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Qin Zhao

Publications and source records attributed to Qin Zhao.

At least 37 records · Page 2Linked to original sources
arXiv2022

Transonic Shocks for 2-D Steady Exothermically Reacting Euler Flows in a Finite Nozzle

This paper concerns the existence of transonic shocks for steady exothermically reacting Euler flows in an almost flat nozzle with the small rate of the exothermic reaction. One of the key points is to quantitatively determine the position of the shock front in the nozzle. We focus on the contributions of the perturbation of the flat nozzle and the exothermic reaction in determining the position of the shock front by comparing the orders of $σ$ and $κ$, where $σ$ represents the scale of the perturbation of the flat nozzle and $κ$ the rate of the exothermic reaction. To this end, a free boundary problem for the linearized reacting Euler system is proposed to catch an approximating position of the shock front as well as the associated approximating shock solution, with which the existence of a shock solution close to it can be established via a nonlinear iteration scheme. One of the key steps is solving the nonlinear equation derived from the solvability condition for the elliptic sub-problem in the domain of the subsonic flow behind the shock front, which determines the free boundary of the proposed problem. Four typical cases are analyzed which describe possible interactions between the geometry of the nozzle boundary and the exothermic reaction. The results also manifest that exothermic reaction has a stabilization effect on transonic shocks in the nozzles.

math.AP↗
arXiv2021

Measurement of the relative Quantum Efficiency of Hamamatsu model R5912-20MOD photomultiplier tubes at liquid argon temperature

The model R5912-20MOD photomultiplier tube(PMT) is made for cryogenic application by Hamamatsu. In this paper, we report on the measurement of relative quantum efficiency (QE) of this model PMT at liquid argon(LAr) temperature. Furthermore, a specially designed setup and relevant test method are introduced. The relative QE is measured in visible wavelengths with the PMT emerged in high purity nitrogen atmosphere. The results show that the change of QE at LAr temperature is within about 5% compared with room temperature around 420 nm. However, the QE increases about 10% in the shorter wavelength range and decreases significantly after 550 nm.

physics.ins-det↗
arXiv2021

Prospects of detecting the reactor $\bar{ν_e}$-Ar coherent elastic scattering with a low threshold dual-phase argon time projection chamber at Taishan

We propose to measure the coherent elastic neutrino nucleus scattering (CE$ν$NS) using a dual-phase liquid argon time projection chamber (TPC) with 200kg fiducial mass. The detector is expected to be adjacent to the JUNO-TAO experiment and to be about 35m from a reactor core with 4.6GW thermal power at Taishan. The antineutrino flux is approximately 6$\times10^{12}$cm$^{-1}$s$^{-1}$ at this location, leading to more than 11,000 coherent scattering events per day in the fiducial mass. However, the nuclear recoil energies concentrate in the sub-keV region, corresponding to less than ten ionisation electrons in the liquid argon. The detection of several ionisation electrons can be achieved in the dual-phase TPC due to the large amplification in the gas region. With a feasible detection threshold of four ionisation electrons, the signal rate is 955 per day. The detector is designed to be shielded well from cosmogenic backgrounds and ambient radioactivities to reach a 16% background-to-signal ratio in the energy region of interest. With the large CE$ν$NS sample, the expected sensitivity of measuring the weak mixing angle $\sin^{2}θ_{W}$, and of limiting the neutrino magnetic moment are discussed. In addition, a synergy between the reactor antineutrino CE$ν$NS experiment and the dark matter experiment is foreseen.

hep-ex↗
arXiv2019

Calibration of liquid argon detector with $^{83m}Kr$ and $^{22}Na$ in different drift field

$^{83m}Kr$ and $^{22}Na$ have been used in calibrating a liquid argon (LAr) detector.$^{83m}Kr$ atoms are produced through the decay of $^{83}Rb$ and introduced into the LAr detector through the circulating purification system. The light yield reaches 7.26$\pm$0.02 photonelectrons/keV for 41.5keV from $^{83m}Kr$ and 7.66$\pm$0.01 photonelectrons/keV for the 511keV from $^{22}Na$, as a comparison. The light yield varies with the drift electric field from 50 to 200V/cm have been also reported. After stopping fill, the decay rate of $^{83m}Kr$ with a fitted half-life of 1.83$\pm$0.11 h, which is consistent with the reported value of 1.83$\pm$0.02 h.

physics.ins-det↗
arXiv2019

Branes and Categorifying Integrable Lattice Models

We elucidate how integrable lattice models described by Costello's 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.

hep-th↗
arXiv2019

Hypersonic limit of two-dimensional steady compressible Euler flows passing a straight wedge

We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken as the adiabatic exponent $γ$ of the polytropic gas decreases to $1$. We proposed a form of the Euler equations which is valid if the unknowns are measures and constructed a measure solution contains Dirac measures supported on the surface of the wedge. It is proved that as $γ\to1$, the sequence of solutions of the compressible Euler equations that containing a shock ahead of the wedge converge vaguely as measures to the measure solution we constructed. This justified the Newton theory of hypersonic flow passing obstacles in the case of two-dimensional straight wedges. The result also demonstrates the necessity of considering general measure solutions in the studies of boundary-value problems of systems of hyperbolic conservation laws.

math.AP↗
arXiv2019

High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: Polytropic gas

We study high Mach number limit of the one dimensional piston problem for the full compressible Euler equations of polytropic gas, for both cases that the piston rushes into or recedes from the uniform still gas, at a constant speed. There are two different situations, and one needs to consider measure solutions of the Euler equations to deal with concentration of mass on the piston, or formation of vacuum. We formulate the piston problem in the framework of Radon measure solutions, and show its consistency by proving that the integral weak solutions of the piston problems converge weakly in the sense of measures to (singular) measure solutions of the limiting problems, as the Mach number of the piston increases to infinity.

