Effective potential for the massless KPZ equation

In previous work we have developed a general method for casting a classical field theory subject to Gaussian noise (that is, a stochastic partial differential equation (SPDE)) into a functional integral formalism that exhibits many of the properties more commonly associated with quantum field theories (QFTs). In particular, we demonstrated how to derive the one-loop effective potential. In this paper we apply the formalism to a specific field theory of considerable interest, the massless KPZ equation (massless noisy Burgers equation), and analyze its behavior in the ultraviolet (short-distance) regime. When this field theory is subject to white noise we can calculate the one-loop effective potential and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions, and fails to be ultraviolet renormalizable in higher dimensions. We show that the one-loop effective potential for the massless KPZ equation is closely related to that for λφ⁴ QFT. In particular, we prove that the massless KPZ equation exhibits one-loop dynamical symmetry breaking (via an analog of the Coleman–Weinberg mechanism) in 1 and 2 space dimensions, and that this behavior does not persist in 3 space dimensions.     

Three-dimensional nanocarbon and the electrochemistry of nanocarbon/tin oxide for lithium ion batteries

In this work, the potential of using coconut shell, which is very cheap and readily available, for the production of graphitic nanocarbon three-dimensional networks is investigated. The three-dimensional carbon has been produced via the wet-impregnation of coconut shell powder with a transition metal catalyst. The novel process employed offers low costs and environmental advantages, with biological waste used in place of carbonaceous precursor as the feedstock. Nanocarbon/tin oxide composites were prepared via wet-impregnation and the solvothermal method, using tin chloride solution with the activated nanocarbon. The electrochemical performances of the three-dimensional nanocarbon doped with tin oxide and of activated nanocarbon alone as anode materials were investigated in rechargeable lithium ion batteries. One composite made by using the solvothermal method shows stable cyclic retention up to 100 cycles and delivers a high reversible capacity of about 405 mAh g⁻¹.

     

Characterization of C-H...π interactions in the structure of the CHClF(2)-HCCH weakly bound complex

The microwave spectra of four isotopologues of the CHClF(2)-HCCH dimer have been measured and used to determine the structure of the complex. An initial scan over the 7-18 GHz region using the chirped-pulse microwave spectrometer at the University of Virginia provided initial assignments of the (35)Cl and (37)Cl isotopologues, with two additional H(13)C(13)CH species assigned using the resonant cavity Balle-Flygare microwave spectrometer at Eastern Illinois University. For the most abundant isotopologue, the rotational constants and quadrupole coupling constants are: A = 3301.21(4) MHz, B = 1353.4268(19) MHz, C = 1153.7351(18) MHz, χ(aa) = 34.681(12) MHz, χ(bb) = -69.70(3) MHz, χ(cc) = 35.02(2) MHz and χ(ab) = -8.8(3) MHz, in good agreement with ab initio calculations at the MP2/6-311++G(2d,2p) level. The alignment of CHClF(2) with respect to acetylene reveals a C-Hπ interaction, with a secondary C-ClH-C interaction also present between the two monomers. The fitted distance between the CHClF(2) hydrogen atom and the center of the triple bond is 2.730(6) ?, the distance between the chlorine atom and the acetylenic hydrogen is 3.061(38) ?, and the C-Hπ angle is 148.2(6)°. In addition, the centrifugal distortion constants give an estimate of the binding energy for the weak interaction of about 4.9(5) kJ mol(-1), in reasonable agreement with several similar complexes.     

