Reduced description method in the kinetic theory of Brownian motion with active fluctuations

We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in presence of active fluctuations. The approach is based on a generalization of Bogolyubov–Peletminskii reduced description method applied to the systems of many active particles. It is shown that the microscopic approach developed allows to construct the kinetic theory of two- and three-dimensional systems of active particles in presence of non-linear friction (dissipative interaction) and an external random field with active fluctuations. The kinetic equations for these systems in case of a weak interaction between the particles (both potential and dissipative ones) and low-intensity active fluctuations are obtained. We demonstrate particular cases in which the derived kinetic equations have solutions that match the results known in the literature. In addition, analysis of particular solutions showed that in the case of a friction force linearly dependent on the speed of structural units, the manifestation of self-propelling properties in the process of evolution of an active medium may be due to the local nature of active fluctuations

Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems

In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function (PDF) without a need to solve the GFPE. We employ our method to obtain the GFPE and PDFs for free generalized Brownian motion and the one in harmonic potential for the case of power-law correlation function of the noise. We prove the fact that the considered systems may be described with Einstein-Smoluchowski equation at high viscosity levels and long times. We also compare the results with those obtained by other authors. At last, we calculate PDF of thermodynamical work in the stochastic system which consists of a particle embedded in a harmonic potential moving with constant velocity, and check the work fluctuation theorem for such a system.Comment: 14 page

Stationary States in Bistable System Driven by L\'evy Noise

We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric L\'evy noise. The shape of the stationary PDF is found analytically for the particular case of the L\'evy index \alpha = 1 (Cauchy noise). For an arbitrary L\'evy index we employ numerical methods based on the solution of the stochastic Langevin equation and space fractional kinetic equation. In contrast with the bistable system driven by Gaussian noise, in the L\'evy case the positions of maxima of the stationary PDF do not coincide with the positions of minima of the bistable potential. We provide a detailed study of the distance between the maxima and the minima as a function of the potential's depth and L\'evy noise parameters.Comment: Accepted to EPJS

Вплив добавок селену в комбікорми на хімічний склад, енергетичну та біологічну цінність м’яса каченят

According to modern classification of trace elements, which is based on their biological significance for living organisms, selenium is classified as a group of vital or biogenic elements. As a biotic element, it has unique physico-chemical and biochemical properties and, with adequate intake into the body of farm animals and poultry has a positive effect on a number of physiological processes. The discovery of biological properties of selenium became the basis for its use first in the prevention and treatment of many diseases associated with a deficiency of this trace element, and later – as a stimulator of growth and development of young animals, as well as in order to increase egg production, poultry safety, improve the incubation characteristics of eggs and several other productive qualities. Scientists who have studied the effects of selenium on poultry have paid relatively little attention to meat quality. The effect of additives of different selenium doses in compound feed on the chemical composition, energy and biological value of Ukrainian white breed ducklings’ meat was studied in the scientific and economic experiment. Four groups of ducklings with 100 heads in each groups were formed to conduct the scientific and economic experiment. The duration of the experiment was 56 days and corresponded to the period of raising ducklings for meat. The ducklings of the first control group did not receive selenium supplementation. Selenium was additionally introduced into compound feed for poultry of the experimental groups in the following amount, mg/kg: the second group – 0.2; the third – 0.4 and the fourth – 0.6. It was established that the introduction of selenium into compound feed in the studied dose did not significantly affect to the quality of ducklings’ meat, although it had a positive effect on some indicators that characterize its chemical composition, nutritional and biological value. Among the experimental groups, ducklings of the third and fourth groups, which were injected with selenium into compound feed at the rate of 0.4 and 0.6 mg/kg, stood out in terms of meat quality.Згідно з сучасною класифікацією мікроелементів, в основі якої лежить їх біологічне значення для живих організмів, селен віднесено до групи життєво необхідних, або біогенних елементів. Як біотичний елемент він володіє унікальними фізико-хімічними та біохімічними властивостями і при адекватному надходженні в організм сільськогосподарських тварин і птиці здійснює позитивний вплив на ряд фізіологічних процесів. Відкриття біологічних властивостей селену стало підставою для використання його спочатку у профілактиці та лікуванні багатьох хвороб, пов’язаних із дефіцитом цього мікроелементу, а згодом – як стимулятора росту і розвитку молодняку, а також з метою підвищення несучості, збереженості птиці, поліпшення інкубаційних характеристик яєць та низки інших продуктивних якостей. Вчені, які вивчали дію селену на організм сільськогосподарської птиці, приділяли відносно мало уваги якості м’яса. У науково-господарському досліді вивчено вплив добавок різних доз селену в комбікорми на хімічний склад, енергетичну та біологічну цінність м’яса каченят української білої породи. Для проведення науково-господарського досліду було сформовано чотири групи каченят по 100 голів у кожній. Тривалість досліду становила 56 дні і відповідала періоду вирощування каченят на м’ясо. Каченята першої контрольної групи добавку селену не одержували. У комбікорми для птиці дослідних груп додатково вводили селен у такій кількості, мг/кг: друга група – 0,2; третя – 0,4 та четверта – 0,6. Встановлено, що введення в комбікорми селену, в дозах які вивчалися, істотно не вплинуло на якість м’яса каченят, хоча позитивно позначилося на деяких показниках, що характеризують його хімічний склад, поживну та біологічну цінність. Серед дослідних груп, вигідно виділялися за якістю м’яса каченята третьої та четвертої групи, яким у комбікорми вводили селен із розрахунку 0,4 та 0,6 мг/кг відповідно

