DEFF Research Database (Denmark)
Bahman, Amir Sajjad; Ma, Ke; Blaabjerg, Frede
2018-01-01
Detailed thermal dynamics of high power IGBT modules are important information for the reliability analysis and thermal design of power electronic systems. However, the existing thermal models have their limits to correctly predict these complicated thermal behavior in the IGBTs: The typically used...... thermal model based on one-dimensional RC lumps have limits to provide temperature distributions inside the device, moreover some variable factors in the real-field applications like the cooling and heating conditions of the converter cannot be adapted. On the other hand, the more advanced three......-dimensional thermal models based on Finite Element Method (FEM) need massive computations, which make the long-term thermal dynamics difficult to calculate. In this paper, a new lumped three-dimensional thermal model is proposed, which can be easily characterized from FEM simulations and can acquire the critical...
Calkins, Michael A; Julien, Keith; Nieves, David; Driggs, Derek; Marti, Philippe
2015-01-01
The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that whereas the leading order system satisfies fixed temperature boundary conditions implicitly, a double boundary layer structure is necessary to satisfy the fixed heat flux thermal boundary conditions. The boundary layers consist of a classical Ekman layer adjacent to the solid boundaries that adjust viscous stresses to zero, and a layer in thermal wind balance just outside the Ekman layers adjusts the temperature such that the fixed heat flux thermal boundary conditions are satisfied. The influence of these boundary layers on the interior geostrophically balanced convection is shown to be asymptotically weak, however. Upon defining a simple rescaling of the thermal variables, the leading order reduced system of governing equations are therefore equivalent for both boundary condit...
Impact of boundary conditions on the development of the thermal plume above a sitting human body
DEFF Research Database (Denmark)
Zukowska, Daria; Popiolek, Zbigniew J.; Melikov, Arsen Krikor
2010-01-01
The phenomenon of the thermal plume above a heat source has been reported in the literature as being influenced by a large number of factors. The objective of the present study is to identify the impact of the boundary conditions on the characteristics and development of the thermal plume above...
General 3D Lumped Thermal Model with Various Boundary Conditions for High Power IGBT Modules
DEFF Research Database (Denmark)
Bahman, Amir Sajjad; Ma, Ke; Blaabjerg, Frede
2016-01-01
Accurate thermal dynamics modeling of high power Insulated Gate Bipolar Transistor (IGBT) modules is important information for the reliability analysis and thermal design of power electronic systems. However, the existing thermal models have their limits to correctly predict these complicated...... thermal behaviors in the IGBTs. In this paper, a new three-dimensional (3D) lumped thermal model is proposed, which can easily be characterized from Finite Element Methods (FEM) based simulation and acquire the thermal distribution in critical points. Meanwhile the boundary conditions including...... the cooling system and power losses are modeled in the 3D thermal model, which can be adapted to different real field applications of power electronic converters. The accuracy of the proposed thermal model is verified by experimental results....
Directory of Open Access Journals (Sweden)
Petar Glišović
2015-01-01
Full Text Available Although there has been significant progress in the seismic imaging of mantle heterogeneity, the outstanding issue that remains to be resolved is the unknown distribution of mantle temperature anomalies in the distant geological past that give rise to the present-day anomalies inferred by global tomography models. To address this question, we present 3-D convection models in compressible and self-gravitating mantle initialised by different hypothetical temperature patterns. A notable feature of our forward convection modelling is the use of self-consistent coupling of the motion of surface tectonic plates to the underlying mantle flow, without imposing prescribed surface velocities (i.e., plate-like boundary condition. As an approximation for the surface mechanical conditions before plate tectonics began to operate we employ the no-slip (rigid boundary condition. A rigid boundary condition demonstrates that the initial thermally-dominated structure is preserved, and its geographical location is fixed during the evolution of mantle flow. Considering the impact of different assumed surface boundary conditions (rigid and plate-like on the evolution of thermal heterogeneity in the mantle we suggest that the intrinsic buoyancy of seven superplumes is most-likely resolved in the tomographic images of present-day mantle thermal structure. Our convection simulations with a plate-like boundary condition reveal that the evolution of an initial cold anomaly beneath the Java-Indonesian trench system yields a long-term, stable pattern of thermal heterogeneity in the lowermost mantle that resembles the present-day Large Low Shear Velocity Provinces (LLSVPs, especially below the Pacific. The evolution of subduction zones may be, however, influenced by the mantle-wide flow driven by deeply-rooted and long-lived superplumes since Archean times. These convection models also detect the intrinsic buoyancy of the Perm Anomaly that has been identified as a unique
