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Xia Zhang

Publications and source records attributed to Xia Zhang.

51 records · Page 3Linked to original sources
arXiv2020

On the Encounter Desorption of Hydrogen Atoms on Ice Mantle

At low temperatures (10 K), hydrogen atoms can diffuse quickly on grain ice mantles and frequently encounter hydrogen molecules, which cover a notable fraction of grain surface. The desorption energy of H atoms on H2 substrates is much less than that on water ice. The H atom encounter desorption mechanism is adopted to study the enhanced desorption of H atoms on H2 substrates. Using a small reaction network, we show that the steady-state surface H abundances predicted by the rate equation model that includes H atom encounter desorption agree reasonably well with the results from the more rigorous microscopic Monte Carlo method. For a full gas-grain model, H atom encounter desorption can reduce surface H abundances. Therefore, if a model adopts the encounter desorption of H atoms, it becomes more difficult for hydrogenation products such as methanol to form, but it is easier for C, O and N atoms to bond with each other on grain surfaces.

astro-ph.SR↗
arXiv2020

The Hille-Yosida generation theorem for almost surely bounded $C_{0}$--semigroups of continuous module homomorphisms$^1$

In this paper, we first study some properties peculiar to $C_{0}$--semigroups of continuous module homomorphisms and give a characterization for such a $C_{0}$--semigroup to be almost surely bounded. Then, based on these, we establish the Hille-Yosida generation theorem for almost surely bounded $C_{0}$--semigroups of continuous module homomorphisms, which generalizes some known results. Moreover, the counterexample constructed in this paper also shows that it is necessary to require the almost sure boundedness for such $C_{0}$--semigroups.

math.FA↗
arXiv2020

Existence of an equilibrium for pure exchange economy with fuzzy preferences

This paper focuses on a new model to reach the existence of equilibrium in a pure exchange economy with fuzzy preferences (PXE-FP). The proposed model integrates exchange, consumption and the agent's fuzzy preference in the consumption set. We set up a new fuzzy binary relation on the consumption set to evaluate the fuzzy preferences. Also, we prove that there exists a continuous fuzzy order-preserving function in the consumption set under certain conditions. The existence of a fuzzy competitive equilibrium for the PXE-FP is confirmed through a new result on the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games. The payoffs of all strategy profiles for any agent are fuzzy numbers in fuzzy non-cooperative games. Finally, we show that the fuzzy competitive equilibrium could be characterized as a solution to an associated quasi-variational inequality, giving rise to an equilibrium solution.

cs.GT↗
arXiv2019

Controlling Thermal Emission by Parity-symmetric Fano Resonance of Optical Absorbers in Metasurfaces

In this study, we designed a metasurface based on Al/SiN/Al nano-sandwich optical absorbers. Parity-symmetric dark magnetic resonance modes, anti-symmetric bright magnetic resonance modes, and surface lattice modes are established simultaneously in such a meta-surface. By changing the structural parameters, the wavelength of the dark mode can be tuned to overlap with the lattice mode. Fano resonance is introduced by coupling between the dark and lattice modes. Angular-resolved thermal emission experiments showed that the thermal emission induced by Fano resonance exhibited a narrow wavelength spectrum and directional radiation angle. Fano-type thermal emitters proposed in this work can possibly be used as coherent infrared light sources in the future.

physics.optics↗
arXiv2019

Planar graphs with girth at least 5 are (3,4)-colorable

A graph is $(d_1, \ldots, d_k)$-colorable if its vertex set can be partitioned into $k$ nonempty subsets so that the subgraph induced by the $i$th part has maximum degree at most $d_i$ for each $i\in\{1, \ldots, k\}$. It is known that for each pair $(d_1, d_2)$, there exists a planar graph with girth $4$ that is not $(d_1, d_2)$-colorable. This sparked the interest in finding the pairs $(d_1, d_2)$ such that planar graphs with girth at least $5$ are $(d_1, d_2)$-colorable. Given $d_1\leq d_2$, it is known that planar graphs with girth at least $5$ are $(d_1, d_2)$-colorable if either $d_1\geq 2$ and $d_1+d_2\geq 8$ or $d_1=1$ and $d_2\geq 10$. We improve an aforementioned result by providing the first pair $(d_1, d_2)$ in the literature satisfying $d_1+d_2\leq 7$ where planar graphs with girth at least $5$ are $(d_1, d_2)$-colorable. Namely, we prove that planar graphs with girth at least $5$ are $(3, 4)$-colorable.

