Strong-coupling electrostatics for two dissimilar charged walls

We study the effective interaction between two parallel charged plates, modelling macromolecules, or colloids, in the strongly coupled Coulomb regime. Neutralizing mobile ions are point-like and confined in the inter-plate slab. A cumulant technique provides exact expansions, beyond the leading strong-coupling order, that are in remarkable agreement with simulation data for both the ionic profile and the inter-plate pressure. The present approach amounts to a summation over relevant excitations around the Wigner Crystal ground state formed at infinite coupling; It thereby differs from previous virial-like strong-coupling theories and generalizes a recent work by the authors to asymmetric plates.     

Astrocyte signaling in the presence of spatial inhomogeneities

Astrocytes, a special type of glial cells, were considered to have just a supporting role in information processing in the brain. However, several recent studies have shown that they can be chemically stimulated by various neurotransmitters, such as ATP, and can generate Ca2+ and ATP waves, which can propagate over many cell lengths before being blocked. Although pathological conditions, such as spreading depression and epilepsy, have been linked to abnormal wave propagation in astrocytic cellular networks, a quantitative understanding of the underlying characteristics is still lacking. Astrocytic cellular networks are inhomogeneous, in the sense that the domain they occupy contains passive regions or gaps, which are unable to support wave propagation. Thus, this work focuses on understanding the complex interplay between single-cell signal transduction, domain inhomogeneity, and the characteristics of wave propagation and blocking in astrocytic cellular networks. The single-cell signal transduction model that was employed accounts for ATP-mediated IP3 production, the subsequent Ca2+ release from the ER, and ATP release into the extracellular space. The model is excitable and thus an infinite range of wave propagation is observed if the domain of propagation is homogeneous. This is not always the case for inhomogeneous domains. To model wave propagation in inhomogeneous astrocytic networks, a reaction-diffusion framework was developed and one-gap as well as multiple-gap cases were simulated using an efficient finite-element algorithm. The minimum gap length that blocks the wave was computed as a function of excitability levels and geometric characteristics of the inhomogeneous network, such as the length of the active regions (cells). Complex transient patterns, such as wave reflection, wave trapping, and generation of echo waves, were also predicted by the model, and their relationship to the geometric characteristics of the network was evaluated. Therefore, the proposed model can help in the formulation of testable hypotheses to explain the observed abnormal wave propagation in pathological situations.     

Membrane stress tensor in the presence of lipid density and composition inhomogeneities

We derive the expression of the stress tensor for one- and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.     

Improving MRI's slice selectivity in the presence of strong,metal-derived inhomogeneities

PurposeTo develop schemes that deliver faithful 2D slices near field heterogeneities of the kind arising from non-ferromagnetic metal implants, with reduced artifacts and shorter scan times.MethodsAn excitation scheme relying on cross-term spatio-temporal encoding (xSPEN) was used as basis for developing the new inhomogeneity-insensitive, slice-selective pulse scheme. The resulting Fully refOCUSED cross-term SPatiotemporal ENcoding (FOCUSED-xSPEN) approach involved four adiabatic sweeps. The method was evaluated in silico, in vitro and in vivo using mice models, and compared against a number of existing and of novel alternatives based on both conventional and swept RF pulses, including an analogous method based on LASER's selectivity spatial selectivity.ResultsCalculations and experiments confirmed that multi-sweep derivatives of xSPEN and LASER can deliver localized excitation profiles, centered at the intended positions and endowed with enhanced immunity to B₀ and B₁ distortions. This, however, is achieved at the expense of higher SAR than non-swept counterparts. Furthermore, single-shot FOCUSED-xSPEN and LASER profiles covered limited off-resonance ranges. This could be extended to bands covering arbitrary off-resonance values with uniform slice widths, by looping the experiments over a number of scans possessing suitable transmission and reception offsets.ConclusionsA series of novel approaches were introduced to select slices near metals, delivering robustness against B_o and B₁⁺ field inhomogeneities.     