Aeroelastic analysis of versatile thermal insulation (VTI) panels with pinched boundary conditions
Carrera, Erasmo; Zappino, Enrico; Patočka, Karel; Komarek, Martin; Ferrarese, Adriano; Montabone, Mauro; Kotzias, Bernhard; Huermann, Brian; Schwane, Richard
2014-03-01
Launch vehicle design and analysis is a crucial problem in space engineering. The large range of external conditions and the complexity of space vehicles make the solution of the problem really challenging. The problem considered in the present work deals with the versatile thermal insulation (VTI) panel. This thermal protection system is designed to reduce heat fluxes on the LH2 tank during the long coasting phases. Because of the unconventional boundary conditions and the large-scale geometry of the panel, the aeroelastic behaviour of VTI is investigated in the present work. Known available results from literature related to similar problem, are reviewed by considering the effect of various Mach regimes, including boundary layer thickness effects, in-plane mechanical and thermal loads, non-linear effects and amplitude of limit cycle oscillations. A dedicated finite element model is developed for the supersonic regime. The models used for coupling the orthotropic layered structural model with Piston Theory aerodynamic models allow the calculations of flutter conditions in case of curved panels supported in a discrete number of points. An advanced computational aeroelasticity tool is developed using various dedicated commercial softwares (CFX, ZAERO, EDGE). A wind tunnel test campaign is carried out to assess the computational tool in the analysis of this type of problem.
Directory of Open Access Journals (Sweden)
Ibukun Sarah Oyelakin
2016-06-01
Full Text Available In this paper we report on combined Dufour and Soret effects on the heat and mass transfer in a Casson nanofluid flow over an unsteady stretching sheet with thermal radiation and heat generation. The effects of partial slip on the velocity at the boundary, convective thermal boundary condition, Brownian and thermophoresis diffusion coefficients on the concentration boundary condition are investigated. The model equations are solved using the spectral relaxation method. The results indicate that the fluid flow, temperature and concentration profiles are significantly influenced by the fluid unsteadiness, the Casson parameter, magnetic parameter and the velocity slip. The effect of increasing the Casson parameter is to suppress the velocity and temperature growth. An increase in the Dufour parameter reduces the flow temperature, while an increase in the value of the Soret parameter causes increase in the concentration of the fluid. Again, increasing the velocity slip parameter reduces the velocity profile whereas increasing the heat generation parameter increases the temperature profile. A validation of the work is presented by comparing the current results with existing literature.
Directory of Open Access Journals (Sweden)
Yinhuan Ao
2017-01-01
Full Text Available This paper reported a comprehensive analysis on the diurnal variation of the Atmospheric Boundary Layer (ABL in summer of Badain Jaran Desert and discussed deeply the effect of surface thermal to ABL, including the Difference in Surface-Air Temperature (DSAT, net radiation, and sensible heat, based on limited GPS radiosonde and surface observation data during two intense observation periods of experiments. The results showed that (1 affected by topography of the Tibetan Plateau, the climate provided favorable external conditions for the development of Convective Boundary Layer (CBL, (2 deep CBL showed a diurnal variation of three- to five-layer structure in clear days and five-layer ABL structure often occurred about sunset or sunrise, (3 the diurnal variation of DSAT influenced thickness of ABL through changes of turbulent heat flux, (4 integral value of sensible heat which rapidly converted by surface net radiation had a significant influence on the growth of CBL throughout daytime. The cumulative effect of thick RML dominated the role after CBL got through SBL in the development stage, especially in late summer, and (5 the development of CBL was promoted and accelerated by the variation of wind field and distribution of warm advection in high and low altitude.
