The Relationship between the Darcy and Poiseuille Laws

The Poiseuille and Darcy laws describe the velocity of groundwater flow under laminar conditions. These laws were deducted empirically in conduit and porous systems, respectively, and are widely used to model the groundwater flow. The analytical relationship between these hydraulic laws has been found by draining a tank-reservoir. Based on equations found, the discharge in a conduit under the Poiseuille law can be transformed in the same amount flowing inside a darcian system, and vice versa. This transformation occurs, for example, in karst aquifers, from the matrix to karst conduits during discharge phases, and from conduits to matrix during recharge phases.

INFLUENCE OF POLYMORPHIC TRANSFORMATIONS ON ANISOTROPY OF THE SURFACE ENERGY AND THE WORK FUNCTION OF THE ELECTRON OF LITHIUM

На базе электронно-статистического метода показана связь и проведена оценка поверхностной энергии и работы выхода электрона граней кристаллов лития с учетом дисперсионного, поляризационного и осцилляционного взаимодействия атомов поверхностного слоя. Считалось, что кристаллическая решетка не имеет дефектов. Модифицированы выражения поправок и аналитического соотношения, связывающего работу выхода электрона и поверхностную энергию с учетом типа кристаллической решетки и ориентации граней. Рассчитана работа выхода электрона и поверхностная энергия гладких граней при предельных температурах существования полиморфных фаз лития. Установлено влияние полиморфных превращений и температуры на анизотропию. Температурный коэффициент работы выхода электрона бездефектного кристалла положителен и составляет порядка 0,1-1 мэВ. Результаты расчетов хорошо согласуются с экспериментальными данными для поликристаллов. On the basis of the electronic-statistical method, a relationship is obtained and the surface energy and the work function of the electron of the faces of lithium crystals are estimated, taking into account the dispersion, polarization, and oscillatory interactions of the atoms of the surface layer. It was assumed that the crystal lattice has no defects. The expressions for the corrections and an analytical relationship between the work function of the electron and the surface energy are modified taking into account the type of the crystal lattice and the orientation of the faces. The work function of the electron and the surface energy of smooth faces are calculated at the limiting temperatures of the existence of polymorphic lithium phases. The influence of polymorphic transformations and temperature on the anisotropy is established. The temperature coefficient of the work function of an electron in a defect-free crystal is positive and amounts to about 0,1-1 meV. The calculation results are in good agreement with the experimental data for polycrystals.

Investigation of the width of the entry of an excavator when loading a mobile crushing plant in the conditions of the Angren coal mine of Uzbekistan

This article presents the results of studies to establish the optimal entry width for an excavator working in conjunction with mobile crushing plants in the development of overburden of the Angren open pit. According to the results of the research, an analytical relationship was established to determine the maximum productivity of the mining system “excavator-mobile crushing-reloading-conveyor complex” with cyclical-flow technology. A structural diagram has been developed that allows you to select the type and determine the main technological parameters of the equipment with the selected criteria for evaluating the effectiveness of the complexes. It has been established that the choice of equipment for conveyor lines should be carried out taking into account the mutual influence of adjacent technological links of the central heating systems, including the influence of the excavator-crushing and crushing-conveyor complexes on the efficiency of their mutual functioning within the framework of the adopted system as a whole. A functional graphical dependence of the excavator performance on the face width was obtained, taking into account the relationship of all technological parameters of the face. It has been established that the maximum excavator productivity of 1478.1 m3/hr is achieved with an excavator entry width of 17.4 m for the conditions of the Angren open pit. The resulting schedule makes it possible to assess the possibility of increasing the operational performance of single-bucket shovel excavators under various conditions of work, as well as to continue the optimization of excavation.

A theory of viscoelastic crack growth-Revisited

A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

A theory of viscoelastic crack growth-Revisited

A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.

Using Parallel Coordinates in Optimization of Nano-Particle Drug Delivery

Nanoparticle drug delivery better targets neoplastic lesions than free drugs and thus has emerged as safer form of cancer therapy. Nanoparticle design variables are important determinants of efficacy as they influence the drug biodistribution and pharmacokinetics. Previously, we determined optimal designs through mechanistic modeling and optimization. However, the numerical nature of the tumor model and numerous candidate nanoparticle designs hinder hypothesis generation and treatment personalization. In this paper, we utilize the parallel coordinates technique to visualize high-dimensional optimal solutions and extract correlations between nanoparticle design and treatment outcomes. We found that at optimality, two major design variables are dependent, and thus the optimization problem can be reduced. In addition, we obtained an analytical relationship between optimal nanoparticle sizes and optimal distribution, which could facilitate the utilization of tumors models in preclincal studies. Our approach has simplified the results of the previously integrated modeling and optimization framework developed for nanotherapy and enhanced the interpretation and utilization of findings. Integrated mathematical frameworks are increasing in the medical field, and our method can be applied outside nanotherapy to facilitate clinical translation of computational methods.

