Addendum to ``Reconciling grand unification with strings by anisotropic compactifications''

In this brief addendum, we clarify a point which we left unaddressed in a previous publication [Phys. Rev. D 78, 066006 (2008)]. In particular, we show that a specific vacuum configuration constructed in one of our models satisfies the condition D=0. In the previous publication, we only showed F=0. Both D=0 and F=0 are necessary to ensure that supersymmetry survives to the weak scale.

Grand unified mass

A recent article on the unified theory of Elementary Particle Forces by Howard Georgi and Sheldon Glashow (September 1980, page 30) points out that the unification of strong, weak and electromagnetic interactions involves the appearance of particles having almost macroscopic masses of about a nanogram (~1014 GeV). Such superheavy particles seem to be an inevitable feature of most grand unified theories Gravitation is still, however, left out of these various schemes.

Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Importance of meridional circulation i flux transport dynamo: the possibility of a maunder-like grand minimum

Meridional circulation is an important ingredient in flux transport dynamo models. We have studied its importance on the period, the amplitude of the solar cycle, and also in producing Maunder-like grand minima in these models. First, we model the periods of the last 23 sunspot cycles by varying the meridional circulation speed. If the dynamo is in a diffusion-dominated regime, then we find that most of the cycle amplitudes also get modeled up to some extent when we model the periods. Next, we propose that at the beginning of the Maunder minimum the amplitude of meridional circulation dropped to a low value and then after a few years it increased again. Several independent studies also favor this assumption. With this assumption, a diffusion-dominated dynamo is able to reproduce many important features of the Maunder minimum remarkably well. If the dynamo is in a diffusion-dominated regime, then a slower meridional circulation means that the poloidal field gets more time to diffuse during its transport through the convection zone, making the dynamo weaker. This consequence helps to model both the cycle amplitudes and the Maunder-like minima. We, however, fail to reproduce these results if the dynamo is in an advection-dominated regime.

Hermite expansions on R(N) for radial functions

It is proved that the Riesz means S(R)(delta)f, delta > 0, for the Hermite expansions on R(n), n greater-than-or-equal-to 2, satisfy the uniform estimates \\S(R)(delta)f\\p less-than-or-equal-to C \\f\\p for all radial functions if and only if p lies in the interval 2n/(n + 1 + 2delta) < p < 2n/(n - 1 - 2delta).

Hydrogen Storage Capacity of Carbon-Foams: Grand Canonical Monte Carlo Simulations

Hydrogen storage in the three-dimensional carbon foams is analyzed using classical grand canonical Monte Carlo simulations. The calculated storage capacities of the foams meet the material-based DOE targets and are comparable to the capacities of a bundle of well-separated similar diameter open nanotubes. The pore sizes in the foams are optimized for the best hydrogen uptake. The capacity depends sensitively on the C-H-2 interaction potential, and therefore, the results are presented for its ``weak'' and ``strong'' choices, to offer the lower and upper bounds for the expected capacities. Furthermore, quantum effects on the effective C-H-2 as well as H-2-H-2 interaction potentials are considered. We find that the quantum effects noticeably change the adsorption properties of foams and must be accounted for even at room temperature.

Dynamo models of grand minima

Since a universally accepted dynamo model of grand minima does not exist at the present time, we concentrate on the physical processes which may be behind the grand minima. After summarizing the relevant observational data, we make the point that, while the usual sources of irregularities of solar cycles may be sufficient to cause a grand minimum, the solar dynamo has to operate somewhat differently from the normal to bring the Sun out of the grand minimum. We then consider three possible sources of irregularities in the solar dynamo: (i) nonlinear effects; (ii) fluctuations in the poloidal field generation process; (iii) fluctuations in the meridional circulation. We conclude that (i) is unlikely to be the cause behind grand minima, but a combination of (ii) and (iii) may cause them. If fluctuations make the poloidal field fall much below the average or make the meridional circulation significantly weaker, then the Sun may be pushed into a grand minimum.

Origin of grand minima in Sunspot cycles

One of the most striking aspects of the 11-year sunspot cycle is that there have been times in the past when some cycles went missing, a most well-known example of this being the Maunder minimum during 1645-1715. Analyses of cosmogenic isotopes (C-14 and Be-10) indicated that there were about 27 grand minima in the last 11 000 yrs, implying that about 2.7% of the solar cycles had conditions appropriate for forcing the Sun into grand minima. We address the question of how grand minima are produced and specifically calculate the frequency of occurrence of grand minima from a theoretical dynamo model. We assume that fluctuations in the poloidal field generation mechanism and in the meridional circulation produce irregularities of sunspot cycles. Taking these fluctuations to be Gaussian and estimating the values of important parameters from the data of the last 28 solar cycles, we show from our flux transport dynamo model that about 1-4% of the sunspot cycles may have conditions suitable for inducing grand minima.