math.CO↗
arXiv2018

Catching the Birth of a Dark Molecular Cloud for the First Time

The majority of hydrogen in the interstellar medium (ISM) is in atomic form. The transition from atoms to molecules and, in particular, the formation of the H$_2$ molecule, is a key step in cosmic structure formation en route to stars. Quantifying H$_2$ formation in space is difficult, due to the confusion in the emission of atomic hydrogen (HI) and the lack of a H$_2$ signal from the cold ISM. Here we present the discovery of a rare, isolated dark cloud currently undergoing H$_2$ formation, as evidenced by a prominent "ring" of HI self-absorption. Through a combined analysis of HI narrow self-absorption, CO emission, dust emission, and extinction, we directly measured, for the first time, the [HI]/[H$_2$] abundance varying from 2% to 0.2%, within one region. These measured HI abundances are orders of magnitude higher than usually assumed initial conditions for protoplanetary disk models. None of the fast cloud formation model could produce such low atomic hydrogen abundance. We derived a cloud formation timescale of 6$\times$10$^6$ years, consistent with the global Galactic star formation rate, and favoring the classical star formation picture over fast star formation models. Our measurements also help constrain the H$_2$ formation rate, under various ISM conditions.

astro-ph.GA↗
arXiv2018

A bound on judicious bipartitions of directed graphs

Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously, which have received a lot of attentions lately. Scott asked the following natural question: What is the maximum constant $c_d$ such that every directed graph $D$ with $m$ arcs and minimum outdegree $d$ admits a bipartition $V(D)= V_1\cup V_2$ satisfying $\min\{e(V_1, V_2), e(V_2, V_1)\}\ge c_d m$? Here, for $i=1,2$, $e(V_{i},V_{3-i})$ denotes the number of arcs in $D$ from $V_{i}$ to $V_{3-i}$. Lee, Loh, and Sudakov %[Judicious partitions of directed graphs, Random Struct. Alg. 48 %(2016) 147--170] conjectured that every directed graph $D$ with $m$ arcs and minimum outdegree at least $d\ge 2$ admits a bipartition $V(D)=V_1\cup V_2$ such that \[ \min\{e(V_1,V_2),e(V_2,V_1)\}\geq \Big(\frac{d-1}{2(2d-1)}+ o(1)\Big)m. \] %While it is not known whether or not the minimum outdegree condition %alone is sufficient, w We show that this conjecture holds under the additional natural condition that the minimum indegree is also at least $d$.

math.CO↗
arXiv2017

Quantum random number generation using an on-chip plasmonic beamsplitter

We report an experimental realisation of a quantum random number generator using a plasmonic beamsplitter. Free-space single photons are converted into propagating single surface plasmon polaritons on a gold stripe waveguide via a grating. The surface plasmons are then guided to a region where they are scattered into one of two possible outputs. The presence of a plasmonic excitation in a given output determines the value of a random bit generated from the quantum scattering process. Using a stream of single surface plasmons injected into the beamsplitter we achieve a quantum random number generation rate of 2.37 Mbits/s even in the presence of loss. We characterise the quality of the random number sequence generated, finding it to be comparable to sequences from other quantum photonic-based devices. The compact nature of our nanophotonic device makes it suitable for tight integration in on-chip applications, such as in quantum computing and communication schemes.

quant-ph↗
arXiv2017

Existence and symmetry of solutions for critical fractional Schrödinger equations with bounded potentials

This paper is concerned with the following fractional Schrödinger equations involving critical exponents: \begin{eqnarray*} (-Δ)^αu+V(x)u=k(x)f(u)+λ|u|^{2_α^{*}-2}u\quad\quad \mbox{in}\ \mathbb{R}^{N}, \end{eqnarray*} where $(-Δ)^α$ is the fractional Laplacian operator with $α\in(0,1)$, $N\geq2$, $λ$ is a positive real parameter and $2_α^{*}=2N/(N-2α)$ is the critical Sobolev exponent, $V(x)$ and $k(x)$ are positive and bounded functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space and the minimax arguments, we obtain the existence of a nontrivial radially symmetric weak solution for the above-mentioned equations without assuming the Ambrosetti-Rabinowitz condition on the subcritical nonlinearity.

