Law Department

The undersigned, under the sanction of the Board of Trustees, will open in Athens, on 1st of October next, a Law School, in connection with the University of Georgia. Believing that such a school is demanded by the wants of the profession and of the State, and looking alone to its own income for the reward of our labor, we shall devote our energies to the effort, which we will not lightly abandon. We expect success only by deserving it. If we deserve it, we shall not fear obtaining it

Yang-Mills Duals for Semiclassical Strings

We consider a semiclassical multiwrapped circular string pulsating on S_5, whose center of mass has angular momentum J on an S_3 subspace. Using the AdS/CFT correspondence we argue that the one-loop anomalous dimension of the dual operator is a simple rational function of J/L, where J is the R-charge and L is the bare dimension of the operator. We then reproduce this result directly from a super Yang-Mills computation, where we make use of the integrability of the one-loop system to set up an integral equation that we solve. We then verify the results of Frolov and Tseytlin for circular rotating strings with R-charge assignment (J',J',J). In this case we solve for an integral equation found in the O(-1) matrix model when J' J. The latter region starts at J'=L/2 and continues down, but an apparent critical point is reached at J'=4J. We argue that the critical point is just an artifact of the Bethe ansatz and that the conserved charges of the underlying integrable model are analytic for all J' and that the results from the O(-1) model continue onto the results of the O(+1) model.Comment: 26 Pages, LaTeX; v2 Typos corrected, reference update

Reconstructing the Equation of State of Tachyon

Recent progress in theoretical physics suggests that the dark energy in the universe might be resulted from the rolling tachyon field of string theory. Measurements to SNe Ia can be helpful to reconstruct the equation of state of the rolling tachyon which is a possible candidate of dark energy. We present a numerical analysis for the evolution of the equation of state of the rolling tachyon and derive the reconstruction equations for the equation of state as well as the potential.Comment: 6 pages, 3 figures, to appear Phys. Rev.

Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near ν=1/2\nu=1/2

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a Composite Fermion Fermi Surface (CF-FS) at $\nu = 1/2$, and we show that the deformation of the (CF-FS) due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the non-local case which corresponds to the SAW experiments. We introduce a new model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\nu = 1/2:$ namely the nonlinear wave vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the CF-FS which are flattened by the applied modulation.Comment: 13 pages, 4 figures, the published versio

Stringing Spins and Spinning Strings

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N =4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L-2J,J], interpolate smoothly between the BMN case of two impurities (J=2) and the extreme case where the number of impurities equals half the total number of fields (J=L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L-2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.Comment: 27 pages, 4 figures, LaTex; v2 reference added, typos fixe

Gauge Theory and the Excision of Repulson Singularities

We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.Comment: 31 pages LaTeX, 2 figures (v3: references added

Multi-fidelity efficient global optimization : Methodology and application to airfoil shape design

Predictions and design engineering decisions can be made using a variety of informa- tion sources that range from experimental data to computer models. These information sources could consist of different mathematical formulations, different grid resolutions, dif- ferent physics, or different modeling assumptions that simplify the problem. This leads to information sources with varying degrees of fidelity, each with an associated accuracy and querying cost. In this paper, we propose a novel and flexible way to use multi-fidelity informa- tion sources optimally in the context of airfoil shape optimization using both Xfoil and ADflow. The new developments are based on Bayesian optimization and kriging metamodeling and allow the aerodynamic optimization to be sped up. In a constrained optimization example with 15-design variables problem, the proposed approach reduces the total cost by a factor of two compared to a single Bayesian based fidelity optimization and by a factor of 1.5 compared to sequential quadratic programming

A Python surrogate modeling framework with derivatives

The surrogate modeling toolbox (SMT) is an open-source Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to training data. It also includes unique surrogate models: kriging by partial least-squares reduction, which scales well with the number of inputs; and energy- minimizing spline interpolation, which scales well with the number of training points. The efficiency and effectiveness of SMT are demonstrated through a series of examples. SMT is documented using custom tools for embedding automatically tested code and dynamically generated plots to produce high-quality user guides with minimal effort from contributors. SMT is maintained in a public version control repository

Cosmic F- and D-strings

Macroscopic fundamental and Dirichlet strings have several potential instabilities: breakage, tachyon decays, and confinement by axion domain walls. We investigate the conditions under which metastable strings can exist, and we find that such strings are present in many models. There are various possibilities, the most notable being a network of (p,q) strings. Cosmic strings give a potentially large window into string physics.Comment: 27 pages, 5 figures; v. 5: JHEP style, added comments in section 2.

Adaptive modeling strategy for constrained global optimization with application to aerodynamic wing design

Surrogate models are often used to reduce the cost of design optimization prob- lems that involve computationally costly models, such as computational fluid dynamics simulations. However, the number of evaluations required by sur- rogate models usually scales poorly with the number of design variables, and there is a need for both better constraint formulations and multimodal function handling. To address this issue, we developed a surrogate-based gradient-free optimization algorithm that can handle cases where the function evaluations are expensive, the computational budget is limited, the functions are multimodal, and the optimization problem includes nonlinear equality or inequality con- straints. The proposed algorithm—super efficient global optimization coupled with mixture of experts (SEGOMOE)—can tackle complex constrained design optimization problems through the use of an enrichment strategy based on a mixture of experts coupled with adaptive surrogate models. The performance of this approach was evaluated for analytic constrained and unconstrained prob- lems, as well as for a multimodal aerodynamic shape optimization problem with 17 design variables and an equality constraint. Our results showed that the method is efficient and that the optimum is much less dependent on the starting point than the conventional gradient-based optimization