On the role of thermal boundary conditions in dynamo scaling laws
Oruba, Ludivine
2016-01-01
In dynamo power-based scaling laws, the power $P$ injected by buoyancy forces is measured by a so-called flux-based Rayleigh number, denoted as ${\\rm Ra}_Q^*$ (see Christensen and Aubert, 2006). Whereas it is widely accepted that this parameter is measured (as opposite to controlled) in dynamos driven by differential heating, the literature is much less clear concerning its nature in the case of imposed heat flux. We clarify this issue by highlighting that in that case, the ${\\rm Ra}_{Q}^*$ parameter becomes controlled only in the limit of large Nusselt numbers (${\\rm Nu} \\gg 1$). We then address the issue of the robustness of the original relation between $P$ and ${\\rm Ra}_Q^*$ with the geometry and the thermal boundary conditions. We show that in the cartesian geometry, as in the spherical geometry with a central mass distribution, this relation is purely linear, in both differential and fixed-flux heating. However, we show that in the geometry commonly studied by geophysicists (spherical with uniform mass ...
Tasawar Hayat; Awatif A. Hendi; Jacob A. Gbadeyan; Philip O. Olanrewaju
2011-01-01
In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable m...
Hori, K.; Wicht, J.; Dietrich, W.; Christensen, U. R.
2012-12-01
The early dynamos of Earth and Mars probably operated without an inner core being present. They were thus exclusively driven by secular cooling and radiogenic heating, whereas the present geodynamo is thought to be predominantly driven by buoyancy fluxes which arise from the release of latent heat and the compositional enrichment associated with inner core solidification. Dynamo simulations model the secular cooling by volumetric internal buoyancy sources and the inner core-related driving by bottom sources. The impact of the inner core growth on the ancient geodynamo has been discussed extensively but is still controversial. As for Mars, the Mars Global Surveyor detected a strong northern-southern dichotomy in the crustal magnetization. A scenario proposed so far is due to such an ancient dynamo, where thermal heterogeneities at the core mantle boundary (CMB) were imposed by the lower mantle structure. A key issue here is how easily influence of the boundary anomalies emerges. Here we show that the dynamos without inner core solidification are much more sensitive to the CMB heat flows imposed by the lower mantle structure. We compare three-dimensional convection-driven MHD dynamo simulations either driven by homogeneously distributed internal heat sources or by buoyancy sources at the inner core boundary (ICB). Several different boundary heat-flux patterns are used. The effects are found even when boundaries are homogeneous. The impact of the outer boundary condition, fixed temperature or fixed heat flux, is large when convection is predominantly driven by volumetric internal heating. In the dynamos driven by ICB buoyancy sources, the lower boundary condition becomes more important. In both cases, a fixed flux condition promotes larger convective scales than a fixed temperature condition. A dipolar magnetic field can further increase the flow scale. This different sensitivity may also extend to cases when CMB heat flows are laterally inhomogeneous. In the dynamos
Maksimov, Vyacheslav I.; Nagornova, Tatiana A.
2014-08-01
The results of mathematical simulation of the heat transfer processes in the closed domain, which corresponds to production accomodation with the gas infrared emitter operation condition are presented. The system of differential Navier-Stokes equations in the approximation of Boussinesq is solved. The comparative analysis of thermal conditions formation in the closed domain is carried out taking into account heat withdrawal through the upper enclosing construction and under the conditions of its heat insulation. The essential transiency of the analyzed heat transfer process and the influence of heat withdrawal from one of the outer boundaries on the mean temperatures values in large-dimension industrial premises are established.
Ben-Mansour, R.; Li, H.; Habib, M. A.; Hossain, M. M.
2018-02-01
Global warming has become a worldwide concern due to its severe impacts and consequences on the climate system and ecosystem. As a promising technology proving good carbon capture ability with low-efficiency penalty, Chemical Looping Combustion technology has risen much interest. However, the radiative heat transfer was hardly studied, nor its effects were clearly declared. The present work provides a mathematical model for radiative heat transfer within fuel reactor of chemical looping combustion systems and conducts a numerical research on the effects of boundary conditions, solid particles reflectivity, particles size, and the operating temperature. The results indicate that radiative heat transfer has very limited impacts on the flow pattern. Meanwhile, the temperature variations in the static bed region (where solid particles are dense) brought by radiation are also insignificant. However, the effects of radiation on temperature profiles within free bed region (where solid particles are very sparse) are obvious, especially when convective-radiative (mixed) boundary condition is applied on fuel reactor walls. Smaller oxygen carrier particle size results in larger absorption & scattering coefficients. The consideration of radiative heat transfer within fuel reactor increases the temperature gradient within free bed region. On the other hand, the conversion performance of fuel is nearly not affected by radiation heat transfer within fuel reactor. However, the consideration of radiative heat transfer enhances the heat transfer between the gas phase and solid phase, especially when the operating temperature is low.