Curve-guided 5-axis CNC flank milling of free-form surfaces using custom-shaped tools

A new method for 5-axis flank milling of free-form surfaces is proposed. Existing flank milling path-planning methods typically use on-market milling tools whose shape is cylindrical or conical, and is therefore not well-suited for meeting fine tolerances for manufacturing of benchmark free-form surfaces like turbine blades, gears, or blisks. In contrast, our optimization-based framework incorporates the shape of the tool into the optimization cycle and looks not only for the milling paths, but also for the shape of the tool itself. Given a free-form reference surface and a guiding path that roughly indicates the motion of the milling tool, tangential movability of quadruplets of spheres centered along a straight line is analyzed to indicate possible shapes and their motions. This results in $G^1$ Hermite data in the space of rigid body motions that are interpolated and further optimized, both in terms of the motion and the shape of the milling tool itself. We demonstrate our algorithm on synthetic free-form surfaces and industrial benchmark datasets, showing that the use of custom-shaped tools is capable of meeting fine industrial tolerances and outperforms the use of classical, on-market tools.RYC-2017-2264

Лікування собак за ентеропатії із PLE

One of the most common and poorly understood diseases in dogs and cats is enteropathy with PLE.  The disease occurs, according to studies, in dogs of 2-6 years old breeds: Yorkshire terrier, German shepherd, and Golden Retriever. The disease in most cases is manifested by anorexia, polydipsia, diarrhea, fever up to 39.7 °C, tachycardia (145–170 bpm), and abdominal pain. In sick dogs, leucocytosis (21.0 ± 0.50 g/l), thrombocytosis (480.0 ± 10.13 g/l), oligocythaemia (4.8 ± 0.12 T/l), oligochromemia (109.0 ± 5.06 g/l), decrease in haematocrit value (29.0 ± 1.21 % in healthy people 42.3 ± 0.65 %). In a biochemical study of blood in dogs with enteropathy with PLE, hypoproteinaemia (38.2 ± 0.65 g/l), hypoalbuminemia (9.6 ± 0.61 g/l); hyperazotemia (8.6 ± 0.37 mmol/l), hypercholesterolemia (8.0 ± 0.23 mmol/l), hyperenzymemia of LF (ALP) and ALT (alanine aminotransferase), hyponatremia, hypokalaemia, hypochloraemia, decreased blood pH values (7.26 ± 0.013), HCO3- (15.3 ± 0.71 mmol/L) and AG (2.85 ± 0.084 mmol/L, in healthy people 14.3 ± 1.17 mmol/L). The diagnosis of enteropathy with PLE was confirmed by studies in feces of α1-antitrypsin, which in sick dogs with PLE was more than 22 mg/dL (in clinically healthy dogs up to 18 mg/dL). A treatment regimen with trometamol, Xylat, Disparkol, Voluven, Reopoliglukin, Maropitant, prednisolone, α-lysine escinat, albumin, Presorb and feed additives Vivonex Ten Elemental and Royal Canin Recoveri promotes the recovery of dogs, prevents their death. Under the action of drugs, erythro- and leuсocytopoiesis, protein-synthesizing (the content of total protein and albumin increased by 34.3 and 246.9 %, respectively) and urea-forming functions of hepatocytes improves. We have developed and tested a treatment scheme that restores the acid-base balance of the body, as indicated by the physiological values of blood pH, bicarbonates, anion gap (AG), Na+, K+, Cl- and Mg+.Одним із поширених і маловивчених захворювань у собак і котів є ентеропатія із PLE. Зустрічається захворювання, згідно досліджень у собак 2–6-річного віку порід: йоркширський тер’єр, німецька вівчарка, голденретривер. Захворювання у більшості випадків проявляється анорексією, полідипсією, діареєю, підвищенням температури тіла до 39,7 оС, тахікардією (145–170 уд./хв), абдомінальним болем. У хворих собак лейкоцитоз (21,0 ± 0,50 Г/л), тромбоцитоз (480,0 ± 10,13 Г/л), олігоцитемія (4,8 ± 0,12 Т/л), олігохромемія (109,0 ± 5,06 г/л), зменшення гематокритної величини (29,0 ± 1,21 % у здорових 42,3 ± 0,65 %). За біохімічного дослідження крові у собак за ентеропатії із PLE гіпопротеїнемія (38,2 ± 0,65 г/л), гіпоальбумінемія (9,6 ± 0,61 г/л); гіперазотемія (8,6 ± 0,37 ммоль/л), гіперхолестеролемія (8,0 ± 0,23 ммоль/л), гіперензимемія ЛФ (лужна фосфатаза) і АлАТ (аланінова амінотрансфераза), гіпонатріємія, Гіпокаліємія, гіпохлоремія, знижені величини рН крові (7,26 ± 0,013), HCO3- (15,3 ± 0,71 ммоль/л) і AG (2,85 ± 0,084 ммоль/л, у здорових 14,3 ± 1,17 ммоль/л). Діагноз на ентеропатію із PLE підтверджували дослідженнями у калі α1-антитрипсину, який у хворих собак із PLE був більше 22 мг/дл (у клінічно здорових до 18 мг/дл). Лікувальна схема із застосуванням Трометамолу, Ксилату, Дизпарколу, Волювену, Реополіглюкіну, Маропітанту, Преднізолону, α-лізину есцинату, альбуміну, Пресорбу і кормових добавок Vivonex Ten Elemental та Royal Canin Recoveri сприяє одужанню собак, попереджує їх загибель. За дії лікарських засобів поліпшується еритро- і лейкоцитопоез, протеїносинтезувальна (уміст загального протеїну і альбумінів підвищився, відповідно, на 34,3 і 246,9 %) і сечовиноутворювальна функції гепатоцитів. Розроблена і апробована нами лікувальна схема відновлює кислотно-основний баланс організму, на що вказують фізіологічні величини рН крові, бікарбонатів, аніонного проміжку (AG), Na+, K+, Cl– і Mg+

