Breakdown of Kolmogorov scaling in models of cluster aggregation

We describe a model of cluster aggregation with a source which provides a rare example of an analytically tractable turbulent system. The steady state is characterized by a constant mass flux from small masses to large. Thus it can be studied using a phenomenological theory, inspired by Kolmogorov's 1941 theory, which assumes constant flux and self-similarity. We prove that such self-similarity is violated in dimensions less than or equal to two. We then use dynamical renormalization group techniques to show that the scaling of multipoint correlation functions implies nontrivial multifractality. The analytical results are supported by Monte Carlo simulations.     

Quantum-to-classical crossover in full counting statistics

The reduction of quantum scattering leads to the suppression of shot noise. In this Letter, we analyze the crossover from the quantum transport regime with universal shot noise to the classical regime where noise vanishes. By making use of the stochastic path integral approach, we find the statistics of transport and the transmission properties of a chaotic cavity as a function of a system parameter controlling the crossover. We identify three different scenarios of the crossover.     

Jordan-Wigner Approach to Dynamic Correlations in 2D Spin-1/2 Models

We discuss the dynamic properties of the square-lattice spin-1/2 XY model obtained using the two-dimensional Jordan-Wigner fermionization approach. We argue the relevance of the fermionic picture for interpreting the neutron scattering measurements in the two-dimensional frustrated quantum magnet Cs₂CuCl₄.     

Fractional vortices and composite domain walls in flat nanomagnets

We provide a simple explanation of complex magnetic patterns observed in ferromagnetic nanostructures. To this end we identify elementary topological defects in the field of magnetization: ordinary vortices in the bulk and vortices with half-integer winding numbers confined to the edge. Domain walls found in experiments and numerical simulations in strips and rings are composite objects containing two or more of the elementary defects.     

Observation of mixed fermionic-bosonic helium clusters by transmission grating diffraction

Small weakly bound boson-fermion 4He(m) 3He(n) clusters formed in a free jet expansion are identified using nondestructive transmission grating diffraction. The observations confirm the existence of more than 11 very tenuous complexes including the three-body halo molecule 4He2 3He and the pseudo-Borromean complex 4He2 3He2. Effective cluster formation temperatures, extracted from a sudden freeze model for cluster growth using theoretical binding energies, increase smoothly with cluster size, thereby confirming the calculations with the possible exception of 4He2 3He2.     

Safe bounds in linear and mixed-integer linear programming

Current mixed-integer linear programming solvers are based on linear programming routines that use floating-point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. An example is given where many state-of-the-art MILP solvers fail. It is then shown how, using directed rounding and interval arithmetic, cheap pre- and postprocessing of the linear programs arising in a branch-and-cut framework can guarantee that no solution is lost, at least for mixed-integer programs in which all variables can be bounded rigorously by bounds of reasonable size. Mathematics Subject Classification (2000):primary 90C11, secondary 65G20     

Dark matter profile in the galactic center

We describe a quasiequilibrium profile of dark matter particles in the inner parsec of the Galaxy, rhodm proportional to r(-3/2). This "minicusp" profile is caused by scattering with the dense stellar cluster around the supermassive black hole in Sgr A* and is independent of the initial conditions. The implications for detection of gamma rays from annihilation of weakly interacting massive dark matter particle in the Galactic center are a mild enhancement of the flux and a characteristic central feature in the angular distribution which could be detectable by high-resolution atmospheric Cherenkov telescopes.     

"Eclipse" effect in the scattering of weakly bound helium clusters

The total cross sections of the helium dimer, trimer, and tetramer for scattering from Kr atoms have been measured for cluster beam velocities between 250 and 820 m/s. The dimer cross section is twice that of the atom within 5% indicating that the Kr atoms scatter from the He atoms independently, which is consistent with the large dimer bond distance of about 50 A. The trimer and tetramer cross sections are somewhat larger and can be described by an impulse approximation with a multiple "eclipse" correction, extending ideas of Glauber for high energy collisions with the deuteron.     

Symmetry and electronic structure of noble-metal nanoparticles and the role of relativity

We present high resolution UV-photoelectron spectra of cold mass selected Cun-, Agn-, and Aun- with n=53-58. The observed electron density of states is not the expected simple electron shell structure, but is strongly influenced by electron-lattice interactions. Only Cu55- and Ag55- exhibit highly degenerate states. This is a direct consequence of their icosahedral symmetry, as is confirmed by density functional theory calculations. Neighboring sizes exhibit perturbed electronic structures, as they are formed by removal or addition of atoms to the icosahedron and therefore have lower symmetries. Gold clusters in the same size range show completely different spectra with almost no degeneracy, which indicates that they have structures of much lower symmetry. This behavior is related to strong relativistic bonding effects in gold, as demonstrated by ab initio calculations for Au55-.     

On the Continuity of Inversion in Countably Compact Inverse Topological Semigroups

Let S be a countably compact Hausdorff space endowed with a continuous semigroup operation turning S into an inverse semigroup. It is shown that the inversion inv : x x^-1 in S is continuous provided one of the following conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is Clifford, inversely regular, and topologically periodic, (3) the semigroup S is Clifford, topologically periodic and the square S × S is regular and countably compact. These results are close to the best possible since there is an example of a quasi-regular sequentially compact commutative inverse topological semigroup with discontinuous inversion.