On stability in the maximum norm of difference scheme for nonlinear parabolic equation with nonlocal condition

We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate the stability and convergence of the difference scheme in the maximum norm. For this purpose, we use the M-matrices theory. We describe some new approach for the estimation of the error of solution and construct the majorant for it. Some conclusions and discussion of our approach are presented

On the stability of a weighted finite difference scheme for wave equation with nonlocal boundary conditions

We consider the stability of a weighted finite difference scheme for a linear hyperbolic equation with nonlocal integral boundary condition. By studying the spectrum of the transition matrix of the three-layered difference scheme we obtain a sufficient stability condition in a special matrix norm. *The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014)

Parabolinio tipo lygčių su nelokaliomis kraštinėmis sąlygomis sprendinių kokybinė analizė

The aim of the work is qualitative analysis of solutions of parabolic equations, non–negativity of solutions, investigation and modelling of physical parameters. All tasks were modelled using numerical analysis methods. Differential equations were solved using implicit finite difference method. Derived results could be used solving one–dimensional tasks with parabolic type equations in physics, biochemistry, chemistry and other sciences.Šio straipsnio tikslas – parabolinio tipo lygčių su nelokalia kraštine sąlyga skirtuminio uždavinio sprendinių neneigiamumo ir fizinių parametrų tyrimas. Buvo išnagrinėtos difuzijos ir difuzijos–konvekcijos lygtys. Siekiant optimizuoti tam tikrus fizinius parametrus, buvo parinkti labiausiai tinkami svoriai. Apskaičiuota srovė, maksimalus srovės gradientas, jautrumas ir reakcijos laikas. Nagrinėtų svorių aibėje kiekvienam parametrui rastas optimizuojantis svoris

Inactivation of Escherichia coli Using Nanosecond Electric Fields and Nisin Nanoparticles: A Kinetics Study

Nisin is a recognized bacteriocin widely used in food processing, however, being ineffective against gram-negative bacteria and in complex food systems. As a result, the research of methods that have cell wall–permeabilizing activity is required. In this study, electroporation to trigger sensitization of gram-negative bacteria to nisin-loaded pectin nanoparticles was used. As a model microorganism, bioluminescent strain of E. coli was introduced. Inactivation kinetics using nanosecond pulsed electric fields (PEFs) and nisin nanoparticles have been studied in a broad range (100–900 ns, 10–30 kV/cm) of pulse parameters. As a reference, the microsecond range protocols (100 μs × 8) have been applied. It was determined that the 20–30 kV/cm electric field with pulse duration ranging from 500 to 900 ns was sufficient to cause significant permeabilization of E. coli to trigger a synergistic response with the nisin treatment. The kinetics of the inactivation was studied with a time resolution of 2.5 min, which provided experimental evidence that the efficacy of nisin-based treatment can be effectively controlled in time using PEF. The results and the proposed methodology for rapid detection of bacteria inactivation rate based on bioluminescence may be useful in the development and optimization of protocols for PEF-based treatments

Modeling of defects in electronic navigation devices operating in extreme conditions

An investigation of the corrosive and mechanical destruction of microelectronic objects such as multipurpose sensors and navigating devices used in the airspace industry in extreme conditions such as variable temperature, pressure and environmental composition is described. The appearance and growth of micro cracks and other defects in metallic parts and conductors of micro devices due to external actions are investigated. The structural features of defect‐testing devices improved on the basis of magnetic modulation sensitive iron elements are analyzed. Mathematical modeling for the most characteristic types of defects is performed and the forecast growth of defects within 6 % accuracy is achieved. Santrauka Atlikti mikroelektronikos objektų, eksploatuojamų ekstremaliomis sąlygomis bei esant kintamoms temperatūroms, slėgiui, darbinės aplinkos sudėčiai, irimo tyrimai, tarp jų – mikroįtrūkimų ir kitų defektų atsiradimo bei augimo mikroprietaisų metalinėse dalyse ir laidininkuose. Pagerinti prietaisų, gaminamų fero-moduliacinių elementų pagrindu ir skirtų mikroprietaisų defektų kontrolei, konstruktyviniai sprendimai. Sudarytas matematinis modelis, leidžiantis analizuoti būdingiausių rūšių defektus ir iki 6 % tikslumu prognozuoti defektų plitimą. First Published Online: 14 Oct 2010 Reikšminiai žodžiai: defektų detektavimas, mikroįtrūkimas, matematinis įtrūkimų modeliavimas