Ben-Mansour, R.; Li, H.; Habib, M. A.; Hossain, M. M.
2017-09-01
Global warming has become a worldwide concern due to its severe impacts and consequences on the climate system and ecosystem. As a promising technology proving good carbon capture ability with low-efficiency penalty, Chemical Looping Combustion technology has risen much interest. However, the radiative heat transfer was hardly studied, nor its effects were clearly declared. The present work provides a mathematical model for radiative heat transfer within fuel reactor of chemical looping combustion systems and conducts a numerical research on the effects of boundary conditions, solid particles reflectivity, particles size, and the operating temperature. The results indicate that radiative heat transfer has very limited impacts on the flow pattern. Meanwhile, the temperature variations in the static bed region (where solid particles are dense) brought by radiation are also insignificant. However, the effects of radiation on temperature profiles within free bed region (where solid particles are very sparse) are obvious, especially when convective-radiative (mixed) boundary condition is applied on fuel reactor walls. Smaller oxygen carrier particle size results in larger absorption & scattering coefficients. The consideration of radiative heat transfer within fuel reactor increases the temperature gradient within free bed region. On the other hand, the conversion performance of fuel is nearly not affected by radiation heat transfer within fuel reactor. However, the consideration of radiative heat transfer enhances the heat transfer between the gas phase and solid phase, especially when the operating temperature is low.
Numerical analysis of energy piles under different boundary conditions and thermal loading cycles
Directory of Open Access Journals (Sweden)
Khosravi Ali
2016-01-01
Full Text Available The thermo- mechanical behavior of energy piles has been studied extensively in recent years. In the present study, a numerical model was adapted to study the effect of various parameters (e.g. heating/cooling temperature, head loading condition and soil stiffness on the thermo-mechanical behavior of an energy pile installed in unsaturated sandstone. The results from the simulations were compared with measurements from a thermal response test on a prototype energy pile installed beneath a 1-story building at the US Air Force Academy (USAFA in Colorado Springs, CO. A good agreement was achieved between the results obtained from the prototype and the numerical models. A parametric evaluation were also carried out which indicated the significance of the stiffness of the unsaturated sandstone and pile’s head loading condition on stress-strain response of the energy pile during heating/cooling cycles.
General 3D Lumped Thermal Model with Various Boundary Conditions for High Power IGBT Modules
Bahman, Amir Sajjad; Ma, Ke; Blaabjerg, Frede
2016-01-01
Accurate thermal dynamics modeling of high power Insulated Gate Bipolar Transistor (IGBT) modules is important information for the reliability analysis and thermal design of power electronic systems. However, the existing thermal models have their limits to correctly predict these complicated thermal behaviors in the IGBTs. In this paper, a new three-dimensional (3D) lumped thermal model is proposed, which can easily be characterized from Finite Element Methods (FEM) based simulation and acqu...
Directory of Open Access Journals (Sweden)
Tasawar Hayat
2011-09-01
Full Text Available In this paper we analyse the effects of internal heat generation, thermal radiation and buoyancy force on the laminar boundary layer about a vertical plate in a uniform stream of fluid under a convective surface boundary condition. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid whilst a stream of cold fluid flows steadily over the right surface; the heat source decays exponentially outwards from the surface of the plate. The similarity variable method was applied to the steady state governing non-linear partial differential equations, which were transformed into a set of coupled non-linear ordinary differential equations and were solved numerically by applying a shooting iteration technique together with a sixth-order Runge–Kutta integration scheme for better accuracy. The effects of the Prandtl number, the local Biot number, the internal heat generation parameter, thermal radiation and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on similar special cases showed excellent agreement.
