The Process " Pbar P -> E- E+ " with Polarized Initial Particles and Proton Form Factors in Time-Like Region

The discussion on the asymptotical behaviour of the form factors in the space-like and time-like regions have been corrected and clarified. Fig.3 has been replaced by an improved analysis of the data.Comment: DFTT 13/93. LaTeX file, 11 pages + 3 figures (included

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio

Thermodynamics of Dipolar Chain Systems

The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculated numerically. Our findings indicate that thermodynamic observables, such as the heat capacity, can be used to probe the signatures of the intralayer interaction between chains. This should be relevant for near future experiments on polar molecules with strong dipole moments.Comment: 15 pages, 5 figures, final versio

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for the high nuclearity spin clusters, Mn_{12}, Fe_8 and V_{15}. The largest calculation involves the Mn_{12} cluster which spans a Fock space of a hundred million. Our results show that the earlier estimates of the exchange constants need to be revised for the Mn_{12} cluster to explain the level ordering of low-lying eigenstates. In the case of the Fe_8 cluster, correct level ordering can be obtained which is consistent with the exchange constants for the already known clusters with butterfly structure. In the V_{15} cluster, we obtain an effective Hamiltonian that reproduces exactly, the eight low-lying eigenvalues of the full Hamiltonian.Comment: Revtex, 12 pages, 16 eps figures; this is the final published versio

Forward Modeling of Space-borne Gravitational Wave Detectors

Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling of space-based gravitational wave detectors and introduce an adiabatic approximation to the detector response that significantly extends the range of the standard low frequency approximation. The adiabatic approximation will aid in the development of data analysis techniques, and improve the modeling of astrophysical parameter extraction.Comment: 14 Pages, 14 Figures, RevTex

Lichenometric dating (lichenometry) and the biology of the lichen genus rhizocarpon:challenges and future directions

Lichenometric dating (lichenometry) involves the use of lichen measurements to estimate the age of exposure of various substrata. Because of low radial growth rates and considerable longevity, species of the crustose lichen genus Rhizocarpon have been the most useful in lichenometry. The primary assumption of lichenometry is that colonization, growth and mortality of Rhizocarpon are similar on surfaces of known and unknown age so that the largest thalli present on the respective faces are of comparable age. This review describes the current state of knowledge regarding the biology of Rhizocarpon and considers two main questions: (1) to what extent does existing knowledge support this assumption; and (2) what further biological observations would be useful both to test its validity and to improve the accuracy of lichenometric dates? A review of the Rhizocarpon literature identified gaps in knowledge regarding early development, the growth rate/size curve, mortality, regeneration, competitive effects, colonization, and succession on rock surfaces. The data suggest that these processes may not be comparable on different rock surfaces, especially in regions where growth rates and thallus turnover are high. In addition, several variables could differ between rock surfaces and influence maximum thallus size, including rate and timing of colonization, radial growth rates, environmental differences, thallus fusion, allelopathy, thallus mortality, colonization and competition. Comparative measurements of these variables on surfaces of known and unknown age may help to determine whether the basic assumptions of lichenometry are valid. Ultimately, it may be possible to take these differences into account when interpreting estimated dates

Electromagnetic Polarization Effects due to Axion Photon Mixing

We investigate the effect of axions on the polarization of electromagnetic waves as they propagate through astronomical distances. We analyze the change in the dispersion of the electromagnetic wave due to its mixing with axions. We find that this leads to a shift in polarization and turns out to be the dominant effect for a wide range of frequencies. We analyze whether this effect or the decay of photons into axions can explain the large scale anisotropies which have been observed in the polarizations of quasars and radio galaxies. We also comment on the possibility that the axion-photon mixing can explain the dimming of distant supernovae.Comment: 18 pages, 1 figur

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules

We consider a bilayer setup with two parallel planes of cold fermionic polar molecules when the dipole moments are oriented perpendicular to the planes. The binding energy of two-body states with one polar molecule in each layer is determined and compared to various analytic approximation schemes in both coordinate- and momentum-space. The effective interaction of two bound dimers is obtained by integrating out the internal dimer bound state wave function and its robustness under analytical approximations is studied. Furthermore, we consider the effect of the background of other fermions on the dimer state through Pauli blocking, and discuss implications for the zero-temperature many-body phase diagram of this experimentally realizable system.Comment: 18 pages, 10 figures, accepted versio