Physical Sciences and Mathematics Commons^™

Doubling Measures, Monotonicity, And Quasiconformality, Leonid V. Kovalev, Diego Maldonado, Jang-Mei Wu

Mathematics - All Scholarship

We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic doubling measure that is not absolutely continuous with respect to the Lebesgue measure.

Model For Light Scalars In Qcd, Joseph Schechter, Amir H. Fariborz, Renata Jora

Physics - All Scholarship

We propose a systematic procedure to study a generalized linear sigma model which can give a physical picture of possible mixing between q{\bar q} and qq{\bar q}{\bar q} low lying spin zero states. In the limit of zero quark masses, we derive the model independent results for the properties of the Nambu Goldstone pseudoscalar particles. For getting information on the scalars it is necessary to make a specific choice of terms. We impose two plausible physical criteria - the modeling of the axial anomaly and the suppression of effective vertices representing too many fermion lines - for limiting the large …

Why Should Primordial Perturbations Be In A Vacuum State?, Christian Armendariz-Picon

Physics - All Scholarship

In order to calculate the power spectrum generated during a stage of inflation, we have to specify the quantum state of the inflaton perturbations, which is conventionally assumed to be the Bunch-Davies vacuum. We argue that this choice is justified only if the interactions of cosmological perturbations are strong enough to drive excited states toward the vacuum. We quantify this efficiency by calculating the decay probabilities of excited states to leading order in the slow-roll expansion in canonical single-field inflationary models. These probabilities are suppressed by a slow-roll parameter and the squared Planck mass, and enhanced by ultraviolet and infrared …

Overinterpolation, Dan Coman, Evgeny A. Poletsky

Mathematics - All Scholarship

In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such a function has specific forms.

Are Domain Walls In Spin Glasses Described By Stochastic Loewner Evolutions?, Alan Middleton, Denis Bernard, Pierre Le Doussal

Physics - All Scholarship

Domain walls for spin glasses are believed to be scale invariant invariant; a stronger symmetry, conformal invariance, has the potential to hold. The statistics of zero-temperature Ising spin glass domain walls in two dimensions are used to test the hypothesis that these domain walls are described by a Schramm-Loewner evolution SLE$_\kappa$. Multiple tests are consistent with SLE$_\kappa$, where $\kappa=2.30(5)$. Both conformal invariance and the domain Markov property are tested. The latter does not hold in small systems, but detailed numerical evidence suggests that it holds in the continuum limit.

A Critique Of The Link Approach To Exact Lattice Supersymmetry, Simon Catterall, Falk Bruckmann, Mark De Kok

Physics - All Scholarship

We examine the link approach to constructing a lattice theory of N=2 super Yang Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at non-zero lattice spacing. We show that this approach suffers from an inconsistency and argue that a maximum of just one of the supersymmetries can be implemented on the lattice.

Twisted Supersymmetric Sigma Model On The Lattice, Simon Catterall, Sofiane Ghadab

Physics - All Scholarship

In this paper we conduct a numerical study of the supersymmetric O(3) non-linear sigma model. The lattice formulation we employ was derived in \cite{sigma1} and corresponds to a discretization of a {\it twisted} form of the continuum action. The twisting process exposes a {\it nilpotent} supercharge Q and allows the action to be rewritten in Q-exact form. These properties may be maintained on the lattice. We show how to deform the theory by the addition of potential terms which preserve the supersymmetry. A Wilson mass operator may be introduced in this way with a minimal breaking of supersymmetry. We additionally …

Some Heuristics About Elliptic Curves, Mark Watkins

Mathematics - All Scholarship

We give some heuristics for counting elliptic curves with certain properties. In particular, we re-derive the Brumer-McGuinness heuristic for the number of curves with positive/negative discriminant up to X, which is an application of lattice-point counting. We then introduce heuristics (with refinements from random matrix theory) that allow us to predict how often we expect an elliptic curve E with even parity to have L(E,1)=0. We find that we expect there to be about c₁X^19/24(log X)^3/8 curves with |Delta|< X with even parity and positive (analytic) rank; since Brumer and McGuinness predict cX^5/6 total curves, this implies that asymptotically almost all even parity curves have rank 0. We …

Preprojective Representations Of Valued Quivers And Reduced Words In The Weyl Group Of A Kac-Moody Algebra, Mark Kleiner, Allen Pelley

Mathematics - All Scholarship

This paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. As a consequence, for any Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced …

Categorification Of The Colored Jones Polynomial And Rasmussen Invariant Of Links, Anna Beliakova, Stephan Wehrli

Mathematics - All Scholarship

We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that, for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the Rasmussen invariant to links and give examples, where this invariant is a …

Scaling And The Smoluchowski Equations, Jerry Goodisman, J. Chaiken

Chemistry - All Scholarship

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K _jk. The K _jk are said to scale if K _λj,γk =λ ^μγ ^μK _jk for j ≤ k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak ^ae ^-bk, where A is a normalization constant (a function of a, …

