A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians

A propagation method for time-dependent Schr\"odinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time-dependence of the time-dependent Schr\"odinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schr\"odinger equation is solved with the Chebychev propagation scheme presented in J. Chem. Phys. 130, 124108 (2009). The iteratively time-ordering Chebychev propagator is shown to be robust, efficient and accurate and compares very favorably to all other available propagation schemes

Microcomputer laboratories in mathematics education

AbstractThis article discusses the mathematical-educational potential of a computational laboratory at the pre-calculus and co-calculus levels. The laboratory envisaged is based on a set of microcomputers, whose use plays a central role in the teaching process, with particular emphasis on algorithmization. A new role for the mathematics teacher and professor is layed out, augmenting the “chalk and talk” methods by active participation as a laboratory instructor. Following a brief description of the integration of such a laboratory into the mathematical education, seven appropriate subjects are discussed, including some new relevant elementary proofs and worked out examples. Emphasis is placed upon the mathematical-educational byproducts (such as error bounds, ill-conditioning, complexity, rate of convergence, etc.) accompanying the implementation of these seven modules. Special attention is given to the removal of “black box” procedures and to the construction of “numerical methods that work”. Extensions and generalizations to more advanced topics are indicated, especially where the results in our modules may serve as points of departure in that direction

On the Interpentadal Variability of the North Atlantic Ocean: Model Simulated Changes in Transport, Meridional Heat Flux and Coastal Sea Level Between 1955-1959 and 1970-1974

Previous studies by Greatbatch et al. (1991) indicate significant changes in the North Atlantic thermohaline structure and circulation between the pentads 1955–1959 and 1970–1974, using data analyzed by Levitus (1989a,b,c) and a simple diagnostic model by Mellor et al. (1982). In this paper these changes are modeled using a three-dimensional, free surface, coastal ocean model. Diagnostic and short-term prognostic calculations are used to infer the dynamically adjusted fields corresponding to the observed hydrographic and wind stress climatology of each pentad. While the results agree with earlier studies indicating that the Gulf Stream was considerably weaker (by about 30 Sv) during the 1970s compared to the 1950s, they also indicate some changes in the poleward heat transport, although the statistical significance of these changes relative to sampling errors in the data is not clear. The change of wind pattern between the two pentads, associated with changes in sea surface temperature, resulted in changes in the Ekman contribution to the poleward heat flux transport. The modeled sea level along the North American coast shows a sea level rise of about 5–10 cm between 1955–1959 and 1970–1974; a comparison with observed sea level at 15 tide gage stations shows good agreement. Most of the coastal sea level change is attributed to changes in thermohaline ocean circulation and wind stress; thermal expansion seems to play a lesser role. The methodology tested here demonstrates an effective way to estimate climate changes in ocean circulation and sea level from observed hydrographic data and winds using ocean models to enhance and analyze the data

An efficient scheme for numerical simulations of the spin-bath decoherence

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of few coupled spins: (i) determining the pointer states of the system, and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For the problems of second type, the Chebyshev-based approach has been 3--4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.Comment: 8 pages (RevTeX), 3 EPS figure

Evolution and Nucleosynthesis of Zero Metal Intermediate Mass Stars

New stellar models with mass ranging between 4 and 8 Mo, Z=0 and Y=0.23 are presented. The models have been evolved from the pre Main Sequence up to the Asymptotic Giant Branch (AGB). At variance with previous claims, we find that these updated stellar models do experience thermal pulses in the AGB phase. In particular we show that: a) in models with mass larger than 6 Mo, the second dredge up is able to raise the CNO abundance in the envelope enough to allow a "normal" AGB evolution, in the sense that the thermal pulses and the third dredge up settle on; b) in models of lower mass, the efficiency of the CNO cycle in the H-burning shell is controlled by the carbon produced locally via the 3alpha reactions. Nevertheless the He-burning shell becomes thermally unstable after the early AGB. The expansion of the overlying layers induced by these weak He-shell flashes is not sufficient by itself to allow a deep penetration of the convective envelope. However, immediately after that, the maximum luminosity of the He flash is attained and a convective shell systematically forms at the base of the H-rich envelope. The innermost part of this convective shell probably overlaps the underlying C-rich region left by the inter-shell convection during the thermal pulse, so that fresh carbon is dredged up in a "hot" H-rich environment and a H flash occurs. This flash favours the expansion of the outermost layers already started by the weak thermal pulse and a deeper penetration of the convective envelope takes place. Then, the carbon abundance in the envelope rises to a level high enough that the further evolution of these models closely resembles that of more metal rich AGB stars. These stars provide an important source of primary carbon and nitrogen.Comment: 28 pages, 5 tables and 17 figures. Accepted for publication in Ap

