Simulations of dimensionally reduced effective theories of high temperature QCD

Quantum chromodynamics (QCD) is the theory describing interaction between quarks and gluons. At low temperatures, quarks are confined forming hadrons, e.g. protons and neutrons. However, at extremely high temperatures the hadrons break apart and the matter transforms into plasma of individual quarks and gluons. In this theses the quark gluon plasma (QGP) phase of QCD is studied using lattice techniques in the framework of dimensionally reduced effective theories EQCD and MQCD. Two quantities are in particular interest: the pressure (or grand potential) and the quark number susceptibility. At high temperatures the pressure admits a generalised coupling constant expansion, where some coefficients are non-perturbative. We determine the first such contribution of order g^6 by performing lattice simulations in MQCD. This requires high precision lattice calculations, which we perform with different number of colors N_c to obtain N_c-dependence on the coefficient. The quark number susceptibility is studied by performing lattice simulations in EQCD. We measure both flavor singlet (diagonal) and non-singlet (off-diagonal) quark number susceptibilities. The finite chemical potential results are optained using analytic continuation. The diagonal susceptibility approaches the perturbative result above 20T_c$, but below that temperature we observe significant deviations. The results agree well with 4d lattice data down to temperatures 2T_c.

Lattice dynamics of hexagonal ice

The lattice dynamics of hexagonal ice is worked out with the force constants deduced from the experimental elastic constants.

Studies in bubble formation—II bubble formation under constant pressure conditions

Bubble formation under constant pressure conditions has been investigated for wide range of variation of liquid properties.Air bubbles were formed from single horizontal orifices submerged in liquids whose viscosity varied from 1·0 to 600 cPs and surface tension from 37 to 72 dyn/cm. Air flow rate was varied from 2 to 250 cm3/sec and the orifice diameter from 0·0515 to 0·4050 cm.

Studies in bubble formation—I bubble formation under constant flow conditions

A model based on two step mechanism of bubble formation is proposed. The resulting equations are used to explain the discrepancies existing in the literature. Data have been collected over a wide range of variables to test the model.

Lattice vibrations in alkali azides

The longwavelength lattice vibrations in potassium, rubidium and caesium azides have been calculated using Born's lattice dynamics.

Stress concentration and load diffusion in rectangular panels with constant stress flanges

The stress concentration that occurs when load is diffused from a constant stress member into thin sheet is an important problem in the design of light weight structures. By using solutions in biharmonic polar-trigonometric series, the stress concentration can be effectively isolated so that highly accurate information necessary for design can be obtained. A method of analysis yielding high accuracy with limited effort is presented for rectangular panels with transverse edges free or supported by inextensional end ribs. Numerical data are given for panels with length twice the width.

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.

Crystallographic Evolution, Dielectric, and Piezoelectric Properties of Bi4Ti3O12:W/Cr Ceramics

W/Cr codoped Bi4Ti3O12 ceramics, Bi4Ti3-xWxO12+x+0.2 wt%Cr2O3 (BITWC, x=0-0.15), were prepared using a solid-state reaction method. The crystallographic evolution and phase analysis were distinctly determined focusing on the X-ray diffraction peak changes in (020)/(200) and (220)/(1115) diffraction planes, by which the lattice parameters, a, b, and c can be refined. The thermal variations of permittivity, dielectric loss (tan delta), impedance, and electrical conductivity properties were characterized. A decrease in the values of Curie temperature from 675 degrees to 640 degrees C and an increase in the values of the dielectric constant due to an increase of W6+/Cr3+ content were observed. The highest piezoelectric constant, d(33) of 22 pC/N, was achieved with the composition of Bi4Ti2.975W0.025O12.025+0.2 wt% Cr2O3. Also, this composition had a lower electrical conductivity than the other investigated compositions.

Vibrational force constant and electron relaxation in H2 and Li2

The force constants of H2 and Li2 are evaluated employing their extended Hartree-Fock wavefunctions by a polynomial fit of their force curves. It is suggested that, based on incomplete multiconfiguration Hartree-Fock wavefunctions, force constants calculated from the energy derivatives are numerically more accurate than those obtained from the derivatives of the Hellmann-Feynman forces. It is observed that electrons relax during the nuclear vibrations in such a fashion as to facilitate the nuclear motions.

Ratio transformer bridge for the measurement of dielectric constant of lossy liquids

A three-terminal capacitance bridge is developed for the measurement of the dielectric constant of lossy liquids. Using this modified ratio transformer bridge, the capacitance shunted by a resistance as low as 50 Omega is measured at 10 kHz. The capacitance error associated with the inductance of the connecting wire is compensated using the novel method of introducing an additional transformer to the existing ratio transformer bridge. Other sources of capacitance errors, such as the non-zero output impedence of the ratio transformer and the shield capacitances of the cables, are discussed.

Voltage delay during constant-current or constant-resistance discharge of Mg-MnO2 dry cells: A comparative study

A theoretical approach has been developed to relate the voltage delay transients of the Mg-MnO2 dry cell observed during discharge by two commonly employed modes, viz., (1) at constant current, and (2) across a constant resistance. The approach has been verified by comparison of experimentally obtained transients with those generated from theory. The method may be used to predict the delay parameters of the Mg-MnO2 dry cell under the two modes of discharge and can, in principle, be extended to lithium batteries.

Triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of "strings." We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low-field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of st phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems; a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.