math.AP↗
arXiv2018

Stabilization effect of frictions for transonic shocks in steady compressible Euler flows passing three-dimensional ducts

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets. For the three-dimensional steady non-isentropic compressible Euler system with frictions, we had constructed a family of transonic shock solutions in rectilinear ducts with square cross-sections, and this paper is devoted to proving rigorously that almost all of these transonic shock solutions are stable, under multidimensional small perturbations of the upcoming supersonic flows and back pressures at the exits of ducts in suitable function spaces. This manifests that friction has a stabilization effect on transonic shocks in ducts, in consideration of previous works have shown that transonic shocks in purely steady Euler flows are not stable in such ducts. Except its implications to applications, since frictions lead to a stronger coupling between the elliptic and hyperbolic parts of the three-dimensional steady subsonic Euler system, we develop the framework established in previous works to study more complex and interesting Venttsel problems of nonlocal elliptic equations.

math.AP↗
arXiv2018

Subsonic flows passing a duct for three-dimensional steady compressible Euler system with friction

For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such flows are called Fanno flow in engineering. We formulate a boundary value problem for subsonic flows, and study their stability under multidimensional small perturbations of boundary conditions. Since the subsonic Euler system is of elliptic-hyperbolic composite-mixed type, this is achieved by using the framework established in [L. Liu; G. Xu; H. Yuan: Stability of spherically symmetric subsonic flows and transonic shocks under multidimensional perturbations. Adv. Math. 291 (2016), 696--757], and establishing an iteration scheme, which involves solving a second order nonlocal elliptic equation.

math.AP↗
arXiv2018

Short Distance Modification of a Gravitational System and its Optical Analog

Motivated by developments in string theory, such as T-duality, it has been proposed that the geometry of spacetime should have an intrinsic minimal length associated with it. This would modify the short distance behavior of quantum systems studied on such a geometry, and an optical analog for such a short distance modification of quantum system has also been realized by using non-paraxial nonlinear optics. As general relativity can be viewed as an effective field theory obtained from string, it is expected that this would also modify the short distance behavior of general relativity. Now the Newtonian approximation is a valid short distance approximation to general relativity, and Schrodinger-Newton equation can be obtained as a non-relativistic semi-classical limit of such a theory, we will analyze the short distance modification of Schrodinger-Newton equation from an intrinsic minimal length in the geometry of spacetime. As an optical analog of the Schrodinger-Newton equation has been constructed, it is possible to optically realize this system. So, this system is important, and we will numerical analyze the solutions for this system. It will be observed that the usual Runge-Kutta method cannot be used to analyze this system. However, we will use a propose and use a new numerical method, which we will call as the two step Runge-Kutta method, for analyzing this system.

physics.gen-ph↗
arXiv2018

Little Strings, Quasi-topological Sigma Model on Loop Group, and Toroidal Lie Algebras

We study the ground states and left-excited states of the A_{k-1} N=(2,0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP^1 with target space the based loop group of SU(k). The ground states, described by L^2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.

hep-th↗
arXiv2017

Non-Local Deformation of a Supersymmetric Field Theory

In this paper, we will analyse a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such deformed N=1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will be only preserved for a free theory and will be broken by the inclusion of interaction terms.

hep-th↗
arXiv2017

Two-dimensional steady supersonic exothermically reacting Euler flows with strong contact discontinuity over Lipschitz wall

In this paper, we established the global existence of supersonic entropy solutions with a strong contact discontinuity over Lipschitz wall governed by the two-dimensional steady exothermically reacting Euler equations, when the total variation of both initial data and the slope of Lipschitz wall is sufficiently small. Local and global estimates are developed and a modified Glimm-type functional is carefully designed. Next the validation of the quasi-one-dimensional approximation in the domain bounded by the wall and the strong contact discontinuity is rigorous justified by proving that the difference between the average of weak solution and the solution of quasi-one-dimensional system can be bounded by the square of the total variation of both initial data and the slope of Lipschitz wall. The methods and techniques developed here is also helpful for other related problems.

math.AP↗
arXiv2017

Four-Dimensional N=2 Supersymmetric Theory with Boundary as a Two-Dimensional Complex Toda Theory

We perform a series of dimensional reductions of the 6d, $\mathcal{N}=(2,0)$ SCFT on $S^2\timesΣ\times I\times S^1$ down to 2d on $Σ$. The reductions are performed in three steps: (i) a reduction on $S^1$ (accompanied by a topological twist along $Σ$) leading to a supersymmetric Yang-Mills theory on $S^2\timesΣ\times I$, (ii) a further reduction on $S^2$ resulting in a complex Chern--Simons theory defined on $Σ\times I$, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of $S^2$ and $S^1$, and (iii) a final reduction to the boundary modes of complex Chern--Simons theory with the Nahm pole boundary condition at both ends of the interval $I$, which gives rise to a complex Toda CFT on the Riemann surface $Σ$. As the reduction of the 6d theory on $Σ$ would give rise to an $\mathcal{N}=2$ supersymmetric theory on $S^2\times I\times S^1$, our results imply a 4d-2d duality between four-dimensional $\mathcal{N}=2$ supersymmetric theory with boundary and two-dimensional complex Toda theory.

hep-th↗
arXiv2017

Short distance modification of the quantum virial theorem

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

hep-th↗
arXiv2017

Modification of Schrödinger-Newton equation due to braneworld models with minimal length

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schrödinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

hep-th↗