math.AP↗
arXiv2016

Temperature Dependent Luminescent Decay Properties of CdTe Quantum Dot Monolayers: Impact of Concentration on Carrier Trapping

We have investigated the temperature dependence of the photoluminescence spectra and average photoluminescence decay rate of CdTe quantum dot monolayers of different sizes as a function of concentration in the range 77 K to 296 K. It is shown that a simple three level analytic model involving bright and dark exciton states can only describe the lower temperature data but is unable to satisfactorily fit the data over the full temperature range. An extended model which includes external trap states is necessary to fit the data above approximately 150 K. Parameters for the model are obtained using both temporal and spectral data. The model indicates that the efficiency of interaction with trap states increases as the QD monolayer concentration increases, which is likely due to an increase in the density of available traps.

cond-mat.mes-hall↗
arXiv2015

Comment on "One-way deficit of two qubit X states"

We improve the recent method of Wang et. al to calculate exactly the one-way information deficit of any X-state. Analytical formulas of the one-way information deficit are given for several nontrivial regions of the parameters.

quant-ph↗
arXiv2015

A Theoretical Investigation of Decay and Energy Transfer Rates and Efficiencies Near Gold Nanospheres

We consider the effect of Au nanospheres of subwavelength sizes on the decay and energy transfer rates of quantum systems placed in the proximity of these nanospheres. We find that, for the sphere sizes considered in this contribution, the radiative decay rate is barely affected by the presence of the nanosphere, whereas the non-radiative decay rate is greatly enhanced due to energy transfer from the quantum system to the nanosphere, leading to a strong quenching of the emission of the quantum system. The emission wavelength of the quantum emitter and its intrinsic quantum yield play an important role and the impact of both has to be considered together when investigating their effect on the non-radiative decay rate. The energy transfer process from the emitter to the nanosphere has a complicated distance dependence, with a 1/r^6 regime, characteristic of the Förster energy transfer mechanism, but also exhibiting other distance dependence regimes. In the case of a donor-acceptor pair in the presence of a Au nanosphere, the donor couples strongly to the nanosphere, acting as an enhanced dipole; the donor-acceptor energy transfer rate then follows a Förster trend, with an increased Förster radius. The angular dependence of the energy transfer efficiency between donor and acceptor has a strong dipole-dipole trend for small spheres and deviates from it for larger spheres, especially when the donor and acceptor are on opposite sides of the sphere. The spectral overlap of the donor emission, acceptor absorption and gold nanosphere extinction shows an interesting trend in that the largest Förster radius is obtained when the donor emission and acceptor absorption maxima are somewhat red-shifted from the localized surface plasmon peak in the extinction spectrum of the Au nanosphere, being located between it and the near-field scattering maximum.

physics.optics↗
arXiv2014

Birefringence of Muscovite Mica Plate Temperature Effect in the Ultraviolet and Visible Spectrum

We developed a method to measure the phase retardation and birefringence of muscovite mica plate in the temperature range of 223K to 358K within the spectrum of 300 to 700 nm. The phase retardation data is gained through the standard transmission ellipsometry using spectroscopic ellipsometer. With the phase retardation and thickness of the mica plate we can calculate its birefringence dispersion. Our results give abundant phase retardation and birefringence data of muscovite mica in the ultraviolet and visible spectrum from 223K to 358K. From the experimental data, the phase retardation and birefringence will drop down at the fixed wavelength when the temperature rises. The accuracy of the birefringence of mica plate is better than 3.5e-5.

physics.optics↗
arXiv2014

Phase Retardation and Birefringence of the Crystalline Quartz Plate in the Ultraviolet and Visible Spectrum

A method for measuring the phase retardation and birefringence of crystalline quartz wave plate in the ultraviolet and visible spectrum is demonstrated using spectroscopic ellipsometer. After the calibration of the crystalline quartz plate, the experimental data are collected by the photodetector and sent to the computer. According to the outputted data, the retardation can be obtained in the range of 190 to 770 nm. With the retardation data, the birefringence for the quartz can be calculated in the same spectrum with an accuracy of better than . The birefringence results enrich the crystalline quartz birefringence data especially in the ultraviolet spectrum.

physics.optics↗