Strings at nonzero temperature

String theory at nonzero temperature is reviewed. A bosonic string at nonzero temperature is studied and the calculation of its free energy in both the one-loop approximation and the case of arbitrary genus (multiloop analysis) is discussed. A string at nonzero temperature is compared with a string compacted on a one-dimensional torus. The properties of modular invariance and dual symmetry are discussed at both the one-loop and multiloop levels. The thermodynamics of superstrings, including also superstrings compactified on a torus, is also studied. Possible cosmological applications are briefly considered. It is shown that many features of string thermodynamics (in particular, the existence of the Hagedorn temperature and dual symmetry) also occur in the theory of noncritical strings.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–49, December, 1991.     

Synthesis of 1-(3-alkyl-2,3-dideoxy-D-pentofuranosyl)uracils with potential anti-HIV activity.

1-(3-Alkyl-2,3-dideoxy-alpha,beta-D-erythro-pentofuranosyl)uracils and 1-(3-alkyl-2,3-dideoxy-alpha,beta-D-threo-pentofuranosyl)uracils have been prepared from (E)-4,5-di-O-acetyl-2,3-dideoxy-aldehydo-D-glycero-pent-2-enose by a Michael addition reaction of the appropriate organocopper reagent followed in subsequent order by glycosidation of the resulting 3-alkyl-4,5-diacetoxypentanal with methanolic hydrogen chloride, protection with p-methoxybenzoyl chloride, and trimethylsilyl triflate catalyzed coupling with 2,4-di-O-(trimethylsilyl)uracil. The nucleosides were deprotected by treatment with 33% methylamine in absolute ethanol and separated by reversed-phase HPLC.     

Estimation of the exchange constants in the Fe sublattice of the Y2Fe17 and Y2Fe17N3−δ compounds from the analysis of Mössbauer measurements

From the analysis of Mössbauer data for Y₂Fe₁₇ and Y₂Fe₁₇N_3−δ at various temperatures the hyperfine fields for 4f, 6g, 12j, 12k iron sites were estimated as a function of temperature. The reduced magnetizations calculated from the values of the hyperfine fields are fitted with a mean field model for four interacting sublattices using a computer program. The estimated exchange interaction from the fitting procedure between the 4f sites is found strongly negative (antiferromagnetic) in Y₂Fe₁₇ whereas in Y₂Fe₁₇N_3−δ it increases and becomes weak negative following a modified Slater-Néel curve. The rest of the exchange interactions are found positive or weak negative depending on the distances between the Fe atoms.     

Trefftz,collocation, and other boundary methods—A comparison

In this article we survey the Trefftz method (TM), the collocation method (CM), and the collocation Trefftz method (CTM). We also review the coupling techniques for the interzonal conditions, which include the indirect Trefftz method, the original Trefftz method, the penalty plus hybrid Trefftz method, and the direct Trefftz method. Other boundary methods are also briefly described. Key issues in these algorithms, including the error analysis, are addressed. New numerical results are reported. Comparisons among TMs and other numerical methods are made. It is concluded that the CTM is the simplest algorithm and provides the most accurate solution with the best numerical stability. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Synthesis and thermal behaviour of salicylaldimine-based liquid crystalline symmetrical dimers

A series of symmetrical dimers consisting of salicylaldimine moieties connected by flexible alkylene central spacer via ether linkages has been synthesized. In order to validate the empirical rule suggested by Date et al. to account for the smectic behaviour of such dimers, the chain length of the terminal alkoxy chain has been kept constant (C₈) while the number of methylene units in the central spacer was varied from C₃ to C₁₁. Another aim of the present investigation was to understand structure-property relationship in these dimers in which the salicylaldimine mesogenic segment has been used for the first time in dimers. The mesomorphic behaviour of these dimers was evaluated using optical microscopy and differential scanning calorimetry and the structure of some of the mesophases has been further investigated with the help of X-ray diffraction. Our studies reveal that the dimers consisting of 3 to 8 methylene units in the flexible spacer show only smectic (smectic C and smectic A) phases. For the dimers containing 4, 6 and 8 methylene units in the central spacer, a unique filament growth pattern has been observed in the smectic A phase while cooling from the isotropic phase. The dimers containing of C₉ to C₁₁ methylene groups exhibit the nematic phase in addition to smectic modifications. This observation indicates that when the terminal chains are shorter than the spacer, the tendency to form smectic phases is not fully extinguished but is perhaps reduced.     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

Adsorption of nonionic surfactant triton X-100 on solids from aqueous and nonaqueous solutions

The adsorption of nonionic surfactant Triton X-100 on quartz sand and methylated quartz sand from water and toluene was investigated by means of spectrophotometry, the radiotracer technique, and wetting angle measurements.     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.