Submerged dunes and breakwater embayments mapped using wave inversions of shore-mounted marine X-Band radar data

Surveying very shallow coastal areas, particularly around coastal defences, can be a logistically difficult and time consuming process. A marine-radar based bathymetry mapping technique has been used to remotely map the embayments around a series of shore-parallel breakwaters at Sea Palling on the south east coast of England during the LEACOAST2 project. The duration of the deployment spanned over 2 years, with the aim of observing any evolution of bathymetric features over that timescale while providing a clear indication of the spatial variability of wave and current patterns contributing to such evolution. The embayments generated by the shore parallel breakwaters at that site are resolved and a field of subtidal dunes with a wavelength of the order of 200m and amplitude around 1m located in approximately 6-10m of water were within the radar field of view and are evident in the remotely sensed bathymetry. Comparisons between bathymetric data obtained using conventional survey techniques and the radar based technique are presented together with measurements of tidal currents mapped using the same remote sensing method and compared with ADCP data during a storm even

The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

The combined solar and tidal influence in climate

To provide an early warning indication of the CO2 warning signal, we are searching for periodic or projectable trends in climate. The strong 20.5 year oscillation in Eastern North American January temperature found by Mock and Hibler shows evidence of a beat between waves with periods of 22.36 (22.21 to 22.55) years and 18.64 (18.45 to 18.79) years with an opposition at about 1880. These are interpreted to be the 22.279 year solar Hale magnetic cycle and the 18.61 year lunar nodal tidal cycle. The lunar nodal cycle is known to produce changes in the sea surface temperature through increased mixing of the mixed layer of the ocean. This beat note is shown to be evident in the Western High Plains drought record of Mitchell, Stockton and Meko and to provide a better bit to the drought series, especially at the beat oppositions in 1880 and 1770

The Positivity Set of a Recurrence Sequence

We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive dominating characteristic root, we establish that the density is positive. Furthermore, we determine the values that can occur as density of such a positivity set, both for the special case just mentioned and in general