Heavy ion beam lifetimes at relativistic and ultrarelativistic colliders

The effects of higher order corrections in ultra-relativistic nuclear collisions are considered. It is found that higher order contributions are small at low energy, large at intermediate energy and small again at very high energy. An explanation for this effect is given. This means that the Weizsacker-Williams formula is a good approximation to use in calculating cross sections and beam lifetimes at energies relevant to RHIC and LHC.Comment: 10 pages, 2 tables, 4 figure

A letter of intent for an experiment to study strong electromagnetic fields at RHIC via multiple electromagnetic processes

An experimental program at the Relativistic Heavy Ion Collider (RHIC) which is designed to study nonperturbative aspects of electrodynamics is outlined. Additional possibilities for new studies of electrodynamics via multiple electromagnetic processes are also described

Biphasic behaviour in malignant invasion

Invasion is an important facet of malignant growth that enables tumour cells to colonise adjacent regions of normal tissue. Factors known to influence such invasion include the rate at which the tumour cells produce tissue-degrading molecules, or proteases, and the composition of the surrounding tissue matrix. A common feature of experimental studies is the biphasic dependence of the speed at which the tumour cells invade on properties such as protease production rates and the density of the normal tissue. For example, tumour cells may invade dense tissues at the same speed as they invade less dense tissue, with maximal invasion seen for intermediate tissue densities. In this paper, a theoretical model of malignant invasion is developed. The model consists of two coupled partial differential equations describing the behaviour of the tumour cells and the surrounding normal tissue. Numerical methods show that the model exhibits steady travelling wave solutions that are stable and may be smooth or discontinuous. Attention focuses on the more biologically relevant, discontinuous solutions which are characterised by a jump in the tumour cell concentration. The model also reproduces the biphasic dependence of the tumour cell invasion speed on the density of the surrounding normal tissue. We explain how this arises by seeking constant-form travelling wave solutions and applying non-standard phase plane methods to the resulting system of ordinary differential equations. In the phase plane, the system possesses a singular curve. Discontinuous solutions may be constructed by connecting trajectories that pass through particular points on the singular curve and recross it via a shock. For certain parameter values, there are two points at which trajectories may cross the singular curve and, as a result, two distinct discontinuous solutions may arise

Stability of patterns with arbitrary period for a Ginzburg-Landau equation with a mean field

We consider the following system of equations A_t= A_{xx} + A - A^3 -AB,\quad x\in R,\,t>0, B_t = \sigma B_{xx} + \mu (A^2)_{xx}, x\in R, t>0, where \mu > \sigma >0. It plays an important role as a Ginzburg-Landau equation with a mean field in several fields of the applied sciences. We study the existence and stability of periodic patterns with an arbitrary minimal period L. Our approach is by combining methods of nonlinear functional analysis such as nonlocal eigenvalue problems and the variational characterization of eigenvalues with Jacobi elliptic integrals. This enables us to give a complete characterization of existence and stability for all solutions with A>0, spatial average =0 and an arbitrary minimal period

Travelling Combustion Waves in a Porous Medium. Part I—Existence

A one-space-dimensional, time-dependent model for travelling combustion waves in a porous medium is analysed. The key variables are the temperature of the solid medium and its density and the temperature of the gaseous phase and its density. The key parameters µ, λ and a are related (respectively) to the driving gas velocity, the specific heat of the combustible solid and the ratio of consumption of oxygen to that of solid. The regions of existence of the different types of combustion waves are found in µ, λ parameter space, with a = 0. The types of combustion wave are classified by the switch mechanism that turns off the combustion, which occurs over a finite, but unknown, interval. Because the model is linear outside the combustion zone, the eigenvalue problem governing the existence of travelling waves may be reformulated as a two-point free boundary problem on a finite domain. Existence and nonexistence theorems are established for this unusual bifurcation problem

Travelling Combustion Waves in a Porous Medium. Part II—Stability

The linear stability properties of the travelling combustion waves found in Part I are examined. The key parameters which determine the stability properties of the waves are found to be the (scaled) driving velocity and the solid specific heat. In particular, the destabilising influence of increasing either of these two parameters is demonstrated. The results indicate that travelling combustion waves whose reaction is turned off because the solid temperature becomes too low are always unstable, whereas travelling waves whose reaction is turned off due to depletion of solid reactant can be stable. Global techniques are employed to prove that, for large enough values of the scaled solid specific heat, combustion cannot be sustained in any form, and all initial conditions lead to extinction

Immunity to Murine Sarcoma Virus Induced Tumors. III. Analysis of the Cell Populations Involved in Protection from Lethal Tumour Progression of Sublethally Irradiated, MSV Inoculated, Mice

A comparison was made between the cells responsible for demonstrable activity against MSV antigens, using both in vivo and in vitro assays. Similar cells (in terms of size and sensitivity to anti-theta serum) were detected in both assays. However, while lymphoid cells from animals at all stages post-MSV infection were active in protecting irradiated mice from the lethal effect of induction of MSV sarcomata, cells from animals at early stages post-MSV infection (when the tumour was in a progressive phase of growth) were not active in the in vitro assay. By manipulation of the in vivo assay conditions a situation was observed in which cells from “progressor animals” were able to suppress both the in vitro and in vivo activity of regressor lymphoid cells. The potential physiological role of this cell type is disussed