Experimental Investigation of Zinc Antimonide Thin Films under Different Thermal Boundary Conditions
DEFF Research Database (Denmark)
Mir Hosseini, Seyed Mojtaba; Rosendahl, Lasse Aistrup; Rezaniakolaei, Alireza
for all cases, showing that the electrical potential difference is increasing by temperature for all cases with the same slope. Also the value of Seebeck coefficient (α) is almost constant for all cases. The obtained value of α can compete with developed bulk TEG materials in literature. The thin film...... is able to operate in relatively high range of temperature with long working period without failure. Furthermore, effects of implementing thermal cycling on stability analysis of a TEG sample are considered. By testing the thermoelectric thin film specimen during a thermal cycling, behavior of the TEG...
Roux, Guilhem; Billardon, René
2006-01-01
International audience; To validate the thermo-metallurgical models that are used during finite element simulations of multi-pass TIG welding, two simple experiments – called "disk-spot" and "disk-cycle" TIG welding tests- have been designed. A procedure has been developed to identify the thermal boundary conditions that are imposed to the specimen during these experiments. These boundary conditions include the heat source that is equivalent to the TIG torch as well as the heat flux by convec...
Directory of Open Access Journals (Sweden)
Sieres Jaime
2016-01-01
Full Text Available This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle φ is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles φ (= 15º, 30º and 45º and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.
Directory of Open Access Journals (Sweden)
V. K. Bityukov
2016-01-01
Full Text Available Analytical study of the processes of heat conduction is one of the main topics of modern engineering research in engineering, energy, nuclear industry, process chemical, construction, textile, food, geological and other industries. Suffice to say that almost all processes in one degree or another are related to change in the temperature condition and the transfer of warmth. It should also be noted that engineering studies of the kinetics of a range of physical and chemical processes are similar to the problems of stationary and nonstationary heat transfer. These include the processes of diffusions, sedimentation, viscous flow, slowing down the neutrons, flow of fluids through a porous medium, electric fluctuations, adsorption, drying, burning, etc. There are various methods for solving the classical boundary value problems of nonstationary heat conduction and problems of the generalized type: the method of separation of variables (Fourier method method; the continuation method; the works solutions; the Duhamel's method; the integral transformations method; the operating method; the method of green's functions (stationary and non-stationary thermal conductivity; the reflection method (method source. In this paper, based on the consistent application of the Laplace transform on the dimensionless time θ and finite sine integral transformation in the spatial coordinates X and Y solves the problem of unsteady temperature distribution on the mechanism of heat conduction in a parallelepiped with boundary conditions of first kind. As a result we have the analytical solution of the temperature distribution in the parallelepiped to a conductive mode free convection, when one of the side faces of the parallelepiped is maintained at a constant temperature, and the others with the another same constant temperature.
Energy Technology Data Exchange (ETDEWEB)
Heggs, P.J.; Dare, J. [University of Manchester, School of Chemical Engineering and Analytical Science (United Kingdom)
2007-07-01
The generation of heat due to chemical reaction will have a significant effect on the temperature profile and heat transfer within a porous body. Most forms of analysis only consider the symmetric situation or else make use of various assumptions that greatly simplify the analysis, for example: the Semenov or the Frak-kamenetskii models. The objective of this paper is to develop an improved understanding of the thermal behaviour of a porous body with uniform internal heat generation, which is in contact with two fluids at different temperatures and with different heat transfer coefficients. The mathematical representation is a one dimensional Poisson equation with asymmetric boundary conditions. The analytical solution reveals four regimes for heat flow: (a) purely conduction at zero heat generation, (b) a combination of heat flow by conduction through the body between the hot and cold fluids and all heat generated passing to the colder fluid, (c) no heat flow by conduction between the two fluids and all heat generated passing the cold flow - the so-called critical heat generation, and (d) the heat generated passes to both the cold and hot fluids and there is a maximum temperature within the body greater than that of the hot fluid, the so-called supercritical region. Expressions are developed to allow predictions of the conditions pertaining to each regime. This new representation covers the Semenov and Frank-Kamenetskii models and all possible solutions intermediate of the them. (authors)
Reweighting twisted boundary conditions
Bussone, Andrea; Hansen, Martin; Pica, Claudio
2015-01-01
Imposing twisted boundary conditions on the fermionic fields is a procedure extensively used when evaluating, for example, form factors on the lattice. Twisting is usually performed for one flavour and only in the valence, and this causes a breaking of unitarity. In this work we explore the possibility of restoring unitarity through the reweighting method. We first study some properties of the approach at tree level and then we stochastically evaluate ratios of fermionic determinants for different boundary conditions in order to include them in the gauge averages, avoiding in this way the expensive generation of new configurations for each choice of the twisting angle, $\\theta$. As expected the effect of reweighting is negligible in the case of large volumes but it is important when the volumes are small and the twisting angles are large. In particular we find a measurable effect for the plaquette and the pion correlation function in the case of $\\theta=\\pi/2$ in a volume $16\\times 8^3$, and we observe a syst...