Geometry and tool motion planning for curvature adapted CNC machining

CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface. On the geometric side, this leads to a new continuous transition between “dual” classical results in surface theory concerning osculating circles of surface curves and oscu- lating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software

Langevin equation in complex media and anomalous diffusion

The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such as the very complex and heterogeneous cell environment. Nevertheless, many questions are still open, such as the joint manifestation of statistical features in agreement with different models that can also be somewhat alternative to each other, e.g. continuous time random walk and fractional Brownian motion. To overcome these limitations, we propose a stochastic diffusion model with additive noise and linear friction force (linear Langevin equation), thus involving the explicit modelling of velocity dynamics. The complexity of the medium is parametrized via a population of intensity parameters (relaxation time and diffusivity of velocity), thus introducing an additional randomness, in addition to white noise, in the particle’s dynamics. We prove that, for proper distributions of these parameters, we can get both Gaussian anomalous diffusion, fractional diffusion and its generalizations.V.S. acknowledges BCAM Internship Program, Bilbao, for the financial support to her internship research period during which she developed her master’s thesis research useful for her master’s degree in Physics at University of Bologna. S.V. acknowledges the University of Bologna for the financial support through the ‘Marco Polo Programme’ for her PhD research period abroad spent at BCAM, Bilbao, useful for her PhD degree in Physics at University of Bologna. P.P. acknowledges financial support from Bizkaia Talent and European Commission through COFUND scheme, 2015 Financial Aid Program for Researchers, project number AYD–000–252 hosted at BCAM, Bilbao

Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable corresponding to this ensemble is statistically equivalent to a process driven by a non-autonomous stochastic differential equation with time-dependent drift and a white noise. In particular, the time scaling and the density function of such variable are driven by the population of timescales and of noise amplitudes, respectively. Moreover, we show that this variable is equivalent in distribution to a randomly-scaled Gaussian process, i.e., a process built by the product of a Gaussian process times a non-negative independent random variable. This last result establishes a connection with the so-called generalized grey Brownian motion and suggests application to model fractional anomalous diffusion in biological systems.”Marco Polo Programme” (University of Bologna

Constant probe orientation for fast contact-based inspection of 3D free-form surfaces using (3+2)-axis inspection machines

A new probe optimization method for contact based (3+2)-axis inspection machines is proposed. Given an inspection path of a stylus on a free-form surface, an optimal orientation of the stylus is computed such that (i) the inclination angle of the stylus is within a given angular range with respect to the surface normal, (ii) the motion of the stylus is globally collision free, and (iii) the stylus remains constant in the coordinate system of the measuring machine. The last condition guarantees that the inspection motion requires only the involvement of the three translational axes of the measuring machine. The numerical simulations were validated through physical experiments on a testcase of a tooth of a bevel gear due to the surface complexity and probe accessibility. This optimized method was compared to 3-axis and 5-axis inspection strategies, showing that the fixed (3+2)-axis stylus returns more accurate inspection results compared to the traditional 3-axis approach and similar to 5-axis approach.RYC-2017-2264