Fluctuations in the alpha-effect and grand solar minima

The parameters of a special type of alpha-effect known in dynamo theory as the Babcock-Leighton mechanism are estimated using the data of sunspot catalogs. The estimates support the presence of the Babcock-Leighton alpha-effect on the Sun. Fluctuations of the alpha-effect are also estimated. The fluctuation amplitude appreciably exceeds themean value, and the characteristic time for the fluctuations is comparable to the period of the solar rotation. Fluctuations with the parameters found are included in a numericalmodel for the solar dynamo. Computations show irregular changes in the amplitudes of the magnetic cycles on time scales of centuries and millennia. The calculated statistical characteristics of the grand solar minima and maxima agree with the data on solar activity over the Holocene.

Beam polarization effects in the radiative production of lightest neutralinos in e(+)e(-) collisions in supersymmetric grand unified models

We study the production of the lightest neutralinos in the process e(+)e(-) -> chi(0)(1)chi(0)(1)gamma in supersymmetric grand unified models for the International Linear Collider energies with longitudinally polarized beams. We consider cases where the standard model gauge group is unified into the grand unified gauge groups SU(5), or SO(10). We have carried out a comprehensive study of this process in the SU(5) and SO(10) grand unified theories which includes the QED radiative corrections. We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and on the different representations of the grand unified gauge group, when the electron and positron beams are longitudinally polarized. To assess the feasibility of experimentally observing the radiative production process, we have also considered in detail the background to this process coming from the radiative neutrino production process e(+)e(-)-> nu(nu) over bar gamma with longitudinally polarized electron and positron beams. In addition we have also considered the supersymmetric background coming from the radiative production of scalar neutrinos in the process e(+)e(-) -> (nu) over tilde(nu) over tilde*gamma with longitudinally polarized beams. The process can be a major background to the radiative production of neutralinos when the scalar neutrinos decay invisibly.

Studies of grand minima in sunspot cycles by using a flux transport solar dynamo model

We propose that grand minima in solar activity are caused by simultaneous fluctuations in the meridional circulation and the Babcock-Leighton mechanism for the poloidal field generation in the flux transport dynamo model. We present the following results: (a) fluctuations in the meridional circulation are more effective in producing grand minima; (b) both sudden and gradual initiations of grand minima are possible; (c) distributions of durations and waiting times between grand minima seem to be exponential; (d) the coherence time of the meridional circulation has an effect on the number and the average duration of grand minima, with a coherence time of about 30 yr being consistent with observational data. We also study the occurrence of grand maxima and find that the distributions of durations and waiting times between grand maxima are also exponential, like the grand minima. Finally we address the question of whether the Babcock-Leighton mechanism can be operative during grand minima when there are no sunspots. We show that an alpha-effect restricted to the upper portions of the convection zone can pull the dynamo out of the grand minima and can match various observational requirements if the amplitude of this alpha-effect is suitably fine-tuned.

On Hermite pseudo-multipliers

In this article we deal with a variation of a theorem of Mauceri concerning the L-P boundedness of operators M which are known to be bounded on L-2. We obtain sufficient conditions on the kernel of the operator M so that it satisfies weighted L-P estimates. As an application we prove L-P boundedness of Hermite pseudo-multipliers. (C) 2014 Elsevier Inc. All rights reserved.

Role of gas in supporting grand spiral structure

The density wave theory for the grand-design two-armed spiral pattern in galaxies is successful in explaining several observed features. However, the long-term persistence of this spiral structure is a serious problem since the group transport would destroy it within about a billion years as shown in a classic paper by Toomre. In this paper, we include the low-velocity dispersion component, namely gas, on an equal footing with stars in the formulation of the density wave theory, and obtain the dispersion relation for this coupled system. We show that the inclusion of gas makes the group transport slower by a factor of few, thus allowing the pattern to persist longer - for several billion years. Though still less than the Hubble time, this helps in making the spiral structure more long-lived. Further we show that addition of gas is essential to get a stable wave for the observed pattern speed for the Galaxy, which otherwise is not possible for a one-component stellar disc.

A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases

In this paper we derive an approach for the effective utilization of thermodynamic data in phase-field simulations. While the most widely used methodology for multi-component alloys is following the work by Eiken et al. (2006), wherein, an extrapolative scheme is utilized in conjunction with the TQ interface for deriving the driving force for phase transformation, a corresponding simplistic method based on the formulation of a parabolic free-energy model incorporating all the thermodynamics has been laid out for binary alloys in the work by Folch and Plapp (2005). In the following, we extend this latter approach for multi-component alloys in the framework of the grand-potential formalism. The coupling is applied for the case of the binary eutectic solidification in the Cr-Ni alloy and two-phase solidification in the ternary eutectic alloy (Al-Cr-Ni). A thermodynamic justification entails the basis of the formulation and places it in context of the bigger picture of Integrated Computational Materials Engineering. (C) 2015 Elsevier Ltd. All rights reserved.