Siewert, C. E.
2003-06-01
A polynomial expansion procedure and an analytical discrete-ordinates method are used to evaluate the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient as defined by a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani-Lampis boundary condition.
Khanday, M. A.; Hussain, Fida
2015-07-01
To predict the behaviour of thermal physiology of a finite biological tissue in severe cold climatic conditions, a mathematical model has been established based on Pennes' bio-heat transfer equation with oscillatory boundary condition and time dependent heat source term. Crank-Nicholson scheme has been employed to obtain the solution of the boundary value problem to understand the change in stable temperature profiles at the peripheral tissues of human body subjected to forced convection due to cold. Thermal stress at these regions with respect to different input parameters has been computed under extreme environmental conditions using MATLAB Software. The results have shown a relative significance and provide a reasonable outcome in terms of variable metabolic heat generation and oscillatory heat source. The oscillations of the temperature profiles from the mean temperatures were computed in relation with tissue medium and other physiological parameters.
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
A model that combines image source modelling and acoustical radiosity with complex boundary condition, thus including phase shifts on reflection has been developed. The model is called PARISM (Phased Acoustical Radiosity and Image Source Model). It has been developed in order to be able to model...... are done using different boundary conditions in order to investigate the influence of phase shifts in reflections, the angle dependence of the reflection coefficient and the scattering coefficient. The focus of the simulations is to investigate the influence of the boundary condition on room acoustic...
Directory of Open Access Journals (Sweden)
Reda G. Abdel-Rahman
2013-01-01
Full Text Available An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.
Directory of Open Access Journals (Sweden)
Rafik Bouakkaz
2017-06-01
Full Text Available In this work, steady flow-field and heat transfer through a copper–water nanofluid around a circular cylinder, under the influence of both the standard thermal boundary conditions i.e. uniform heat flux (UHF and constant wall temperature (CWT was investigated numerically by using a finite-volume method for Reynolds numbers of 10 to 40. Furthermore, the range of nanoparticle volume fractions (φ considered is 0 ≤ φ ≤ 5%. The variation of the local and the average Nusselt numbers with Reynolds number, and volume fractions are presented for the range of conditions. The average Nusselt number is found to increase with increasing the nanoparticle volume fractions.
Zaib, A.; Bhattacharyya, K.; Khalid, M.; Shafie, S.
2017-05-01
The thermal radiation effect on a steady mixed convective flow with heat transfer of a nonlinear (non-Newtonian) Williamson fluid past an exponentially shrinking porous sheet with a convective boundary condition is investigated numerically. In this study, both an assisting flow and an opposing flow are considered. The governing equations are converted into nonlinear ordinary differential equations by using a suitable transformation. A numerical solution of the problem is obtained by using the Matlab software package for different values of the governing parameters. The results show that dual nonsimilar solutions exist for the opposing flow, whereas the solution for the assisting flow is unique. It is also observed that the dual nonsimilar solutions exist only if a certain amount of mass suction is applied through the porous sheet, which depends on the Williamson parameter, convective parameter, and radiation parameter.
Grain boundary engineering to enhance thermal stability of electrodeposited nickel
DEFF Research Database (Denmark)
Alimadadi, Hossein
by miniaturization of the grains down to nano-meter scale. However, this augments the total grain boundary energy stored in the material, hence, making the material less thermally stable. Coherent twin boundaries are of very low energy and mobility compared to all other boundaries in a FCC material. Accordingly......, grain boundary engineering of electrodeposited nickel to achieve high population of coherent twin boundaries and, hence, higher thermal stability is a promising method to achieve simultaneous improvement in mechanical properties and thermal stability. This is of particular scientific and practical...... interest. The evolution of microstructure in as-deposited and annealed condition was investigated with a combination of complementary microscopic techniques, electron backscatter diffraction (EBSD), electron channelling contrast imaging (ECCI), ion channelling contrast imaging (ICCI), and, for the as...
