 26 February 1998     

Recursive intermediate factorization and complete computational linearization of the coupled-cluster single,double, triple,and quadruple excitation equations

Summary The nonlinear CCSDTQ equations are written in a fully linearized form, via the introduction of computationally convenient intermediates. An efficient formulation of the coupled cluster method is proposed. Due to a recursive method for the calculation of intermediates, all computational steps involve the multiplication of an intermediate with aT vertex. This property makes it possible to express the CC equations exclusively in terms of matrix products which can be directly transformed into a highly vectorized program.This work has been supported by the U.S. Air Force Office of Scientific Research, Grant No. 90-0079     

Vapour—liquid equilibria in binary systems formed by N-Methylpyrrolidone with hydrocarbons and hydroxyl derivatives

The vapour—liquid equilibria (VLE) determined by an ebulliometric total pressure method under isothermal conditions for binary systems formed by N-methylpyrrolidone with hexane (333.25 and 343.15 K), dodecane (393.25 K), cyclohexane (333.25 and 354.15 K), methyl-cyclohexane (354.15 and 373.25 K), benzene (333.25 and 354.15 K), toluene (362.15 and 383.35 K), propylbenzene (352.15 and 373.75 K), butylbenzene (352.15 and 373.75 K), propanol-1 (354.15 K), hexanol-1 (351.75 and 393.35 K) and at 393.55 K for cyclohexanol, 4-methylphenol and 2,4-dimethylphenol are reported. The vapour pressures of the pure substances are given. The least squares analysis of VLE data by means of the Redlich-Kister equation is given.     

Dependence of calculated collective nuclear properties on the form of the potential energy and inertia tensor

A systematic study of the dependence of the collective quantities (energies and matrix elements of the E2, M1 and E0 moments) on the form of approximations to the potential energy V and the inertia tensor B is performed. Various approximations used up to now are tested. Macroscopic-microscopic values for V and cranking results for B are taken as a reference. The collective quantities are calculated by solving the Schrödinger equation corresponding to the collective Bohr hamiltonian. The contribution of all nucleons is explicitly taken into account; no renormalization factors are used. Spherical, transitional and deformed even-even nuclei are considered. The quality of various approximations for V and B used in the boson-expansion method is discussed. Large effects of the microstructure of the inertia tensor B are obtained and commented on.     

Some Remarks on Absolute Mathematics

We calculate Hochschild cohomology groups of the integers treated as an algebra over so-called field with one element. We compare our results with calculation of the topological Hochschild cohomology groups of the integers—this is the case when one considers integers as an algebra over the sphere spectrum.     

Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.     

Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability theory (for an introduction see [9]). The analogue of entropy in the free context was introduced by the second named author in [8]. Here we show that Shannon's entropy power inequality ([6, 1]) has an analogue for the free entropy (X) (Theorem 2.1).The free entropy, consistent with Boltzmann's formulaS=klogW, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question.Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of addable points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent 1/n replaced by 2/n. Its proof uses the rearrangement inequality of Brascamp-Lieb-Lüttinger ([2]). Besides the free entropy power inequality, note that the inequality for restricted Minkowski sums may also underlie the classical Shannon entropy power inequality (see 3.2 below).Research supported in part by grants from the National Science Foundation.     

Level crossing resonance due to chlorine nuclei in a free radical

Muonium adds to allyl chloride, CH₂=CHCH₂Cl, to form two radicals: MuCH₂CHCH₂Cl (main product) and CH₂CHMuCH₂Cl (minor product). Both radicals were fully characterized bySR andLCR. In the main product, the LCR lines due to the³⁵Cl and³⁷Cl nuclei were observed. Also, the temperature dependence of various hyperfine coupling constants (hfc) indicates that both Mu and Cl eclipse the unpaired electronp ₂-orbital in the minimum energy conformation. For the fragment-CH₂Cl, the presence of Mu in the-position is found to affect significantly the hfc of Cl in the-position; an internal rotational barrier of 12 kJ mol^–1 was estimated using a simpleV ₂ torsional potential.     

μSR Investigation of ethyl radicals adsorbed on silica

SR spectra of the ethyl radical adsorbed on porous silica were observed in transverse and in longitudinal magnetic fields in the temperature range 190–298 K. The line widths reflect the dynamic partial averaging of the hyperfine anisotropy due to reorientation and surface diffusion.     

Cognitive ability experiment with photosensitive organic molecular thin films

We present an optical experiment which permits us to evaluate the information exchange necessary to self-induce cooperatively a well-organized pattern in a randomly activated molecular assembly. A low-power coherent beam carrying polarization and wavelength information is used to organize a surface relief grating on a photochromic polymer thin film which is photoactivated by a powerful incoherent beam. We demonstrate experimentally that less than 1% of the molecules possessing information cooperatively transmit it to the entire photoactivated polymer film.