Constant Eta Research Articles

Phase separation and exotic vortex phases in a two-species holographic superfluid

At finite temperature, the stable equilibrium states of coupled two-component Bose Einstein condensations (BECs) with the same conformal mass in both non-rotating and rotating condition can be obtained by studying its real dynamics via holography. The equilibrium state is the state where the free energy reaches the minimum and does not change any more. In the case of no rotation, the spatial phase separated states of the two components become more stable than the miscible condensates state when the direct repulsive inter-component coupling constant eta>eta _c>0. Under rotation, the quantum fluid reveals four equilibrium structures of vortex states by varying the eta from the miscible region to the phase separated region. Among the four structures, the vortex sheet solution is the most exotic one that appears in the phase separated region.

Gauss\u2013Bonnet inflation with a constant rate of roll

In the model of the inflaton nonminimal coupling to the Gauss–Bonnet term, we discuss the constant-roll inflation with constant epsilon _1, constant epsilon _2 and constant eta _H, respectively, with the additional assumption that delta _1 is a constant. Using the Bessel function approximation, we get the analytical expressions for the scalar and tensor power spectrum and derive the scalar spectral index n_{mathcal {R}} and the tensor to scalar ratio r to the first order of epsilon _1. By using the Planck 2018 observations constraint on n_{mathcal {R}} and r, we obtain some feasible parameter space and show the result on the n_{mathcal {R}}-r region. The scalar potential is also reconstructed in some special cases.

The eta invariant on two-step nilmanifolds

The eta invariant appears regularly in index theorems but is known to be directly computable from the spectrum only in certain examples of locally symmetric spaces of compact type. In this work, we derive some general formulas useful for calculating the eta invariant on closed manifolds. Specifically, we study the eta invariant on nilmanifolds by decomposing the spin Dirac operator using Kirillov theory. In particular, for general Heisenberg three-manifolds, the spectrum of the Dirac operator and the eta invariant are computed in terms of the metric, lattice, and spin structure data. There are continuous families of geometrically, spectrally different Heisenberg three-manifolds whose Dirac operators have constant eta invariant. In the appendix, some needed results of L. Richardson and C. C. Moore are extended from spaces of functions to spaces of spinors.

Cooperative Interaction of Hydronium Ion with an Ethereally Fenced Hexaarylbenzene-Based Receptor: An NMR and Theoretical Study

Using (1)H and (13)C NMR and DFT calculations, the structure and interactions of the symmetric ethereally fenced hexaarylbenzene receptor 1 with hydronium ions were studied. Both 1 and its equimolecular complex 1.H(3)O(+) exhibit C(3v) symmetry. According to DFT, two similar optimal structures of the complex exist, the more stable one being 15.4 kJ/mol lower in energy. The equilibrium between 1 and 1.H(3)O(+) complexes is characterized by the stabilization constant K = 1.97 x 10(6) (i.e., the binding constant eta = 6.3) according to both proton and carbon NMR spectra. The exchange dynamics between 1 and the complex measured by the delay-varied CPMG sequence had to be corrected for the internal exchange processes in both 1 (conformation change) and the complex (vacillation between the two minima). After this correction, the correlation time of exchange was found to be 4.76 x 10(-5) s. Such relatively fast exchange can be explained only by it being mediated by the excess water molecules present in the system.

Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter Gamma, defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter eta(Gamma). The resulting master equation is formally identical to that of Bouchaud's trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant eta, the annealing curve when eta is varied cyclically in time, and memory effects observed for a discontinuous shift in eta. Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.

Yielding of sensitive clays: micromechanical considerations

Test results reported on several natural sensitive soils show significant anisotropy of the yield curves, which are generally oriented along the coefficient of earth pressure at rest (K0) axis. An attempt is made in this paper to explain the anisotropy in yielding from microstructural considerations. An elliptic pore, with particle domains aligned along the periphery of the pore, and with the major axis of the pore being oriented along the direction of the in situ major principal stress, is chosen as the unit of microstructure. An analysis of forces at the interdomain contacts around the ellipse is carried out with reference to experimentally determined yield stress conditions of one soil, and a yield criteria is defined. The analysis, with the proposed yield criteria, enables one to define the complete yield curve for any other soil from the results of only two tests (one constant eta compression test with eta close to eta sub K0, where eta is the stress ratio (= q/p) and eta sub K0 is the stress ratio corresponding to anisotropic K0 compression, and another undrained shear test). Predicted yield curves are compared with experimental yield curves of several soils reported in the literature.Key words: sensitive clays, yield criteria, anisotropy, microstructure.