On filter boundary conditions in topology optimization
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik
2017-01-01
Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...
Boundary Conditions of Methamphetamine Craving
Lopez, Richard B.; Onyemekwu, Chukwudi; Hart, Carl L.; Ochsner, Kevin N.; Kober, Hedy
2015-01-01
Methamphetamine use has increased significantly and become a global health concern. Craving is known to predict methamphetamine use and relapse following abstinence. Some have suggested that cravings are automatic, generalized, and uncontrollable, but experimental work addressing these claims is lacking. In two exploratory studies we tested the boundary conditions of methamphetamine craving by asking: (1) is craving specific to users’ preferred route of administration? and (2) can craving be regulated by cognitive strategies? Two groups of methamphetamine users were recruited. In Study 1, participants were grouped by their preferred route of administration (intranasal vs. smoking), and rated their craving in response to photographs and movies depicting methamphetamine use (via the intranasal vs. smoking route). In Study 2, methamphetamine smokers implemented cognitive regulation strategies while viewing photographs depicting methamphetamine smoking. Strategies involved either focusing on the positive aspects of smoking methamphetamine or the negative consequences of doing so – the latter strategy based on treatment protocols for addiction. In Study 1, we found a significant interaction between group and route of administration, such that participants who preferred to smoke methamphetamine reported significantly stronger craving for smoking stimuli, whereas those who preferred the intranasal route reported stronger craving for intranasal stimuli. In Study 2, participants reported significantly lower craving when focusing on the negative consequences associated with methamphetamine use. Taken together, these findings suggest that strength of craving for methamphetamine is moderated by users’ route of administration and can be reduced by cognitive strategies. This has important theoretical, methodological, and clinical implications. PMID:26302338
Absorption boundary conditions for geomertical acoustics
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, the absorption coefficients or surface impedances of the boundary surfaces can be used, but no guideline has been developed...... solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. It is concluded that the impedance and random incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials....
Green's functions for Neumann boundary conditions
Franklin, Jerrold
2012-01-01
Green's functions for Neumann boundary conditions have been considered in Math Physics and Electromagnetism textbooks, but special constraints and other properties required for Neumann boundary conditions have generally not been noticed or treated correctly. In this paper, we derive an appropriate Neumann Green's function with these constraints and properties incorporated.
Maxwell boundary condition and velocity dependent accommodation coefficient
Energy Technology Data Exchange (ETDEWEB)
Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2013-11-15
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Maxwell boundary condition and velocity dependent accommodation coefficient
Struchtrup, Henning
2013-11-01
A modification of Maxwell's boundary condition for the Boltzmann equation is developed that allows to incorporate velocity dependent accommodation coefficients into the microscopic description. As a first example, it is suggested to consider the wall-particle interaction as a thermally activated process with three parameters. A simplified averaging procedure leads to jump and slip boundary conditions for hydrodynamics. Coefficients for velocity slip, temperature jump, and thermal transpiration flow are identified and compared with those resulting from the original Maxwell model and the Cercignani-Lampis model. An extension of the model leads to temperature dependent slip and jump coefficients.
Global boundary conditions for the Dirac operator
Falomir, H A
1997-01-01
Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional determinants for Dirac operators on manifolds with boundary are considered. The functional determinant for a Dirac operator on a bidimensional disk, in the presence of an Abelian gauge field and subject to global boundary conditions of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship with the index theorem is also commented.
