Asymptotics for the number of n-quasigroups of order 4

The asymptotic form of the number of n-quasigroups of order 4 is $3^{n+1} 2^{2^n +1} (1+o(1))$. Keywords: n-quasigroups, MDS codes, decomposability, reducibility.Comment: 15 p., 3 fi

On the structure of non-full-rank perfect codes

The Krotov combining construction of perfect 1-error-correcting binary codes from 2000 and a theorem of Heden saying that every non-full-rank perfect 1-error-correcting binary code can be constructed by this combining construction is generalized to the $q$-ary case. Simply, every non-full-rank perfect code $C$ is the union of a well-defined family of $\mu$-components $K_\mu$, where $\mu$ belongs to an "outer" perfect code $C^*$, and these components are at distance three from each other. Components from distinct codes can thus freely be combined to obtain new perfect codes. The Phelps general product construction of perfect binary code from 1984 is generalized to obtain $\mu$-components, and new lower bounds on the number of perfect 1-error-correcting $q$-ary codes are presented.Comment: 8 page

Quantum Phase Shift in Chern-Simons Modified Gravity

Using a unified approach of optical-mechanical analogy in a semiclassical formula, we evaluate the effect of Chern-Simons modified gravity on the quantum phase shift of de Broglie waves in neutron interferometry. The phase shift calculated here reveals, in a single equation, a combination of effects coming from Newtonian gravity, inertial forces, Schwarzschild and Chern-Simons modified gravity. However the last two effects, though new, turn out to be too tiny to be observed, and hence only of academic interest at present. The approximations, wherever used, as well as the drawbacks of the non-dynamical approach are clearly indicated.Comment: 16 pages, minor errors corrected. Accepted for publication in Phys. Rev.

Bitangential interpolation in generalized Schur classes

Bitangential interpolation problems in the class of matrix valued functions in the generalized Schur class are considered in both the open unit disc and the open right half plane, including problems in which the solutions is not assumed to be holomorphic at the interpolation points. Linear fractional representations of the set of solutions to these problems are presented for invertible and singular Hermitian Pick matrices. These representations make use of a description of the ranges of linear fractional transformations with suitably chosen domains that was developed in a previous paper.Comment: Second version, corrected typos, changed subsection 5.6, 47 page

Fragmentation of a Circular Disc by Impact on a Frictionless Plate

The break-up of a two-dimensional circular disc by normal and oblique impact on a hard frictionless plate is investigated by molecular dynamics simulations. The disc is composed of numerous unbreakable randomly shaped convex polygons connected together by simple elastic beams that break when bent or stretched beyond a certain limit. It is found that for both normal and oblique impacts the crack patterns are the same and depend solely on the normal component of the impact velocity. Analysing the pattern of breakage, amount of damage, fragment masses and velocities, we show the existence of a critical velocity which separates two regimes of the impact process: below the critical point only a damage cone is formed at the impact site (damage), cleaving of the particle occurs at the critical point, while above the critical velocity the disc breaks into several pieces (fragmentation). In the limit of very high impact velocities the disc suffers complete disintegration (shattering) into many small fragments. In agreement with experimental results, fragment masses are found to follow the Gates-Gaudin-Schuhmann distribution (power law) with an exponent independent of the velocity and angle of impact. The velocity distribution of fragments exhibit an interesting anomalous scaling behavior when changing the impact velocity and the size of the disc.Comment: submitted to J. Phys: Condensed Matter special issue on Granular Medi

Force Distribution in a Granular Medium

We report on systematic measurements of the distribution of normal forces exerted by granular material under uniaxial compression onto the interior surfaces of a confining vessel. Our experiments on three-dimensional, random packings of monodisperse glass beads show that this distribution is nearly uniform for forces below the mean force and decays exponentially for forces greater than the mean. The shape of the distribution and the value of the exponential decay constant are unaffected by changes in the system preparation history or in the boundary conditions. An empirical functional form for the distribution is proposed that provides an excellent fit over the whole force range measured and is also consistent with recent computer simulation data.Comment: 6 pages. For more information, see http://mrsec.uchicago.edu/granula

Transition from damage to fragmentation in collision of solids

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid discs we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged and a fragmented state with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.Comment: Revtex, 12 figures included. accepted by Phys. Rev.

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too

Outer-Sphere Contributions to the Electronic Structure of Type Zero Copper Proteins

Bioinorganic canon states that active-site thiolate coordination promotes rapid electron transfer (ET) to and from type 1 copper proteins. In recent work, we have found that copper ET sites in proteins also can be constructed without thiolate ligation (called “type zero” sites). Here we report multifrequency electron paramagnetic resonance (EPR), magnetic circular dichroism (MCD), and nuclear magnetic resonance (NMR) spectroscopic data together with density functional theory (DFT) and spectroscopy-oriented configuration interaction (SORCI) calculations for type zero Pseudomonas aeruginosa azurin variants. Wild-type (type 1) and type zero copper centers experience virtually identical ligand fields. Moreover, O-donor covalency is enhanced in type zero centers relative that in the C112D (type 2) protein. At the same time, N-donor covalency is reduced in a similar fashion to type 1 centers. QM/MM and SORCI calculations show that the electronic structures of type zero and type 2 are intimately linked to the orientation and coordination mode of the carboxylate ligand, which in turn is influenced by outer-sphere hydrogen bonding