Orbits of arcs in PG(N,K) under projectivities

The symmetric group on k symbols is made to operate on a certain set of matrices in such a way that its orbits are in one-to-one correspondence with the orbits of the k-arcs of an N-dimensional projective space under the group of projectivities. This leads to a formula for the number of such orbits.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Transportation problems which can be solved by the use of hirsch-paths for the dual problems

Balinski uses his signature method for the proof of the Hirsch-conjecture for dual transportation polyhedra to obtain an efficient algorithm for the assignment problem. We will show how to extend this method to other primal transportation problems, including transportation problems with unit demands. We then prove that Balinski's assignment algorithm is equivalent, cycle by cycle, to that of Hung and Rom. We demonstrate that, under some assumptions for our probability model, a modification of the latter algorithm has an average complexity of O(n ²logn) and present some computational results confirming this. We also present results that indicate that this modification compares favorably with Balinski's algorithm and other codes. Research of both authors supported, in part, by grants of the Alexander von Humboldt-Stiftung. Supported, in part, by NSF grant DMS-8504050.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Electrochemical characterization of core@shell CoFe2O4/Au composite

Quantum dots (QDs) have received considerable attention due to their unique optical and electrical properties. Although substantial research has focused on the potential applications and toxicological impacts of QDs, far less effort has been directed toward understanding their fate and transport in the environment. In this work, the effect of four coatings, polyethylene glycol functionalized polymer (PEGP), carboxyl derivatized polymer (COOHP), linoleic acid (LA), and polyacrylic acid-octylamine (PAA-OA), on the transport and retention of QDs in porous media were evaluated under environmentally relevant conditions. Aqueous QD suspensions (ca. 10 nM) were introduced into water-saturated columns packed with 40–50 mesh Ottawa sand at a pore-water velocity of 7.6 m/day. At an ionic strength (IS) of 3 mM and pH of 7, PEGP-coated QDs were completely retained within the column, while more than 60 % of COOHP-coated QDs were transported through a column run under identical conditions. When PAA-OA and LA were used as coatings, effluent QD recoveries increased to more than 65 and 89 % of the injected mass, respectively. Additionally, a decrease in pH from 9.5 to 5.0, or an increase of IS from 0 to 30 mM reduced the eluted mass of PAA-OA-coated QDs by more than 2 and 15 times, respectively. The relative mobility of coated QDs (LA > PAA-OA > COOHP > PEGP) was consistent with total interaction energy profiles between QDs and sand surfaces calculated based on Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. At an IS of 3 mM (NaCl) and pH 7, a linear correlation was obtained between the fraction of eluted QDs and the magnitude of the primary interaction energy barrier. These findings demonstrate the strong dependence of QD transport on coating type and indicate that interaction energies based on DLVO theory can be used to predict the relative mobility of QDs in porous media.     

Magnetic circular dichroism of the first spin-forbidden transition in 2[Cr(en)3Cl3] . KCl . 6H2O

The longitudinal Zeeman effect of the ² E ←⁴ A ₂ transition of the Cr⁺³ ion in single crystals of 2[Cr(en)₃Cl₃] . KCl . 6H₂O has been measured using circularly polarized light as a function of magnetic field strength between 0 and 160 kgauss at ～80 K. The g factor for the ground state was determined to be g _‖(⁴ A ₂) = 2·01±0·05, in agreement with the E.S.R.-determined value. The ratio between the excited state g values and that of the ground state was determined; using the value g _‖(⁴ A ₂) = 1·99, the g factors g _‖(2) = 2·61±0·04 and g _‖() = 1·47±0·04 were obtained.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Determining the efficacy of a nanotechnology media product in enhancing children’s engagement with nanotechnology

Public engagement in nanotechnology media products can lead to a greater interest in understanding of nanotechnology. A study was undertaken to determine middle school student engagement in Nanooze, a magazine featuring nanotechnology research that has been developed for a young adult audience. Teachers at 116 Detroit middle schools distributed two issues of the magazine to their students, and surveys were collected from 870 students after reading the magazines. Results suggest that the majority of students liked reading the magazine and learned something about nanotechnology. Engagement in nanotechnology led to understanding of nanotechnology. The Nanooze magazine was an effective medium for engaging middle school students in learning about nanotechnology.     

Emergent <Emphasis Type=Italic>SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.