Minimal resistance of curves under the single impact assumption

We consider the hollow on the half-plane $\{ (x,y) : y \le 0 \} \subset \mathbb{R}^2$ defined by a function $u : (-1,\, 1) \to \mathbb{R}$, $u(x) < 0$, and a vertical flow of point particles incident on the hollow. It is assumed that $u$ satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph$(u)$ and goes away without hitting the graph of $u$ anymore. We solve the problem: find the function $u$ minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the $y$-axis. Assuming that the resistance of $u \equiv 0$ equals 1, we show that the minimal resistance equals $\pi/2 - 2\arctan(1/2) \approx 0.6435$. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730--2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space $\{(x_1,\ldots,x_d, y) : y \le 0 \} \subset \mathbb{R}^{d+1}$ is defined by a radial function $U$ satisfying the SIC, $U(x) = u(|x|)$, with $x = (x_1,\ldots,x_d)$, $u(\xi) < 0$ for $0 \le \xi < 1$, and $u(\xi) = 0$ for $\xi \ge 1$, and the flow is parallel to the $y$-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as $d \to \infty$

Ballistic magnon heat conduction and possible Poiseuille flow in the helimagnetic insulator Cu2_2OSeO3_3

We report on the observation of magnon thermal conductivity $\kappa_m\sim$ 70 W/mK near 5 K in the helimagnetic insulator Cu$_2$OSeO$_3$, exceeding that measured in any other ferromagnet by almost two orders of magnitude. Ballistic, boundary-limited transport for both magnons and phonons is established below 1 K, and Poiseuille flow of magnons is proposed to explain a magnon mean-free path substantially exceeding the specimen width for the least defective specimens in the range 2 K $<T<$ 10 K. These observations establish Cu$_2$OSeO$_3$ as a model system for studying long-wavelength magnon dynamics.Comment: 10pp, 9 figures, accepted PRB (Editor's Suggestion

COMPARATIVE ANALYSIS OF THE MOTIVATIONAL COMPONENT OF THE INDUSTRY-OUTPUT TARIFF AGREEMENTS IN THE INDUSTRIES OF FUEL & ENERGY COMPLEX

Industry tariff agreements have been studied from the point of view of the motivational component of staff labor in organizations of the fuel and energy complex. Criteria of comparison have been selected and the optimal labor motivation strategy in the oil, gas, coal and electric power industries has been revealed. Features and similar approaches in the organization of the motivation of the industries of the fuel and energy complex have been identified. World experience of the labor motivation in the fuel and energy industries, such as in the USA, Japan and in Europe has been examined in comparison with domestic practice in these sectors

Influence of severe plastic deformation on the structure and mechanical properties of eutectic Al-Zn-Mg-Fe-Ni alloy

The structure and phase evolution of the new eutectic high strength aluminium alloy Nikalin were investigated under high pressure torsion (HPT) by several numbers of the revolution of the anvil. The chemical composition of the investigated Nikalin alloy was as follows: Al (base)- 7.22Zn-2.95 Mg-0.52 Fe-0.57 Ni-0.2 Zr. (wt.%). The initial material was a coarse grained cast ingot after homogenization. It was established that the HPT process resulted in the deformation dissolution of the nanosized T-phase precipitates and the formation of a supersaturated aluminum solid solution simultaneously with the strong refinement of the structure to the grain-subgrain size of 130-150 nm. Due to that, the yield stress of the HPT alloy increased by a factor of 1.5, the ultimate tensile strength increased by a factor of 1.4, while preserving good ductility of 6-7%. The observed effect of the additional supersaturated solution upon HPT relative to the homogenized state appeared upon post-deformation annealing at 140 °C. An increase in the microhardness of the HPT alloy due to the MgZn2 phase precipitation was observed at 0.5- hours of annealing. © Published under licence by IOP Publishing Ltd.Russian Foundation for Basic Research, RFBR: 18-03-00102Ministry of Science and Higher Education of the Russian Federation: АААА-А18-118020190116-6The research was carried out within the state assignment of the Ministry of Science and Higher Education of the Russian Federation (theme “Structura”, № АААА-А18-118020190116-6) supported in part by RFBR (project № 18-03-00102). The electron microscopy investigations were performed at the Center of Collaborative Access “Testing Center of Nanotechnologies and Advanced Materials” of the M.N. Mikheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences

ON THE 75TH BIRTHDAY OF PROFESSOR VITALII VLADIMIROVICH ARESTOV

July 16, 2018, was the 75th birthday of famous Russian scientist, prominent mathematician, Doctor of Physics and Mathematics, Professor Vitalii Vladimirovich Arestov

Contemplation as a Special Psychological Phenomenon and a Form of Self-Therapy

Созерцание представляется важной составной частью ментальных процессов, состояний, а также свойств личности, не совпадая полностью ни с одним из базисных психических процессов. Особенностью процесса созерцания является его фактическое осознание индивидом как особого состояния, при том что не вполне осознается содержание созерцания и его трехчастная структура (предсозерцание, собственно созерцание и постсозерцание). Функциональной особенностью созерцания является внутренняя, скрытая переработка либо коррекция или трансформация микро-, мезо- и макросмыслов жизнедеятельности человека. Немаловажно также то, что этот процесс переосмысления, согласно полученным данным, весьма эмоционально позитивен для индивида. Процесс созерцания можно квалифицировать так же, как спонтанную психологическую самотерапию личности.Contemplation seems to be an important component of mental processes, states, and personality traits, not completely coinciding with any of the basic mental processes. A feature of the process of contemplation is its actual awareness by the individual as a special state, despite the fact that the content of contemplation and its tripartite structure (pre-contemplation, contemplation proper and post-contemplation) are not fully realized. A functional feature of contemplation is the internal, hidden processing, or correction or transformation of micro-, meso- and macro-meanings of human life. It is also important that this process of rethinking, according to the data obtained, is very emotionally positive for the individual. The process of contemplation can also be qualified as a spontaneous psychological self-therapy of the individual

Voltage Responses to Optical Pulses of Unbiased Normal and Superconducting Samples

The direct transformation of the energy of an incident high-energy photon into a measurable potential difference within an absorbing metal is investigated. Experimental evidence is presented that the effect arises from the inherent energy dependence of the electronic density of states, rather than from a simple temperature excursion. The similarities between the results on Al and YBa2Cu3O7 samples indicate that the effect is universal in nature. We assert it may be used as the basis of a fast, energy resolving, individual photon detector for the ultraviolet radiation and x-rays