State-Dependent Weights for Neural Associative Memories

In this article we study the effect of dynamically modifying the weight matrix on the performance of a neural associative memory. The dynamic modification is implemented by adding, at each step, the outer product of the current state, scaled by a suitable constant eta, to the correlation weight matrix. For single-shot synchronous dynamics, we analytically obtain the optimal value of eta. Although knowledge of the noise percentage is required for calculating the optimal value of eta, a fairly good choice of eta can be made even when the amount of noise is not known. Experimental results are provided in support of the analysis. The efficacy of the proposed modification is also experimentally verified for the case of asynchronous updating with transient length > 1.

Some notes on perceptron learning

The author extends the geometrical approach to the perceptron and shows that, given n examples, learning is of maximal difficulty when the number of inputs d is such that n=5d. He then presents a new perceptron algorithm that takes advantage of the peculiarities of the cost function. In his tests it is more than two times faster than the standard algorithm. More importantly it does not have fixed parameters, like the usual learning constant eta , but it adapts them to the cost function. He shows that there exist an optimal choice for beta , the steepness of the transfer function. He presents also a brief systematic study of the parameters eta and beta of the standard perceptron algorithm.

Afocal coupled etalons DEM: a high-resolution double-etalon modulator spectrometer

The properties of a spectroscopic device consisting of two etalons coupled by an afocal system, and which behaves as a high-luminosity single-etalon single-aperture Fabry-Perot spectrometer, have been investigated. Although the high-luminosity behavior is one of the many states in which a coupled dual-etalon system can exist, mainly the high-luminosity condition has been studied in detail here. This condition is reached when the orders of the etalons comprising the device are related by n(01) = n(02)eta(-2), where the coupling constant is defined as eta = micro(1)micro(-1)(2)f(1)f(-1)(2) micro(i) and f(i) are the indices of refraction and coupling lens focal length associated with the ith etalon. In high-luminosity conditions, one of the etalons serves as a multiple annuli mask for the other thus making it possible to use many of these annuli to achieve the desired high throughput. The limitation on the number of orders usable is given by the (small) nonlinearity in the matching of these orders, because of the different etalon gaps. The results of the study show that luminosity gains near 100 (when compared with a single-etalon single-aperture Fabry-Perot spectrometer) are possible at high resolving powers. This occurs when the coupling constant eta is not too far from unity. It is also shown that this device, or double-etalon modulator (DEM), is a compensated spectrometer since the gain increases with increasing resolving power. Other practical limitations, such as the beam walk-off from the edges of finite size etalons, are discussed.

Effect of solvent structure on electron reactivity: 1-butanol/water mixtures

The solvent dependence of e/sub s//sup -/ reaction rate constants k/sub 2/ and their Arrhenius parameters differ for efficient (nitrobenzene, acetone) and inefficient (phenol, toluene) scavengers. The n-butyl group is so large that 1-butanol is not completely miscible with water. The complex changes of physical properties of 1-propanol/water mixtures produced four different zones of e/sub s//sup -/ behavior on going from 0 to 1.00 mole fraction water. Zone c, 0.75-0.97 mole fraction water, which displays Stokes-Smoluchowski behavior of k/sub 2/, is inaccessible in 1-butanol/water solvents because it is in the immiscible region. In zone a the viscosity normalized rate constant eta k/sub 2/ for inefficient scavengers decreases in spite of the decrease of the electron optical absorption energy E/sub r/. Hydrogen-bonded structures, for example H/sub 2/O(ROH)/sub 8/, apparently make the positive hydrogens on the OH groups less accessible to solvate the electrons and less accessible to protonate S/sup -/.

Nuclear resonance of27Al in three rare earth aluminates from room temperature to 1.4K

From an analysis of the room temperature nuclear resonance of 27Al principal values are obtained for the electric field gradient eq Vzz/h and the anisotropy constant eta at an aluminium site for GdAlO3 (0.589+or-0.01 MHz and 0.878), TbAlO3(0.890+or-0.01 MHz and 0.01 MHz and 0.613) and DyAlO3 (1.30+or-0.03 MHz and 0.655). The directions of the principal axes of the electric field gradient relative to the crystal axes are obtained. At low temperatures the nuclear resonance of 27Al is measured in GdAlO3 in the paramagnetic region (T>3.87 K) and the antiferromagnetic region (1.4 K<T<3.87K). The results obtained are shown to agree with a simple model based on the currently held view of the ordered magnetic structure of this salt. There remains a large discrepancy between the magnitude of the observed internal magnetic field at an 27Al site and that calculated assuming classical magnetic dipole coupling. The possibility of a large anisotropic transferred hyperfine interaction is discussed.