Angular scattering pattern of waves in the ocean in the presence of anisotropic inhomogeneities

Closed integrodifferential equations are derived for the coherence function and the ray intensity in the ocean. Random inhomogeneities of the medium are assumed to be large-scale and statistically anisotropic. The influence of anisotropy on the angular scattering pattern is analyzed.     

Strong-coupling method in the kronig-penny model

The strong-coupling approximation is investigated in a model one-dimensional potential. It is shown that even for large values of the overlap integrals S = 0.5 the approximation gives good results when a sufficiently large number of neighbors is taken into account. Otherwise, the approximation can give spurious extrema in the density of states. A modified strong-coupling method is formulated having considerable advantage over the usual method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, March, 1975.     

Triple-quantum-filtered imaging of sodium in presence of B(0) inhomogeneities

Triple quantum filtered sodium MRI techniques have been recently demonstrated in vivo. These techniques have been previously advocated as a means to separate the sodium NMR signal from different physiological compartments based on the differences between their relaxation rates. Among the different triple quantum coherence transfer filters, the three-pulse coherence transfer filter has been demonstrated to be better suited for human imaging than the traditional four-pulse implementation. While the three-pulse structure has distinct advantages in terms of RF efficiency, the lack of a refocusing pulse in the filter introduces an increased dependence on the main magnetic field inhomogeneities, which can sometimes lead to significant signal loss. In this paper, we characterize these dependencies and introduce a method for their compensation through the acquisition of a B(0) map and the use of a modified phase cycling scheme.     

Vacuum energy in the presence of dielectric and conducting surfaces

The polarization of the electromagnetic vacuum is examined in the neighborhood of dielectric and conducting surfaces and the energy associated with this polarization is shown to depend on a cutoff related to the microstructure of the boundary. The appearance of the cutoff permits the vacuum energy to be expressed in terms of a surface tension and certain higher shape tensions. For the case of a dielectric boundary the surface tension reproduces the Schmitt-Lucas formula which accounts reasonably for the observed surface tensions of many materials. The curvature tension is also calculated and it seems the effect of this energy may well be accessible to experimental verification. For the case of perfectly conducting surfaces the first four shape tensions are calculated. It is shown that previous calculations of the vacuum energy due to perfectly conducting surfaces are in error and these errors are corrected.     

Strong-coupling thermodynamics of the Hubbard model

Thermodynamic properties of the half-filled-band Hubbard model are calculated in the strong-coupling regime for a simple cubic structure, using the Bogoliubov variational principle. When the Coulomb-interactionV _o exceeds the bandwidthJ, we find a phase transition from a condensed phase of itinerant electrons into a state of localized ones at a transition temperature which exhibits the asymptotic behaviourT ₀J ²/V ₀ at largeV ₀.     

Gaussian approximation in the theory of MR signal formation in the presence of structure-specific magnetic field inhomogeneities

A detailed theoretical analysis of the free induction decay (FID) and spin echo (SE) MR signal formation in the presence of mesoscopic structure-specific magnetic field inhomogeneities is developed in the framework of the Gaussian phase distribution approximation. The theory takes into account diffusion of nuclear spins in inhomogeneous magnetic fields created by arbitrarily shaped magnetized objects with permeable boundaries. In the short-time limit the FID signal decays quadratically with time and depends on the objects' geometry only through the volume fraction, whereas the SE signal decays as 5/2 power of time with the coefficient depending on both the volume fraction of the magnetized objects and their surface-to-volume ratio. In the motional narrowing regime, the FID and SE signals for objects of finite size decay mono-exponentially; a simple general expression is obtained for the relaxation rate constant deltaR2. In the case of infinitely long cylinders in the motional narrowing regime the theory predicts non-exponential signal decay lnS approximately -tlnt in accordance with previous results. For specific geometries of the objects (spheres and infinitely long cylinders) exact analytical expressions for the FID and SE signals are given. The theory can be applied, for instance, to biological systems where mesoscopic magnetic field inhomogeneities are induced by deoxygenated red blood cells, capillary network, contrast agents, etc.     