Effects of sulfate position on heparin octasaccharide binding to CCL2 examined by tandem mass spectrometry

Chemokine-glycosaminoglycan (GAG) interactions have been shown to be essential for in vivo chemokine signaling, which functions in such diverse processes as inflammation, development, and cancer metastasis. Despite the importance of these interactions, the saccharide sequence dependency of chemokine-GAG interactions is poorly understood. In a recent study, FT-ICR mass spectrometry was used to show that the chemokine CCL2 (monocyte chemoattractant protein 1) binds only to the 11- and 12-sulfated components of a heparin octasaccharide library. Although the exact structure of the fully sulfated, 12-sulfated octasaccharide is known, the 11-sulfated species could have a number of sulfated disaccharide sequences. In the current study, the composition of the 11-sulfated heparin octasaccharides, as well as the composition of CCL2 affinity purified 11-sulfated heparin octasaccharides, were examined by tandem MS. Of the three possible singly desulfated disaccharides, one species, III-S, is enriched by CCL2 affinity purification, indicating that the 11-sulfated heparin octasaccharides containing this disaccharide are preferentially bound to CCL2. These data suggest that 2-O and N sulfation of heparin may be of greater importance to CCL2-heparin binding than 6-O sulfation.     

Parallel algorithm for the computation of the Hartree-Fock exchange matrix: gas phase and periodic parallel ONX

In this paper we present an efficient parallelization of the ONX algorithm for linear computation of the Hartree-Fock exchange matrix [J. Chem. Phys. 106, 9708 (1997)]. The method used is based on the equal time (ET) partitioning recently introduced [J. Chem. Phys. 118, 9128 (2003)] and [J. Chem. Phys. 121, 6608 (2004)]. ET exploits the slow variation of the density matrix between self-consistent-field iterations to achieve load balance. The method is presented and some benchmark calculations are discussed for gas phase and periodic systems with up to 128 processors. The current parallel ONX code is able to deliver up to 77% overall efficiency for a cluster of 50 water molecules on 128 processors (2.56 processors per heavy atom) and up to 87% for a box of 64 water molecules (two processors per heavy atom) with periodic boundary conditions.     

Hawking-like radiation does not require a trapped region

We discuss the issue of quasiparticle production by "analogue black holes" with particular attention paid to the possibility of reproducing Hawking radiation in a laboratory. By constructing simple geometric acoustic models, we obtain a somewhat unexpected result: We show that, in order to obtain a stationary and Planckian emission of quasiparticles, it is not necessary to create a trapped region in the acoustic spacetime (corresponding to a supersonic regime in the fluid flow). It is sufficient to set up a dynamically changing flow asymptotically approaching a sonic regime with sufficient rapidity in laboratory time. This result is generic to curved-space quantum field theory, the "analogue spacetimes" we consider providing a guide to physical intuition, and a possible route to laboratory experiments.     

Motion correction properties of the shells k-space trajectory

The feasibility of a k-space trajectory that samples data on a set of 3D shells is demonstrated with phantom and volunteer experiments. Details of an interleaved multi-shot, helical spiral pulse sequence and a gridding reconstruction algorithm that uses Voronoi diagrams are provided. The motion-correction properties of the shells k-space trajectory are described. It is shown that when used in conjunction with three point markers, k-space data acquired with the shells trajectory provide a generalization of the RINGLET method, allowing for correction of arbitrary rigid-body motion with six degrees of freedom. Use of dedicated navigator echoes or redundant acquisitions of k-space data are not required. Retrospective motion correction is demonstrated with controlled phantom experiments and with seven healthy human volunteers. The motion correction is shown to improve the images, both qualitatively and quantitatively with a metric calculated from image entropy. Advantages and challenges of the shells trajectory are discussed, with particular attention to acquisition efficiency.     

Jordan structures of alternating matrix polynomials

Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We investigate the Smith forms of alternating matrix polynomials, showing that each invariant factor is an even or odd scalar polynomial. Necessary and sufficient conditions are derived for a given Smith form to be that of an alternating matrix polynomial. These conditions allow a characterization of the possible Jordan structures of alternating matrix polynomials, and also lead to necessary and sufficient conditions for the existence of structure-preserving strong linearizations. Most of the results are applicable to singular as well as regular matrix polynomials.     

Billiards in L-Shaped Tables with Barriers

We compute the volumes of the eigenform loci in the moduli space of genus-two Abelian differentials. From this, we obtain asymptotic formulas for counting closed billiards paths in certain L-shaped polygons with barriers.