21,573 research outputs found
Mathematics from China to Virginia by Way of Singapore
Our article follows from an interesting concurrence of mathematical and educational lines. At least the concurrence seems so to us and we hope that those who read on will agree. The lines or streams are a joint minimester program at St. Catherine’s and St. Christopher‘s Schools, an interest in problem solving, and a Singapore connection. We shall describe the lines first and then describe the mathematics that we found at their intersection
Travelling waves in hyperbolic chemotaxis equations
Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically
Probing multipartite entanglement in a coupled Jaynes-Cummings system
We show how to probe multipartite entanglement in coupled Jaynes-Cummings
cells where the degrees of freedom are the electronic energies of each of the
atoms in separate single-mode cavities plus the single-mode fields
themselves. Specifically we propose probing the combined system as though it is
a dielectric medium. The spectral properties and transition rates directly
reveal multipartite entanglement signatures. It is found that the Hilbert space
of the cell system can be confined to the totally symmetric subspace of two
states only that are maximally-entangled W states with 2N degrees of freedom
Continuous Multipartite Entangled State in Wigner Representation and the Violation of Zukowski-Brukner Inequality
We construct an explicit Wigner function for N-mode squeezed state. Based on
a previous observation that the Wigner function describes correlations in the
joint measurement of the phase-space displaced parity operator, we investigate
the non-locality of multipartite entangled state by the violation of
Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for
such squeezed state violate these inequalities by an amount that grows with the
number N.Comment: 5 pages, rewritten version, accepted by Phys. Rev.
Modeling the Broadband Spectral Energy Distribution of the Microquasars XTE J1550-564 and H 1743-322
We report results from a systematic study of the spectral energy distribution
(SED) and spectral evolution of XTE J1550--564 and H 1743--322 in outburst. The
jets of both sources have been directly imaged at both radio and X-ray
frequencies, which makes it possible to constrain the spectrum of the radiating
electrons in the jets. We modelled the observed SEDs of the jet `blobs' with
synchrotron emission alone and with synchrotron emission plus inverse Compton
scattering. The results favor a pure synchrotron origin of the observed jet
emission. Moreover, we found evidence that the shape of the electron spectral
distribution is similar for all jet `blobs' seen. Assuming that this is the
case for the jet as a whole, we then applied the synchrotron model to the radio
spectrum of the total emission and extrapolated the results to higher
frequencies. In spite of significant degeneracy in the fits, it seems clear
that, while the synchrotron radiation from the jets can account for nearly 100%
of the measured radio fluxes, it contributes little to the observed X-ray
emission, when the source is relatively bright. In this case, the X-ray
emission is most likely dominated by emission from the accretion flows. When
the source becomes fainter, however, the jet emission becomes more important,
even dominant, at X-ray energies. We also examined the spectral properties of
the sources during outbursts and the correlation between the observed radio and
X-ray variabilities. The implication of the results is discussed.Comment: 9 pages, 11 figures, MNRAS, accepted; the paper has been much
expanded (e.g., arguments strengthened, another source H 1743-322 added) and
rewritten (e.g., title changed, abstract revised); the main conclusions
remain unchange
A comprehensive numerical study of aerosol-cloud-precipitation interactions in marine stratocumulus
Three-dimensional large-eddy simulations (LES) with detailed bin-resolved microphysics are performed to explore the diurnal variation of marine stratocumulus (MSc) clouds under clean and polluted conditions. The sensitivity of the aerosol-cloud-precipitation interactions to variation of sea surface temperature, free tropospheric humidity, large-scale divergence rate, and wind speed is assessed. The comprehensive set of simulations corroborates previous studies that (1) with moderate/heavy drizzle, an increase in aerosol leads to an increase in cloud thickness; and (2) with non/light drizzle, an increase in aerosol results in a thinner cloud, due to the pronounced effect on entrainment. It is shown that for higher SST, stronger large-scale divergence, drier free troposphere, or lower wind speed, the cloud thins and precipitation decreases. The sign and magnitude of the Twomey effect, droplet dispersion effect, cloud thickness effect, and cloud optical depth susceptibility to aerosol perturbations (i.e., change in cloud optical depth to change in aerosol number concentration) are evaluated by LES experiments and compared with analytical formulations. The Twomey effect emerges as dominant in total cloud optical depth susceptibility to aerosol perturbations. The dispersion effect, that of aerosol perturbations on the cloud droplet size spectrum, is positive (i.e., increase in aerosol leads to spectral narrowing) and accounts for 3% to 10% of the total cloud optical depth susceptibility at nighttime, with greater influence in heavier drizzling clouds. The cloud thickness effect is negative (i.e., increase in aerosol leads to thinner cloud) for non/light drizzling cloud and positive for a moderate/heavy drizzling clouds; the cloud thickness effect contributes 5% to 22% of the nighttime total cloud susceptibility. Overall, the total cloud optical depth susceptibility ranges from ~0.28 to 0.53 at night; an increase in aerosol concentration enhances cloud optical depth, especially with heavier precipitation and in a more pristine environment. During the daytime, the range of magnitude for each effect is more variable owing to cloud thinning and decoupling. The good agreement between LES experiments and analytical formulations suggests that the latter may be useful in evaluations of the total cloud susceptibility. The ratio of the magnitude of the cloud thickness effect to that of the Twomey effect depends on cloud base height and cloud thickness in unperturbed (clean) clouds
Microscopic theory of single-electron tunneling through molecular-assembled metallic nanoparticles
We present a microscopic theory of single-electron tunneling through metallic
nanoparticles connected to the electrodes through molecular bridges. It
combines the theory of electron transport through molecular junctions with the
description of the charging dynamics on the nanoparticles. We apply the theory
to study single-electron tunneling through a gold nanoparticle connected to the
gold electrodes through two representative benzene-based molecules. We
calculate the background charge on the nanoparticle induced by the charge
transfer between the nanoparticle and linker molecules, the capacitance and
resistance of molecular junction using a first-principles based Non-Equilibrium
Green's Function theory. We demonstrate the variety of transport
characteristics that can be achieved through ``engineering'' of the
metal-molecule interaction.Comment: To appear in Phys. Rev.
Orientation and strain modulated electronic structures in puckered arsenene nanoribbons
Orthorhombic arsenene was recently predicted as an indirect bandgap
semiconductor. Here, we demonstrate that nanostructuring arsenene into
nanoribbons can successfully transform the bandgap to be direct. It is found
that direct bandgaps hold for narrow armchair but wide zigzag nanoribbons,
which is dominated by the competition between the in-plane and out-of-plane
bondings. Moreover, straining the nanoribbons also induces a direct bandgap and
simultaneously modulates effectively the transport property. The gap energy is
largely enhanced by applying tensile strains to the armchair structures. In the
zigzag ones, a tensile strain makes the effective mass of holes much higher
while a compressive strain cause it much lower than that of electrons. Our
results are crutial to understand and engineer the electronic properties of two
dimensional materials beyond the planar ones like graphene
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