Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Heat exchanger design for hot air ericsson-brayton piston engine

One of the solutions without negative consequences for the increasing energy consumption in the world may be use of alternative energy sources in micro-cogeneration. Currently it is looking for different solutions and there are many possible ways. Cogeneration is known for long time and is widely used. But the installations are often large and the installed output is more suitable for cities or industry companies. When we will speak about decentralization, the small machines have to be used. The article deals with the principle of hot-air engines, their use in combined heat and electricity production from biomass and with heat exchangers as primary energy transforming element. In the article is hot air engine presented as a heat engine that allows the conversion of heat into mechanical energy while heat supply can be external. In the contribution are compared cycles of hot-air engine. Then are compared suitable heat exchangers for use with hot air Ericsson-Brayton engine. In the final part is proposal of heat exchanger for use in closed Ericsson-Brayton cycle

New ways of renewable sources utilization for electricity production

Nowadays, different solutions for increasing energy production are investigated in the world. One of the ways is utilization of renewable energy sources in cogeneration devices - combined production of electricity and heat in one device, with a high overall efficiency. The article deals with principle of hot-air engine, its basic division and use in combined production of heat and electricity from biomass. The basic principle of engine is conversion of heat into mechanical energy, which is subsequently used for production of electricity. In the contribution is presented Stirling engine, which is driven by thermal energy from a concentrating solar collector and from biomass boiler

Influence of volume working fluid and ambient temperature on cooling efficiency of loop thermosyphon

Article deal with research of device for electrical component cooling used to heat transfer working fluid phase change. Amount of heat flux transferred by thermosyphon loop depend from amount working fluid and from ambient temperature where is heat removal too. In article is described proposal construction of thermosyphon loop, comparisons of his cooling efficiency if is filled 40 % and 50 % volume of working fluid and condenser (ambient) temperature from 20, 30 up to 40 °C at heat load from 40 to 360 W

Experimental determination of the working fluid volume for optimal function of the loop heat pipe

This experiment is concentrated on the working fluid of the heat pipe. The working fluid is an important part for the function of the heat pipe regarding the transfer of the heat. The measurements point out the appropriate quantity of the working fluid regarding the correct function of the loop heat pipe in the cooling of electronic components

Optimization principle of operating parameters of heat exchanger by using CFD simulation

Design of effective heat transfer devices and minimizing costs are desired sections in industry and they are important for both engineers and users due to the wide-scale use of heat exchangers. Traditional approach to design is based on iterative process in which is gradually changed design parameters, until a satisfactory solution is achieved. The design process of the heat exchanger is very dependent on the experience of the engineer, thereby the use of computational software is a major advantage in view of time. Determination of operating parameters of the heat exchanger and the subsequent estimation of operating costs have a major impact on the expected profitability of the device. There are on the one hand the material and production costs, which are immediately reflected in the cost of device. But on the other hand, there are somewhat hidden costs in view of economic operation of the heat exchanger. The economic balance of operation significantly affects the technical solution and accompanies the design of the heat exchanger since its inception. Therefore, there is important not underestimate the choice of operating parameters. The article describes an optimization procedure for choice of cost-effective operational parameters for a simple double pipe heat exchanger by using CFD software and the subsequent proposal to modify its design for more economical operation

The model of product distortion in AWJ cutting

V článku uvedeno Libor M. HlaváčThe abrasive water jet (AWJ) retardation inside the cut material, the characteristic phenomenon of the AWJ cutting, causes declination of the kerf sidewalls especially in corners and curvatures. This paper is aimed at a description of the origin of these negative consequences of jet retardation. The model for calculation of the limit traverse speed from both the jet parameters and material properties has been derived using laws of conservation. The equation expressing dependence of the angle between the tangent to the striation curve and the impinging jet axis on the depth of jet penetration into material has been used for evaluation of the product distortion in the cutting process. Proposed model has been applied for setting up the tilting angle of the cutting head during the AWJ cutting process to reduce the product shape distortion. The model was supplemented by geometrical analysis of curved parts of cut trajectories. The resulting equation makes possible to calculate the shift of the jet trajectory at the outlet side of the workpiece from its regular position determined by projection of the trajectory at the inlet side of the workpiece along the jet axis. The model is capable to determine the appropriate tilting angles of the cutting head for compensation of the jet retardation and the taper. The experimental data measured on metal samples seem to be in a good accordance with the proposed model.Web of Science621-416615