On step approximations for water-wave problems

The scattering of water waves by a varying bottom topography is considered using two-dimensional linear water-wave theory. A new approach is adopted in which the problem is first transformed into a uniform strip resulting in a variable free-surface boundary condition. This is then approximated by a finite number of sections on which the free-surface boundary condition is assumed to be constant. A transition matrix theory is developed which is used to relate the wave amplitudes at fm. The method is checked against examples for which the solution is known, or which can be computed by alternative means. Results show that the method provides a simple accurate technique for scattering problems of this type

Final Report On Submerged Cylinder Wave Energy Device

A first overall assessment of the submerged cylinder device has been prepared, from which at outline design for the principal components has been produced. A budget estimate for this design has been made, including allowances for annual operation and maintenance charges. The efficiency characteristics of the device have been determined from selected tank tests. With these efficiencies, the energy captured by each cylinder of an array has been estimated. Allowances have been made for the probable energy losses in each component through to the National network at Perth. On the basis of the preliminary specification for the device agreed in June 1979, at the end of Stage 1 of this Contract, the price of electricity delivered to the network is estimated to be 11. 4 p/kWh. This assumes a 5% discount rate and a 20 year operating life. A number of improvements to the reference design are already clear. Principally its tuned frequency should be increased so that the efficiency characteristics match the wave spectrum more closely. This single improvement in gross output appears sufficient to reduce the unit cost to about 8.5 p/kWh because of the significance of annual maintenance charges on the net annual revenue from sales of electricity. There is considerable scope to improve the design. Other power take off and energy transfer techniques deserve attention, and there is scope to rationalise the mooring and foundation arrangements. Because of the nature of its working environment, the same philosophy of using proven components or reasonable derivatives therefrom should be retained. The stable behaviour of the device in all sea conditions studied, and its high efficiency in the more persistent waves, confirm that this further step towards a comprehensive design of the basically simple, efficient and robust system is justified

Spectral measures of small index principal graphs

The principal graph $X$ of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If $\Delta$ is the adjacency matrix of $X$ we consider the equation $\Delta=U+U^{-1}$. When $X$ has square norm $\leq 4$ the spectral measure of $U$ can be averaged by using the map $u\to u^{-1}$, and we get a probability measure $\epsilon$ on the unit circle which does not depend on $U$. We find explicit formulae for this measure $\epsilon$ for the principal graphs of subfactors with index $\le 4$, the (extended) Coxeter-Dynkin graphs of type $A$, $D$ and $E$. The moment generating function of $\epsilon$ is closely related to Jones' $\Theta$-series.Comment: 23 page

The phase free, longitudinal, magnetic component of vacuum electromagnetism

A charge $q$ moving in a reference laboratory system with constant velocity {\bf V} in the $X$-axis produces in the $Z$-axis a longitudinal, phase free, vacuum magnetic field which is identified as the radiated ${\bf B}^{(3)}$ field of Evans, Vigier and others.Comment: ReVTeX file, 7pp., no figure

A lattice model for the kinetics of rupture of fluid bilayer membranes

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion), the thickness of the hydrophobic part of the bilayer, the hydrophobicity and a parameter characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium ``phase diagram'' is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first order rupture line is found with increasing tension, and a continuous increase in proto-pore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated PC lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.Comment: 15 pages, 8 figure

Deep electronic states in ion-implanted Si

In this paper we present an overview of the deep states present after ion-implantation by various species into n-type silicon, measured by Deep Level Transient Spectroscopy (DLTS) and high resolution Laplace DLTS (LDLTS). Both point and small extended defects are found, prior to any anneal, which can therefore be the precursors to more detrimental defects such as end of range loops. We show that the ion mass is linked to the concentrations of defects that are observed, and the presence of small interstitial clusters directly after ion implantation is established by comparing their behaviour with that of electrically active stacking faults. Finally, future applications of the LDLTS technique to ion-implanted regions in Si-based devices are outlined.</p

Quantum Mechanics and Black Holes in Four-Dimensional String Theory

In previous papers we have shown how strings in a two-dimensional target space reconcile quantum mechanics with general relativity, thanks to an infinite set of conserved quantum numbers, ``W-hair'', associated with topological soliton-like states. In this paper we extend these arguments to four dimensions, by considering explicitly the case of string black holes with radial symmetry. The key infinite-dimensional W-symmetry is associated with the $\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a model-independent feature of spherically symmetric four-dimensional strings. Arguments are also given that the enormous number of string {\it discrete (topological)} states account for the maintenance of quantum coherence during the (non-thermal) stringy evaporation process, as well as quenching the large Hawking-Bekenstein entropy associated with the black hole. Defining the latter as the measure of the loss of information for an observer at infinity, who - ignoring the higher string quantum numbers - keeps track only of the classical mass,angular momentum and charge of the black hole, one recovers the familiar a quadratic dependence on the black-hole mass by simple counting arguments on the asymptotic density of string states in a linear-dilaton background.Comment: 18 page

On the connection between Quantum Mechanics and the geometry of two-dimensional strings

On the basis of an area-preserving symmetry in the phase space of a one-dimensional matrix model - believed to describe two-dimensional string theory in a black-hole background which also allows for space-time foam - we give a geometric interpretation of the fact that two-dimensional stringy black holes are consistent with conventional quantum mechanics due to the infinite gauged `W-hair' property that characterises them.Comment: 19 page

The Origin of Space-Time as WW Symmetry Breaking in String Theory

Physics in the neighbourhood of a space-time metric singularity is described by a world-sheet topological gauge field theory which can be represented as a twisted $N=2$ superconformal Wess-Zumino model with a $W_{1+\infty} \otimes W_{1+\infty}$ bosonic symmetry. The measurable $W$-hair associated with the singularity is associated with Wilson loop integrals around gauge defects. The breaking of $W_{1+\infty}$ $\otimes$ $W_{1+\infty}$ $\rightarrow$ $W_{1+\infty}$ is associated with expectation values for open Wilson lines that make the metric non-singular away from the singularity. This symmetry breaking is accompanied by massless discrete `tachyon' states that appear as leg poles in $S$-matrix elements. The triviality of the $S$-matrix in the high-energy limit of the $c=1$ string model, after renormalisation by the leg pole factors, is due to the restoration of double $W$-symmetry at the singularity.Comment: 13 page

Water wave propagation and scattering over topographical bottoms

Here I present a general formulation of water wave propagation and scattering over topographical bottoms. A simple equation is found and is compared with existing theories. As an application, the theory is extended to the case of water waves in a column with many cylindrical steps