Интегральные методы решения задач тепломассопереноса: новая концепция (условие Дирихле)

On the basic of consideration of the heat-conduction problem for a semi-bounded space with a temperature profile defined by a parabola with an exponent n, a new concept of construction of constitutive involves the introduction of a local function for a heat flow or for the temperature, with is determined from the heat-conduction equation. The approach proposed made it possible to obtain a number of new integral relation: an improved integral for the temperature momentum, an integral of a quadratic heat flow, and an integral of a quadratic temperature function. Two Schemes of optimizing the exponent n with the use of the error norms E1 and are proposed. As compared to the Langford norm, the indicated error norms made it possible to substantially increase the approximation accuracy of solutions of the problem posed.На основе рассмотрения задачи теплопроводности для полуограниченного пространства с описанием температурного профиля параболой степени n предложена новая концепция построения определяющих интегральных соотношений. Данная концепция основана на введении локальной функции для теплового потока либо температуры, которые определяются из уравнения теплопроводности. Такой подход позволил получить ряд новых интегральных соотношений: улучшенное интегральное соотношение для температурного момента, интеграл квадратичного теплового потока, интеграл квадратичной температурной функции. Предложены две схемы оптимизации степени n на основе новых норм ошибки E1 и E1L. По сравнению с нормой Лангфорда удалось значительно повысить аппроксимационную точность решений поставленной задачи

ВЫСОКОТОЧНЫЕ ПОЛИНОМИАЛЬНЫЕ РЕШЕНИЯ КЛАССИЧЕСКОЙ ЗАДАЧИ СТЕФАНА

The Stefan problem is of extreme importance in investigating many physical processes and technologies. Solving the Stefan problem reduces to calculating a temperature (concentration) profile when an interphase boundary is to be determined. High-accuracy polynomial solutions of the Stefan problem for a semi-infinite medium with Dirichlet/Neumann boundary conditions and general conditions are presented. An initial medium temperature is assumed to be equal to a phase change temperature. With the use of the integral method of boundary characteristics, based on multiple integration of the heat conduction equation, sequences of identical equalities with different boundary conditions are obtained and, as a result, polynomial solutions are constructed. The high efficiency of the approach proposed is illustrated with various examples. The solutions based on the 2nd and 3rd degree polynomials are more exact in comparison to the known solutions. The accuracy of calculating the position of the interphase boundary by means of 4th and 5th degree polynomials is several orders of magnitude higher than that of numerical methods. The solutions obtained can be considered as conditionally exact because of negligibly small errors in determining the interphase boundary and the temperature profile.Задача Стефана, под которой понимают класс математических моделей, описывающих в основном тепловые и диффузионные процессы с фазовыми превращениями, занимает чрезвычайно важное место во многих физических процессах и технических приложениях. Решение задачи Стефана состоит в вычислении температурного (концентрационного) профиля с определением закона перемещения межфазной границы. Представлены высокоточные полиномиальные решения задачи Стефана для полуограниченного пространства с граничными условиями Дирихле, Неймана, а также общего вида. Начальная температура принималась равной температуре фазового превращения. На основе интегрального метода граничных характеристик, основанного на многократном интегрировании уравнения теплопроводности, получены последовательности из тождественных равенств для разных граничных условий. Далее построены полиномиальные решения. На тестовых примерах продемонстрирована высокая эффективность предложенного подхода. При полиномах второй и третьей степени полученные решения значительно превзошли по точности аппроксимации известные. При полиномах четвертой и пятой степени точность расчета межфазной границы на несколько порядков превзошла точность численных методов. Полученные решения можно условно считать точными, поскольку ошибки расчета межфазной границы и температурного профиля составляют ничтожно малые величины.

Heritability and Artificial Selection on Ambulatory Dispersal Distance in Tetranychus urticae: Effects of Density and Maternal Effects

Dispersal distance is understudied although the evolution of dispersal distance affects the distribution of genetic diversity through space. Using the two-spotted spider mite, Tetranychus urticae, we tested the conditions under which dispersal distance could evolve. To this aim, we performed artificial selection based on dispersal distance by choosing 40 individuals (out of 150) that settled furthest from the home patch (high dispersal, HDIS) and 40 individuals that remained close to the home patch (low dispersal, LDIS) with three replicates per treatment. We did not observe a response to selection nor a difference between treatments in life-history traits (fecundity, survival, longevity, and sex-ratio) after ten generations of selection. However, we show that heritability for dispersal distance depends on density. Heritability for dispersal distance was low and non-significant when using the same density as the artificial selection experiments while heritability becomes significant at a lower density. Furthermore, we show that maternal effects may have influenced the dispersal behaviour of the mites. Our results suggest primarily that selection did not work because high density and maternal effects induced phenotypic plasticity for dispersal distance. Density and maternal effects may affect the evolution of dispersal distance and should be incorporated into future theoretical and empirical studies