Loop Current Warming by Hurricane Wilma

Hurricanes mix and cool the upper ocean, as shown here in observations and modeling of the Caribbean Sea and the Gulf of Mexico during the passage of hurricane Wilma. Curiously, the upper ocean around the Loop Current warmed prior to Wilma\u27s entrance into the Gulf. The major cause was increased volume and heat transports through the Yucatan Channel produced by storm-induced convergences in the northwestern Caribbean Sea. Such oceanic variability may have important impacts on hurricane predictions

An Assessment of Dynamical Mass Constraints on Pre-Main Sequence Evolutionary Tracks

[abridged] We have assembled a database of stars having both masses determined from measured orbital dynamics and sufficient spectral and photometric information for their placement on a theoretical HR diagram. Our sample consists of 115 low mass (M < 2.0 Msun) stars, 27 pre-main sequence and 88 main sequence. We use a variety of available pre-main sequence evolutionary calculations to test the consistency of predicted stellar masses with dynamically determined masses. Despite substantial improvements in model physics over the past decade, large systematic discrepancies still exist between empirical and theoretically derived masses. For main-sequence stars, all models considered predict masses consistent with dynamical values above 1.2 Msun, some models predict consistent masses at solar or slightly lower masses, and no models predict consistent masses below 0.5 Msun but rather all models systematically under-predict such low masses by 5-20%. The failure at low masses stems from the poor match of most models to the empirical main-sequence below temperatures of 3800 K where molecules become the dominant source of opacity and convection is the dominant mode of energy transport. For the pre-main sequence sample we find similar trends. There is generally good agreement between predicted and dynamical masses above 1.2 Msun for all models. Below 1.2 Msun and down to 0.3 Msun (the lowest mass testable) most evolutionary models systematically under-predict the dynamically determined masses by 10-30% on average with the Lyon group models (e.g. Baraffe et al. 1998) predicting marginally consistent masses *in the mean* though with large scatter.Comment: accepted for publication in ApJ (2004

Severe Brain Injury, Disability, and the Law: Achieving Justice for a Marginalized Population

Thousands of persons with severe brain injury who are minimally conscious or locked in are wrongly treated as if they are unconscious. Such individuals are unable to advocate for themselves and are typically segregated from society in hospitals or nursing homes. As a result, they constitute a class of persons who often lack access to adequate medical care, rehabilitation, and assistive devices that could aid them in communication and recovery. While this problem is often approached from a medical or scientific point of view, here we frame it as a legal issue amenable to legal remedies. This Article comprehensively explores and analyzes sources of federal, state, and international human rights law that can be leveraged- both in traditional and novel ways-to improve the lives and protect the rights of persons with severe brain injury. We argue that state laws may be the most promising basis for legal action to ameliorate the clinical marginalization and societal neglect faced by persons with severe brain injury, and to promote their recovery and reintegration into their communities

The Many Faces of a Character

We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine $su(2)$ algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9

Quantum Dynamics of Spin Wave Propagation Through Domain Walls

Through numerical solution of the time-dependent Schrodinger equation, we demonstrate that magnetic chains with uniaxial anisotropy support stable structures, separating ferromagnetic domains of opposite magnetization. These structures, domain walls in a quantum system, are shown to remain stable if they interact with a spin wave. We find that a domain wall transmits the longitudinal component of the spin excitations only. Our results suggests that continuous, classical spin models described by LLG equation cannot be used to describe spin wave-domain wall interaction in microscopic magnetic systems