Microwave Radar for Non-Destructive Express Testing of Electrical Properties of Semiconductor Materials

Microwave radar for non-destructive express testing of electrical properties of semiconductor materials which consists of pulsed magnet, transmitting and receiving antennas, high frequency generator, pulsed modulator and digital oscilloscope is described. In semiconductor specimen placed in pulsed magnetic field a magnetoplasmic wave is excited and propagated through the specimen. Delay time and attenuation of transmitted and reference signals are measured to find a value of concentration and mobility of free charge carriers in semiconductors. Experimental data of testing of InSb, n-InSb specimens are presented and acceptable for express testing correspondence of results was achieve

Baigtinių skirtumų schemų hiperbolinei lygčiai su integralinėmis kraštinėmis sąlygomis stabilumo tyrimas

The doctoral dissertation deals with the hyperbolic problem with nonlocal integral boundary conditions. The research object is the stability of finite difference approximation of the hyperbolic problem and eigenspectrum analysis. Partial differential equations of the hyperbolic type with integral conditions often occur in problems related to fluid mechanics, linear thermoelasticity, vibrations, etc. We consider hyperbolic equation on a rectangular domain, with classical initial conditions and nonlocal integral boundary conditions. We investigate the eigenstructure of the explicit finite difference scheme (FDS) for the hyperbolic problem with two integral boundary conditions, formulate and prove the sufficient stability condition of such scheme. We also investigate a class of weighted FDS with one weight parameter. We use the generalized characteristic functions to investigate eigenspectrum (complex and real) of discrete problem. We obtain the structure of eigenspectrum, formulate and prove stability conditions according to boundary parameters and weights of the scheme. We also consider a class of weighted schemes with two weights. Numerically modelling characteristic functions we obtain stability regions and restrictions on FDS weights. We obtain equivalence conditions for the Sturm–Liouville problem (which can be generalized to the evolution equations) to the algebraic eigenvalue problem

Analysis of microelectrode arrays for dielectrophoresis using the finite element method

Dielectrophoresis (DEP) force dependence on microelectrode array size parameters is presented in this work. Using finite element method numerical calculations for golden interdigitated electrodes have been performed and DEP force at nanometer heights dependence plots were made. Using theoretical modelling microelectrode width, spacing and thickness has been altered and gradient of electric field dependence plots have been analyzed. It was showed that electrode spacing reduction is the most effective way to achieve higher DEP forces. Also the influence of one size parameter on the gradient of electric field when the other two size parameters are being altered has been studied. It was determined that reduction of width below 10 μm when the spacing of the electrodes is less than 5 μm doesn’t have any impact on the gradient of electric field

On the stability of an explicit difference scheme for hyperbolic equation with integral conditions

On the stability of an explicit difference scheme for hyperbolic equation with integral conditions. The aim of the work is stability analysis of solution of finite difference method for hyperbolic equations. Trying to achieve formulated aim these tasks were solved: • a method of transformation of three-layered finite difference scheme into two-layered one was investigated; • a spectrum of transition matrix subject to the properties of second order differential operator Lambda was studied; • stability conditions of hyperbolic type equations with nonlocal conditions subject to boundary parameters were obtained; • numerical experiments, confirming theoretical derivations were made. Derived results could be used to solve one-dimensional tasks with hyperbolic equations in different sciences, to analyse spectrum structure of mathematical models and construct new numerical methods for solving hyperbolic PDEs

The application of pulsed magnets for investigations of electrical properties of semiconductors and manganites

The system for high magnetic field generation up to 50 T was developed and applied for measurements of resistance, concentration and mobility of free charge carriers of semiconductors and manganites. High frequency interferometer had expanded ranges of measurements and specimens of InSb, CdHgTe samples were investigated at room and liquid nitrogen temperature. Magnetoresistance of epitaxial and polycrystalline films was measured by two electrodes method. The resistance response to high magnetic field pulses up to 50 T was studied for thin films of LaCaMnO, Bi, BiSb with different magnetic and electric properties. Polycrystalline La-Ca-MnO films have no saturation effects in high magnetic fields and can be used to measure absolute value of the fields up to 35 T. Axial magnetic field was estimated by analytical and numerical methods and verified experimentally. Numerical analysis of pulsed magnets was performed by the finite element method. New constructing materials were applied in pulsed magnet design and multilayer construction of metal-matrix Cu-Nb micro composite wire wounded Zylon-epoxy composite reinforced inductor was developed