Part I. Hydraulics of tidal inlets: simple analytic models for the engineer

Inlets are common coastal features around the world. Essentially an inlet connects a lagoon, a bay or an estuary to the ocean (or sea), and the flow through the inlet channel is primarily induced by the tidal rise and fall of water level in the ocean. When speaking of the hydraulics of an inlet, one is interested mainly in determining the flow through the inlet and the tidal variation in the bay, given the following: (1) Inlet geometry (2) Bay geometry (3) Bottom sediment characteristics in the inlet (4) Fresh water inflow into the bay (and out through the inlet) (5) Ocean tide characteristics A combination of all these factors can produce a rather complex situation. (PDF contains 34 pages.

Inlet stability and case histories, Part II

Inlets which require frequent channel dredging due to gradual shoaling, exhibit migration, or shoal up during storms, are in general unstable and pose a problem to the engineer. This problem of inlet stability is a complex one, because of the rather large number of variables that go into defining stability. The reference here is to inlets on sandy coasts only, because the absence of sand or similar sedimentary material the problem does not arise. Shell is also found in varying proportions with sand. Some of this is. new, whereas in some areas it is ancient reworked material whose size distribution is close to that of the sand with which it is associated. (PDF has 24 pages.

A column of grains in the jamming limit: glassy dynamics in the compaction process

We investigate a stochastic model describing a column of grains in the jamming limit, in the presence of a low vibrational intensity. The key control parameter of the model, $\epsilon$, is a representation of granular shape, related to the reduced void space. Regularity and irregularity in grain shapes, respectively corresponding to rational and irrational values of $\epsilon$, are shown to be centrally important in determining the statics and dynamics of the compaction process.Comment: 29 pages, 14 figures, 1 table. Various minor changes and updates. To appear in EPJ

Slow synaptic dynamics in a network: from exponential to power-law forgetting

We investigate a mean-field model of interacting synapses on a directed neural network. Our interest lies in the slow adaptive dynamics of synapses, which are driven by the fast dynamics of the neurons they connect. Cooperation is modelled from the usual Hebbian perspective, while competition is modelled by an original polarity-driven rule. The emergence of a critical manifold culminating in a tricritical point is crucially dependent on the presence of synaptic competition. This leads to a universal $1/t$ power-law relaxation of the mean synaptic strength along the critical manifold and an equally universal $1/\sqrt{t}$ relaxation at the tricritical point, to be contrasted with the exponential relaxation that is otherwise generic. In turn, this leads to the natural emergence of long- and short-term memory from different parts of parameter space in a synaptic network, which is the most novel and important result of our present investigations.Comment: 12 pages, 8 figures. Phys. Rev. E (2014) to appea

Universality in survivor distributions: Characterising the winners of competitive dynamics

We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might not survive the predatory dynamics: all stochasticity is brought in by the initial state. Every such initial state leads to a unique and extended pattern of survivors and non-survivors, which is known as an attractor of the dynamics. We show that the number of such attractors grows exponentially with system size, so that their exact characterisation is limited to only very small systems. Given this, we construct an analytical approach based on inhomogeneous mean-field theory to calculate survival probabilities for arbitrary networks. This powerful (albeit approximate) approach shows how universality arises in survivor distributions via a key concept -- the {\it dynamical fugacity}. Remarkably, in the large-mass limit, the survival probability of a node becomes independent of network geometry, and assumes a simple form which depends only on its mass and degree.Comment: 12 pages, 6 figures, 2 table

Matrices coupled in a chain. I. Eigenvalue correlations

The general correlation function for the eigenvalues of $p$ complex hermitian matrices coupled in a chain is given as a single determinant. For this we use a slight generalization of a theorem of Dyson.Comment: ftex eynmeh.tex, 2 files, 8 pages Submitted to: J. Phys.