Application Of Scaling And Kinetic Equations To Helium Cluster Size Distributions: Homogeneous Nucleation Of A Nearly Ideal Gas, J. Chaiken, Jerry Goodisman, Oleg Komilov, J. Peter Toennies

Chemistry - All Scholarship

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of ⁴He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over …

Sequences Of Reflection Functors And The Preprojective Component Of A Valued Quiver, Mark Kleiner, Helene R. Tyler

Mathematics - All Scholarship

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan …

Formation Of Monofunctional Cisplatin-Dna Adducts In Carbonate Buffer, Alexandra Binter, Jerry Goodisman, James C. Dabrowiak

Chemistry - All Scholarship

Carbonate in its various forms is an important component in blood and the cytosol. Since, under conditions that simulate therapy, carbonate reacts with cisplatin to form carbonato complexes, one of which is taken up and/or modified by the cell [C.R. Centerwall, J. Goodisman, D.J. Kerwood, J. Am. Chem. Soc., 127 (2005) 12768–12769], cisplatin-carbonato complexes may be important in the mechanism of action of cisplatin. In this report we study the binding of cisplatin to pBR322 DNA in two different buffers, using gel electrophoresis. In 23.8 mM HEPES, N-(2-hydroxyethyl)-piperazine-N′-2-ethanesulfonic acid, 5 mM NaCl, pH 7.4 buffer, cisplatin produces …

Admissible Sequences, Preprojective Modules, And Reduced Words In The Weyl Group Of A Quiver, Mark Kleiner, Allen Pelley

Mathematics - All Scholarship

This paper studies connections between the preprojective modules over the path algebra of a finite connected quiver without oriented cycles, the (+)-admissible sequences of vertices, and the Weyl group. For each preprojective module, there exists a unique up to a certain equivalence shortest (+)-admissible sequence annihilating the module. A (+)-admissible sequence is the shortest sequence annihilating some preprojective module if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. These statements have the following application that strengthens known results of Howlett and Fomin-Zelevinsky. For any fixed …

Measuring Functional Renormalization Group Fixed-Point Functions For Pinned Manifolds, Alan Middleton, Pierre Le Doussal, Kay Jorg Wiese

Physics - All Scholarship

Exact numerical minimization of interface energies is used to test the functional renormalization group (FRG) analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1,2,3), random field (d=0,2,3), and periodic (d=2,3) disorders. The functional shocks that lead to this cusp are seen. Small, but significant, deviations from 1-loop FRG results are compared to 2-loop corrections. The cross-correlation for two copies of disorder is compared with a recent FRG study of chaos.

Near Scale Invariance With Modified Dispersion Relations, Christian Armendariz-Picon

Physics - All Scholarship

No abstract provided.

An Approach To Permutation Symmetry For The Electroweak Theory, Joseph Schechter, Renata Jora, Salah Nasri

Physics - All Scholarship

The form of the leptonic mixing matrix emerging from experiment has, in the last few years, generated a lot of interest in the so-called tribimaximal type. This form may be naturally associated with the possibility of a discrete permutation symmetry (S_3) among the three generations. However, trying to implement this attractive symmetry has resulted in some problems and it seems to have fallen out of favor. We suggest an approach in which the S_3 holds to first approximation, somewhat in the manner of the old SU(3) flavor symmetry of the three flavor quark model. It is shown that in the …

Sound-Propagation Gap In Fluid Mixtures, Supurna Sinha, M. Cristina Marchetti

Physics - All Scholarship

We discuss the behavior of the extended sound modes of a dense binary hard-sphere mixture. In a dense simple hard-sphere fluid the Enskog theory predicts a gap in the sound propagation at large wave vectors. In a binary mixture the gap is only present for low concentrations of one of the two species. At intermediate concentrations sound modes are always propagating. This behavior is not affected by the mass difference of the two species, but it only depends on the packing fractions. The gap is absent when the packing fractions are comparable and the mixture structurally resembles a metallic glass.

Mode-Coupling Theory Of The Stress-Tensor Autocorrelation Function Of A Dense Binary Fluid Mixture, Supurna Sinha, M. Cristina Marchetti

Physics - All Scholarship

We present a generalized mode-coupling theory for a dense binary fluid mixture. The theory is used to calculate molecular-scale renormalizations to the stress-tensor autocorrelation function (STAF) and to the long-wavelength zero-frequency shear viscosity. As in the case of a dense simple fluid, we find that the STAF appears to decay as t−3/2 over an intermediate range of time. The coefficient of this long-time tail

is more than two orders of magnitude larger than that obtained from conventional mode-coupling theory. Our study focuses on the effect of compositional disorder on the decay of the STAF in a dense mixture.

