Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 Post-Newtonian order

Using the NRGR effective field theory formalism we calculate the remaining source multipole moments necessary to obtain the spin contributions to the gravitational wave amplitude to 2.5 Post-Newtonian (PN) order. We also reproduce the tail contribution to the waveform linear in spin at 2.5PN arising from the nonlinear interaction between the current quadrupole and the mass monopole.Comment: 17 pages, 4 figures. v2 Minor changes, to appear in JCA

Optimized minigaps for negative differential resistance creation in strongly delta-doped (1D) superlattices

The "atomic saw method" uses the passage of dislocations in two-dimensional (2D) quantum-well superlattices to create periodic slipping layers and one-dimensional (1D) quantum wire superlattices. The effects of this space structuring of the samples on the allowed energies are analysed in the case of GaAs d-doped superlattices. If they are sufficiently large, the various minigaps appearing in the 1D band structure could be responsible for the presence of negative differential resistance (NDR) with high critical current in these systems. The purpose is to determine the evolution of the minigaps in terms of the sample parameters and to obtain the means to determine both the 2D and 1D structural characteristics where NDR could appear.Comment: see erratum 10.1006/spmi.1998.070

Study and characterization by magnetophonon resonance of the energy structuring in GaAs/AlAs quantum-wire superlattices

We present the characterization of the band structure of GaAs/AlAs quantum-wire 1D superlattices performed by magnetophonon resonance with pulsed magnetic fields up to 35 T. The samples, generated by the "atomic saw method" from original quantum-well 2D superlattices, underwent substantial modifications of their energy bands built up on the X-states of the bulk. We have calculated the band structure by a finite element method and we have studied the various miniband structures built up of the masses m_t and m_l of GaAs and AlAs at the point X. From an experimental point of view, the main result is that in the 2D case we observe only resonances when the magnetic field B is applied along the growth axis whereas in the 1D case we obtain resonances in all magnetic field configurations. The analysis of the maxima (or minima for B // E) in the resistivity rho_xy as a function of B allows us to account, qualitatively and semi-quantitatively, for the band structure theoretically expected

On the exponential Diophantine equation p⋅3x+py=z2{\displaystyle p\cdot 3^{x}+p^{y}=z^2} with pp a prime number

In this paper we find non-negative integer solutions for exponential Diophantine equations of the type $p \cdot 3^x+ p^y=z^2,$ where $p$ is a prime number. We prove that such equation has a unique solution $\displaystyle{(x,y,z)=\left(\log_3(p-2), 0, p-1\right)}$ if $2 \neq p \equiv 2 \pmod 3$ and $(x,y,z)=(0,1,2)$ if $p=2$. We also display the infinite solution set of that equation in the case $p=3$. Finally, a brief discussion of the case $p \equiv 1 \pmod 3$ is made, where we display an equation that does not have a non-negative integer solution and leave some open questions. The proofs are based on the use of the properties of the modular arithmetic

Sediment source fingerprinting as an aid to catchment management: a review of the current state of knowledge and a methodological decision-tree for end-users

The growing awareness of the environmental significance of fine-grained sediment fluxes through catchment systems continues to underscore the need for reliable information on the principal sources of this material. Source estimates are difficult to obtain using traditional monitoring techniques, but sediment source fingerprinting or tracing procedures, have emerged as a potentially valuable alternative. Despite the rapidly increasing numbers of studies reporting the use of sediment source fingerprinting, several key challenges and uncertainties continue to hamper consensus among the international scientific community on key components of the existing methodological procedures. Accordingly, this contribution reviews and presents recent developments for several key aspects of fingerprinting, namely: sediment source classification, catchment source and target sediment sampling, tracer selection, grain size issues, tracer conservatism, source apportionment modelling, and assessment of source predictions using artificial mixtures. Finally, a decision-tree representing the current state of knowledge is presented, to guide end-users in applying the fingerprinting approach

The consistency condition for the three-point function in dissipative single-clock inflation

We generalize the consistency condition for the three-point function in single field inflation to the case of dissipative, multi-field, single-clock models. We use the recently introduced extension of the effective field theory of inflation that accounts for dissipative effects, to provide an explicit proof to leading (non-trivial) order in the generalized slow roll parameters and mixing with gravity scales. Our results illustrate the conditions necessary for the validity of the consistency relation in situations with many degrees of freedom relevant during inflation, namely that there is a preferred clock. Departures from this condition in forthcoming experiments would rule out not only single field but also a large class of multi-field models.Comment: 26+11 page

Probability Distribution of the Shortest Path on the Percolation Cluster, its Backbone and Skeleton

We consider the mean distribution functions Phi(r|l), Phi(B)(r|l), and Phi(S)(r|l), giving the probability that two sites on the incipient percolation cluster, on its backbone and on its skeleton, respectively, connected by a shortest path of length l are separated by an Euclidean distance r. Following a scaling argument due to de Gennes for self-avoiding walks, we derive analytical expressions for the exponents g1=df+dmin-d and g1B=g1S-3dmin-d, which determine the scaling behavior of the distribution functions in the limit x=r/l^(nu) much less than 1, i.e., Phi(r|l) proportional to l^(-(nu)d)x^(g1), Phi(B)(r|l) proportional to l^(-(nu)d)x^(g1B), and Phi(S)(r|l) proportional to l^(-(nu)d)x^(g1S), with nu=1/dmin, where df and dmin are the fractal dimensions of the percolation cluster and the shortest path, respectively. The theoretical predictions for g1, g1B, and g1S are in very good agreement with our numerical results.Comment: 10 pages, 3 figure