Mathematical simulation of the influence of surface roughness and mass loss on thermal protection

A mathematical model of the thermochemical destruction of carbon fiber-reinforced plastic in the presence of surface roughness and composite ablation is refined based on known theoretical results. It is shown that mass loss through rough surface ambiguously influences the intensity of heat exchange processes in thermal protective material. Results of numerical calculations are compared with known data

Poisson trace orders

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two approaches leading to the notion of Poisson trace orders. It is proved that all regular and reduced traces are always compatible with any Poisson order structure. The modified discriminant ideals of all Poisson trace orders are proved to be Poisson ideals and the zero loci of discriminant ideals are shown to be unions of symplectic cores, under natural assumptions (maximal orders and Cayley--Hamilton algebras). A base change theorem for Poisson trace orders is proved. A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3 and 4-dimensional Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum cluster algebras.Comment: 24 page

Mathematical modeling of heat and mass transfer in a thermal protection coating with gas flow fluctuations

The thermochemical destruction of a carbon fiber-reinforced polymer when affected by a high enthalpy fluctuating gas flow is simulated numerically. The possibility of controlling the heat transfer process in the composite material is studied

Weak splittings of quotients of Drinfeld and Heisenberg doubles

We investigate the fine structure of the simplectic foliations of Poisson homogeneous spaces. Two general results are proved for weak splittings of surjective Poisson submersions from Heisenberg and Drinfeld doubles. The implications of these results are that the torus orbits of symplectic leaves of the quotients can be explicitly realized as Poisson-Dirac submanifolds of the torus orbits of the doubles. The results have a wide range of applications to many families of real and complex Poisson structures on flag varieties. Their torus orbits of leaves recover important families of varieties such as the open Richardson varieties.Comment: 20 pages, AMS Late

AC Conductance in Dense Array of the Ge0.7_{0.7}Si0.3_{0.3} Quantum Dots in Si

Complex AC-conductance, $\sigma^{AC}$, in the systems with dense Ge$_{0.7}$Si$_{0.3}$ quantum dot (QD) arrays in Si has been determined from simultaneous measurements of attenuation, $\Delta\Gamma=\Gamma(H)-\Gamma(0)$, and velocity, $\Delta V /V=(V(H)-V(0)) / V(0)$, of surface acoustic waves (SAW) with frequencies $f$ = 30-300 MHz as functions of transverse magnetic field $H \leq$ 18 T in the temperature range $T$ = 1-20 K. It has been shown that in the sample with dopant (B) concentration 8.2$\times 10^{11}$ cm$^{-2}$ at temperatures $T \leq$4 K the AC conductivity is dominated by hopping between states localized in different QDs. The observed power-law temperature dependence, $\sigma_1(H=0)\propto T^{2.4}$, and weak frequency dependence, $\sigma_1(H=0)\propto \omega^0$, of the AC conductivity are consistent with predictions of the two-site model for AC hopping conductivity for the case of $\omega \tau_0 \gg$1, where $\omega=2\pi f$ is the SAW angular frequency and $\tau_0$ is the typical population relaxation time. At $T >$ 7 K the AC conductivity is due to thermal activation of the carriers (holes) to the mobility edge. In intermediate temperature region 4$< T<$ 7 K, where AC conductivity is due to a combination of hops between QDs and diffusion on the mobility edge, one succeeded to separate both contributions. Temperature dependence of hopping contribution to the conductivity above $T^*\sim$ 4.5 K saturates, evidencing crossover to the regime where $\omega \tau_0 <$1. From crossover condition, $\omega \tau_0(T^*)$ = 1, the typical value, $\tau_0$, of the relaxation time has been determined.Comment: revtex, 3 pages, 6 figure

Numerical study of the effect of rotation on the behavior of the conjugate heat and mass transfer on the surface of a spherically blunted cone exposed to a hypersonic flow at an angle of attack with ablation from the surface

The processes of heating a body in a high-enthalpy spatial flow with allowance for body rotation around its longitudinal axis and ablation of the thermal protection material are studied by means of mathematical simulation. The obtained solution of the problem in conjugate formulation allowed us to take into account the effect of nonisothermic characteristics of the shell on the heat and mass transfer in the boundary layer

Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio

Phonon bottleneck in p-type Ge/Si quantum dots

We study the effect of quantum dot size on the mid-infrared photo- and dark current, photoconductive gain, and hole capture probability in ten-period p-type Ge/Si quantum dot heterostructures. The dot dimensions are varied by changing the Ge coverage and the growth temperature during molecular beam epitaxy of Ge/Si(001) system in the Stranski-Krastanov growth mode. In all samples, we observed the general tendency: with decreasing the size of the dots, the dark current and hole capture probability are reduced, while the photoconductive gain and photoresponse are enhanced. Suppression of the hole capture probability in small-sized quantum dots is attributed to a quenched electron-phonon scattering due to phonon bottleneck