Analysis of Free Vibration of Hydraulic Opposing Cylinder Controlled by Servo Valve

The fluid transmission medium has large compressibility and low rigidity, and its physical properties are extremely sensitive to state parameters such as flow, pressure and temperature. Therefore, compared with the mechanical transmission system, the natural frequency of the fluid transmission system is relatively low and has time-varying characteristics. After a wide frequency range changing of the load frequency and long-term operation, the excitation frequency of the fluid transmission system is more likely to approach its natural frequency and causes resonance, which seriously affects the normal operation of the system. Therefore, taking the hydraulic opposing cylinder controlled by servo valve as the research object, based on the analytical relationship between the dynamic bulk modulus and the equivalent stiffness of oil, the vibration dynamics models and equations of the system is established by using the lumped parameter method. Through the free vibration analysis, the natural frequencies and main vibration modes of the system are determined and the sensitivity changes of the natural frequencies to the design parameters are revealed. The maximum error between the theoretical modal frequency and the experimental one is 3.77%, which verifies the correctness of the dynamic model of the system. This research can provide a theoretical reference for the optimization of the dynamic performance of the hydraulic transmission system.

Studies on Frequency Response Characteristics of High-Speed Railway Train End Relationship Test System with Flexible Bases

A train end relationship test system was installed with a Stewart parallel robot on the reaction bases perpendicular to the ground, to test the fatigue and durability of train end relationship components, such as the transfixion way of a high-speed railway train. The flexibility of the reaction bases affected the test accuracy of the train end relationship components within a test frequency band range. In this paper, a coupling characteristic model was established between the flexible bases and the parallel robot. Then, the analytical relationship was analyzed between the natural frequency of the bases and the natural frequency of the parallel robot. Moreover, a design criterion was proposed for the natural frequency of the reaction bases. It was considered that when the natural frequency of the bases was not less than five times the natural frequency of the parallel robot, the influence of the flexibility of the bases on the test accuracy can be ignored. The validity of the design criterion was verified by the simulation results.

Drug-induced resistance evolution necessitates less aggressive treatment

Increasing body of experimental evidence suggests that anticancer and antimicrobial therapies may themselves promote the acquisition of drug resistance by increasing mutability. The successful control of evolving populations requires that such biological costs of control are identified, quantified and included to the evolutionarily informed treatment protocol. Here we identify, characterise and exploit a trade-off between decreasing the target population size and generating a surplus of treatment-induced rescue mutations. We show that the probability of cure is maximized at an intermediate dosage, below the drug concentration yielding maximal population decay, suggesting that treatment outcomes may in some cases be substantially improved by less aggressive treatment strategies. We also provide a general analytical relationship that implicitly links growth rate, pharmacodynamics and dose-dependent mutation rate to an optimal control law. Our results highlight the important, but often neglected, role of fundamental eco-evolutionary costs of control. These costs can often lead to situations, where decreasing the cumulative drug dosage may be preferable even when the objective of the treatment is elimination, and not containment. Taken together, our results thus add to the ongoing criticism of the standard practice of administering aggressive, high-dose therapies and motivate further experimental and clinical investigation of the mutagenicity and other hidden collateral costs of therapies.

A theory of viscoelastic crack growth-Revisited (Revised)

A theory of viscoelastic crack growth developed nearly five decades ago is generalized to express traction in the so-called fracture process zone or failure zone as a function of the crack opening displacement (COD). In earlier work, except for minor exceptions, traction was specified as a function of location. The new model leads to a nonlinear double integral that has to be solved for the COD before crack growth can be predicted. First, a closed-form, accurate approximation is found for a linear elastic body. We then show that this COD may be easily and accurately extended to linear viscoelasticity using a realistic, broad spectrum creep compliance. An analytical relationship connecting the stress intensity factor to crack speed then follows. Consistent with earlier work, it is defined almost entirely by the creep compliance. Five different failure zone tractions are employed; their differences are shown to have little effect on crack growth other than through a speed shift factor. The Appendix discusses initiation of growth.