Determination of quantum numbers for several excited charmed mesons observed in B- -> D*(+)pi(-) pi(-) decays

A four-body amplitude analysis of the B − → D * + π − π − decay is performed, where fractions and relative phases of the various resonances contributing to the decay are measured. Several quasi-model-independent analyses are performed aimed at searching for the presence of new states and establishing the quantum numbers of previously observed charmed meson resonances. In particular the resonance parameters and quantum numbers are determined for the D 1 ( 2420 ) , D 1 ( 2430 ) , D 0 ( 2550 ) , D ∗ 1 ( 2600 ) , D 2 ( 2740 ) and D ∗ 3 ( 2750 ) states. The mixing between the D 1 ( 2420 ) and D 1 ( 2430 ) resonances is studied and the mixing parameters are measured. The dataset corresponds to an integrated luminosity of 4.7     fb − 1 , collected in proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV with the LHCb detector

Updated measurement of decay-time-dependent CP asymmetries in D-0 -> K+ K- and D-0 -> pi(+)pi(-) decays

A search for decay-time-dependent charge-parity (CP) asymmetry in D0 \u2192 K+ K 12 and D0 \u2192 \u3c0+ \u3c0 12 decays is performed at the LHCb experiment using proton-proton collision data recorded at a center-of-mass energy of 13 TeV, and corresponding to an integrated luminosity of 5.4 fb^ 121. The D0 mesons are required to originate from semileptonic decays of b hadrons, such that the charge of the muon identifies the flavor of the neutral D meson at production. The asymmetries in the effective decay widths of D0 and anti-D0 mesons are determined to be A_\u393(K+ K 12) = ( 124.3 \ub1 3.6 \ub1 0.5) 7 10^ 124 and A_\u393(\u3c0+ \u3c0 12) = (2.2 \ub1 7.0 \ub1 0.8) 7 10^ 124 , where the uncertainties are statistical and systematic, respectively. The results are consistent with CP symmetry and, when combined with previous LHCb results, yield A_\u393(K+ K 12) = ( 124.4 \ub1 2.3 \ub1 0.6) 7 10^ 124 and A_\u393(\u3c0+ \u3c0 12) = (2.5 \ub1 4.3 \ub1 0.7) 7 10^ 124

Updated measurement of decay-time-dependent CP asymmetries in D-0 -> K+ K- and D-0 -> pi(+)pi(-) decays

A search for decay-time-dependent charge-parity (CP) asymmetry in D-0 -> K+ K- and D-0 -> pi(+)pi(-) eff decays is performed at the LHCb experiment using proton-proton collision data recorded at a center-of-mass energy of 13 TeV, and corresponding to an integrated luminosity of 5.4 fb(-1). The D-0 mesons are required to originate from semileptonic decays of b hadrons, such that the charge of the muon identifies the flavor of the neutral D meson at production. The asymmetries in the effective decay widths of D-0 and (D) over bar (0) mesons are determined to be A(Gamma)(K+ K-) = (-4.3 +/- 3.6 +/- 0.5) x 10(-4) and A(Gamma) (K+ K- ) = (2.2 +/- 7.0 +/- 0.8) x 10(-4), where the uncertainties are statistical and systematic, respectively. The results are consistent with CP symmetry and, when combined with previous LHCb results, yield A(Gamma) (K+ K-) = (-4.4 +/- 2.3 +/- 0.6) x 10(-4) and A(Gamma) (pi(+)pi(-))= (2.5 +/- 4.3 +/- 0.7) x 10(-4)

Investigation of the influence of gear milling modes of cylindrical gears on the quality parameters of tooth surfaces

Summary. The current state of the problem of studying the influence of gear milling modes of cylindrical gears on the quality parameters of the tooth surfaces is considered. Insufficient study of this problem and inconsistency of the available results is shown. The relevance and possible areas of application of this research are shown. The research objects are described (the effect of the cutting speed V and feed S during hobbing of cylindrical gears on the roughness parameter Ra, microhardness Hμ, residual stresses 1 and 2, σ1 and σ2 in the tooth surfaces), the accepted methods of planning experiments and presenting results. The results obtained are presented. It is established that the considered relationships can be modeled with sufficient accuracy by statistical methods and can be described by polynomials of the first or second degree. Shows the nature of the change Ra, Hμ, σ1 and σ2, with changes of V and S. Given are calculated according to Ra, Hμ, σ1 and σ2 from V and S