2,952 research outputs found
The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
We consider the dimer-monomer problem for the rectangular lattice. By mapping
the problem into one of close-packed dimers on an extended lattice, we rederive
the Tzeng-Wu solution for a single monomer on the boundary by evaluating a
Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by
identifying it as the product of the nonzero eigenvalues of the Kasteleyn
matrix.Comment: 4 Pages to appear in the Physical Review E (2006
Theory of resistor networks: The two-point resistance
The resistance between arbitrary two nodes in a resistor network is obtained
in terms of the eigenvalues and eigenfunctions of the Laplacian matrix
associated with the network. Explicit formulas for two-point resistances are
deduced for regular lattices in one, two, and three dimensions under various
boundary conditions including that of a Moebius strip and a Klein bottle. The
emphasis is on lattices of finite sizes. We also deduce summation and product
identities which can be used to analyze large-size expansions of two-and-higher
dimensional lattices.Comment: 30 pages, 5 figures now included; typos in Example 1 correcte
Retention or defection? Chinese consumers’ decision-making styles for domestic and global brands
This study explores consumers’ decision-making in terms of intention to switch to foreign brands from domestic brands when purchasing cell phones and sports shoes. A survey of 584 undergraduates in Guangdong, China, shows that domestic brands retain their low quality-conscious, low fashion-and-recreational-conscious and low price-conscious customers and attract low brand-conscious and high choice-confused buyers from foreign brands. Foreign brands typically retain their consumers who are highly conscious of fashion and recreation and keep and draw customers with low choice confusion. High-price-conscious consumers and those who are highly brand-confused will assess foreign and domestic brands when searching for bargains. Regarding managerial implications, local brands should offer products of high quality at low prices
and constantly invest in R&D; foreign brands may expand their customer bases and build interactive brand channels; all companies can retain brand-confused customers with preferential packages and design their marketing strategies based on decision-making styles of their target consumers
Theory of impedance networks: The two-point impedance and LC resonances
We present a formulation of the determination of the impedance between any
two nodes in an impedance network. An impedance network is described by its
Laplacian matrix L which has generally complex matrix elements. We show that by
solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the
effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p}
- u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically
equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting
of inductances (L) and capacitances (C), the formulation leads to the
occurrence of resonances at frequencies associated with the vanishing of
lambda_a. This curious result suggests the possibility of practical
applications to resonant circuits. Our formulation is illustrated by explicit
examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63)
correcte
Influence of realistic parameters on state-of-the-art LWFA experiments
We examine the influence of non-ideal plasma-density and non-Gaussian
transverse laser-intensity profiles in the laser wakefield accelerator
analytically and numerically. We find that the characteristic amplitude and
scale length of longitudinal density fluctuations impacts on the final energies
achieved by electron bunches. Conditions that minimize the role of the
longitudinal plasma density fluctuations are found. The influence of higher
order Laguerre-Gaussian laser pulses is also investigated. We find that higher
order laser modes typically lead to lower energy gains. Certain combinations of
higher order modes may, however, lead to higher electron energy gains.Comment: 16 pages, 6 figures; Accepted for publication in Plasma Physics and
Controlled Fusio
Dye lasing in optically manipulated liquid aerosols
We report lasing in airborne, rhodamine B-doped glycerol-water droplets with diameters ranging between 7.7 and 11.0 mu m, which were localized using optical tweezers. While being trapped near the focal point of an infrared laser, the droplets were pumped with a Q-switched green laser. Our experiments revealed nonlinear dependence of the intensity of the droplet whispering gallery modes (WGMs) on the pump laser fluence, indicating dye lasing. The average wavelength of the lasing WGMs could be tuned between 600 and 630 nm by changing the droplet size. These results may lead to new ways of probing airborne particles, exploiting the high sensitivity of stimulated emission to small perturbations in the droplet laser cavity and the gain medium
Two-frequency shell model for hypernuclei and meson-exchange hyperon-nucleon potentials
A two-frequency shell model is proposed for investigating the structure of hypernuclei starting with a hyperon-nucleon potential in free space. In a calculation using the folded-diagram method for Λ¹⁶O, the Λ single particle energy is found to have a saturation minimum at an oscillator frequency ħωΛ≈10MeV, for the Λ orbit, which is considerably smaller than ħωN=14MeV for the nucleon orbit. The spin-dependence parameters derived from the Nijmegen NSC89 and NSC97f potentials are similar, but both are rather different from those obtained with the Jülich-B potential. The ΛNN three-body interactions induced by ΛN-ΣN transitions are important for the spin parameters, but relatively unimportant for the low-lying states of Λ¹⁶O.Yiharn Tzeng, S. Y. Tsay Tzeng, T. T. S. Kuo, T.-S.H. Lee, and V. G. D. Stok
Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle
Closed-form expressions are obtained for the partition function of the Ising
model on an M x N simple-quartic lattice embedded on a Moebius strip and a
Klein bottle for finite M and N. The finite-size effects at criticality are
analyzed and compared with those under cylindrical and toroidal boundary
conditions. Our analysis confirms that the central charge is c=1/2.Comment: 8 pages, 3 eps figure
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