Dactinomycin Impairs Cellular Respiration And Reduces Accompanying Atp Formation, Zhimin Tao, Syed S. Ahmad, Harvey S. Penefsky, Jerry Goodisman, Abdul Kader Souid

Chemistry - All Scholarship

The effect of dactinomycin on cellular respiration and accompanying ATP formation was investigated in Jurkat and HL-60 cells. Cellular mitochondrial oxygen consumption (measured by a homemade phosphorescence analyzer) and ATP content (measured by the luciferin-luciferase bioluminescence system) were determined as functions of time t during continuous exposure to the drug. The rate of respiration, k, was the negative of the slope of [O2] versus t. Oxygen consumption and ATP content were diminished by cyanide, confirming that both processes involved oxidations in the mitochondrial respiratory chain. In the presence of dactinomycin, k decreased gradually with t, the decrease being more pronounced …

Factoring The Adjoint And Maximal Cohen-Macaulay Modules Over The Generic Determinant, Ragnar-Olaf Buchweitz, Graham J. Leuschke

Mathematics - All Scholarship

A question of Bergman asks whether the adjoint of the generic square matrix over a field can be factored nontrivially as a product of square matrices. We show that such factorizations indeed exist over any coefficient ring when the matrix has even size. Establishing a correspondence between such factorizations and extensions of maximal Cohen-Macaulay modules over the generic determinant, we exhibit all factorizations where one of the factors has determinant equal to the generic determinant. The classification shows not only that the Cohen-Macaulay representation theory of the generic determinant is wild in the tame-wild dichotomy, but that it is quite …

Symmetric Powers Of Elliptic Curve L-Functions, Phil Martin, Mark Watkins

Mathematics - All Scholarship

The conjectures of Deligne, Beuilinson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their L-functions. We make a numerical study for symmetric power L-functions of elliptic curves, obtaining data about the validity of their functional equations, frequency of vanishing of central values, and divisibility of Bloch-Kato quotients.

Some Remarks On Heegner Point Computations, Mark Watkins

Mathematics - All Scholarship

We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Delaunay. These are notes from a short course given at the Institut Henri Poincare in December 2004.

On The Growth Of The Betti Sequence Of The Canonical Module, David A. Jorgensen, Graham J. Leuschke

Mathematics - All Scholarship

We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.

Constancy In Integrated Cisplatin Plasma Concentrations Among Pediatric Patients, Jerry Goodisman, Abdul-Kader Souid

Chemistry - All Scholarship

The authors report on the variability in the integrated quantity of free (unbound) plasma cisplatin (area under curve of plasma concentration versus time, AUC). The AUC was measured in 19 patients receiving cisplatin doses proportional to body surface areas (BSA), 30mg/m2 over 1 hour. The relative standard deviation (RSD, population standard deviation divided by mean value) for the maximum free plasma cisplatin concentration (Cmax, μM) was 0.338; for the half-life (t½, minute), 0.210; and for the AUC (μM minute), 0.320. Thus, BSA-based dosing gave significant variability in the AUC. We attempted to use (weight)a(height)b, seeking values of a and b …

Secondary Terms In The Number Of Vanishings Of Quadratic Twists Of Elliptic Curve L-Functions, J. Brian Conrey, Atul Pocharel, Michael O. Rubinstein, Mark Watkins

Mathematics - All Scholarship

We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical L-values we obtain a conjecture for the first two terms in the ratio of the number of vanishings of twists sorted according to arithmetic progressions.

Simulations Of {\Cal N}=2 Super Yang-Mills Theory In Two Dimensions, Simon Catterall

Physics - All Scholarship

We present results from lattice simulations of {\cal N}=2 super Yang-Mills theory in two dimensions. The lattice formulation we use was developed in \cite{2dpaper} and retains both gauge invariance and an exact (twisted) supersymmetry for any lattice spacing. Results for both U(2) and SU(2) gauge groups are given. We focus on supersymmetric Ward identities, the phase of the Pfaffian resulting from integration over the Grassmann fields and the nature of the quantum moduli space.

Influence Of Surface Tension On The Conical Miniscus Of A Magnetic Fluid In The Field Of A Current-Carrying Wire, Thomas John, Dirk Rannacher, Adreas Engel

Mathematics - All Scholarship

We study the influence of surface tension on the shape of the conical miniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function zeta(r) describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile.

String Gas Cosmology, Scott Watson, Thorsten Battefeld

Physics - All Scholarship

We present a critical review and summary of String Gas Cosmology. We include a pedagogical derivation of the effective action starting from string theory, emphasizing the necessary approximations that must be invoked. Working in the effective theory, we demonstrate that at late-times it is not possible to stabilize the extra dimensions by a gas of massive string winding modes. We then consider additional string gases that contain so-called enhanced symmetry states. These string gases are very heavy initially, but drive the moduli to locations that minimize the energy and pressure of the gas. We consider both classical and quantum gas …