Strong-coupling constant in coordinate space

The coordinate-space behavior of (vector) strong-coupling constant in the background field α_B(r) is compared with that in standard perturbation theory α_v(r). The numerically calculated two-loop coupling constant α_B(r) is shown to exceed α_v(r) by 1–5% at very small distances, r?0.02 fm, and to be in agreement with lattice measurements of the static potential. At large distances, α_B(r) approaches the freezing value at r?0.5 fm. An analytic form of α_B(r) is proposed that approximates α_B(r) with a precision ?2% in the region r?0.5 fm.     

Sound scattering by spatially localized inhomogeneities in a shallow-water waveguide in the presence of internal waves

A method is developed for solving the problem of sound scattering by concentrated inhomogeneities in a waveguide of small depth in the presence of internal waves (IW) typical of an oceanic shelf. The sound field fluctuations related to the motion of a model scatterer (a soft spheroid) and to the propagation of the IW are calculated and analyzed. It is shown that the field of internal waves considerably affects the scattered sound field even when the source-receiver and source-scatterer distances are relatively small (about several kilometers). This effect depends not only on the amplitude of the IW, but on their propagation direction as well.     

Strong-coupling thermodynamics of the Hubbard model

Thermodynamic properties of the half-filled-band Hubbard model are calculated in the strong-coupling regime for a simple cubic structure, using the Bogoliubov variational principle. When the Coulomb-interactionV _o exceeds the bandwidthJ, we find a phase transition from a condensed phase of itinerant electrons into a state of localized ones at a transition temperature which exhibits the asymptotic behaviourT ₀J ²/V ₀ at largeV ₀.     

Strong-coupling effects in high-T c superconductors

It is conceivable that the high-T _c superconducting perovskites are conventional electronphonon superconductors. In this case one expects significant strong-coupling effects because of the unusually high ratiok _B T _c / of the order 0.1 and greater. We use a set of reasonable models for the Eliashberg function ² F() (which takes into account available information on the phonon spectra and which fit the measuredT _c 's) and calculate strong-coupling effects in the specific heatc _s (T)/T _c , the ratio ₀/k _B T _c , the critical fieldsH _c (T) andH _c2 (T) including Pauli limiting, and other measurable quantities. Strongcoupling corrections turn out to be in the range of 0 to about 100%, depending on the quantity of interest. We discuss the perspectives of using strong-coupling effects as indicators for conventional electron-phonon superconductivity in the new materials.     

The inversion of the dielectric function in the presence of an interface

For a system containing a metal-vacuum interface an exact formal solution is presented for the inverse RPA dielectric function. The solution is valid for an arbitrary shape of the electron density profile at the surface. It contains(a) the inverse dielectric Lindhard function representing the bulk screening effects and (b) surface terms which describe the modification of the screening propertles near the interface. From the pole contribution of the surface term an exact equation for the surface plasmon dispersion is derived. In order to check the applicability of the general result for ?^?1, the surface plasmon dispersion and the screening length of a homogenous field applied perpendicular to the surface are briefly discussed by adopting the infinite barrier model.     

Matter-wave solitons in the presence of collisional inhomogeneities: Perturbation theory and the impact of derivative terms

We study the dynamics of bright and dark matter-wave solitons in the presence of a spatially varying nonlinearity. When the spatial variation does not involve zero crossings, a transformation is used to bring the problem to a standard nonlinear Schrödinger form, but with two additional terms: an effective potential one and a non-potential term. We illustrate how to apply perturbation theory of dark and bright solitons to the transformed equations. We develop the general case, but primarily focus on the non-standard special case whereby the potential term vanishes, for an inverse square spatial dependence of the nonlinearity. In both cases of repulsive and attractive interactions, appropriate versions of the soliton perturbation theory are shown to accurately describe the soliton dynamics.