Implementation of Boundary Condition to THALES Code
Energy Technology Data Exchange (ETDEWEB)
Jang, Beomjun; Chun, Chong Kuk; Park, Ho Young; Woo, Hae-Seuk [KEPCO Nuclear Fuel, Daejeon (Korea, Republic of)
2016-10-15
The boundary condition of momentum equation of THALES code utilizes the exit pressure boundary to solve the elliptic partial difference momentum equations. This method is the same as the most of the subchannel analysis codes. Other codes such as VIPRE utilize the uniform pressure distribution as outlet boundary condition. In this case, uniform inlet flow rate is assumed. In order to test the core flow field regarding the boundary conditions, analysis was performed for two core conditions. One condition is nominal plant operating condition. In this paper, generic THALES power distribution is used. For nominal operation case, there are no different results depending on the type of outlet pressure boundary condition. But low-power and high-peaking case, density difference for lateral direction becomes large due to high peaking power of core. Since density change causes pressure change, In this case, uniform outlet pressure distribution can't be assumed anymore. Design outlet pressure distribution is measured at nominal core condition. Therefore, design outlet pressure distribution also can't be used due to the difference in core power and flow rate. As a result, it is reasonable that neumann boundary condition is applied in low-power and high peaking core condition including various accident condition.
Symmetries and Boundary Conditions with a Twist
Zawadzki, Krissia; D'Amico, Irene; Oliveira, Luiz N.
2017-10-01
Interest in finite-size systems has risen in the last decades, due to the focus on nanotechnological applications and because they are convenient for numerical treatment that can subsequently be extrapolated to infinite lattices. Independently of the envisioned application, special attention must be given to boundary condition, which may or may not preserve the symmetry of the infinite lattice. Here, we present a detailed study of the compatibility between boundary conditions and conservation laws. The conflict between open boundary conditions and momentum conservation is well understood, but we examine other symmetries, as well: we discuss gauge invariance, inversion, spin, and particle-hole symmetry and their compatibility with open, periodic, and twisted boundary conditions. In the interest of clarity, we develop the reasoning in the framework of the one-dimensional half-filled Hubbard model, whose Hamiltonian displays a variety of symmetries. Our discussion includes analytical and numerical results. Our analytical survey shows that, as a rule, boundary conditions break one or more symmetries of the infinite-lattice Hamiltonian. The exception is twisted boundary condition with the special torsion Θ = πL/2, where L is the lattice size. Our numerical results for the ground-state energy at half-filling and the energy gap for L = 2-7 show how the breaking of symmetry affects the convergence to the L → ∞ limit. We compare the computed energies and gaps with the exact results for the infinite lattice drawn from the Bethe-Ansatz solution. The deviations are boundary-condition dependent. The special torsion yields more rapid convergence than open or periodic boundary conditions. For sizes as small as L = 7, the numerical results for twisted condition are very close to the L → ∞ limit. We also discuss the ground-state electronic density and magnetization at half filling under the three boundary conditions.
Approximate solution to a singular perturbed boundary value problem of thermal shielding
Latypov, I. I.
2017-11-01
The paper aims to investigate the problem of distribution of a non-regular, non-steady-state thermal field in the porous thermal shield material irradiated by a high flow of energy. A mathematical model of the original problem is stated in the form of a singular perturbed boundary value problem of a thermal conductivity equation with the nonlinear boundary conditions on moving boundaries. Its solution is obtained as asymptotic Poincare-type expansions in powers of small parameters.
Directory of Open Access Journals (Sweden)
Mohamad Yaghoub Abdollahzadeh Jamalabadi
2015-02-01
Full Text Available Investigation of the effect of thermal radiation on a fully developed magnetohydrodynamic (MHD convective flow of a Newtonian, incompressible and electrically conducting fluid in a vertical microchannel bounded by two infinite vertical parallel plates with constant temperature walls through a lateral magnetic field of uniform strength is presented. The Rosseland model for the conduction radiation heat transfer in an absorbing medium and two plates with slip-flow and no-slip conditions are assumed. In addition, the induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The non-dimensional governing equations are solved numerically using Runge–Kutta–Fehlberg method with a shooting technique. The channel is optimized based on the Second Law of Thermodynamics by changing various parameters such as the thermal radiation parameter, the temperature parameter, Hartmann number, Grashof to Reynolds ratio, velocity slip length, and temperature jump.
Reconstruction of boundary conditions from internal conditions using viability theory
Hofleitner, Aude
2012-06-01
This article presents a method for reconstructing downstream boundary conditions to a HamiltonJacobi partial differential equation for which initial and upstream boundary conditions are prescribed as piecewise affine functions and an internal condition is prescribed as an affine function. Based on viability theory, we reconstruct the downstream boundary condition such that the solution of the Hamilton-Jacobi equation with the prescribed initial and upstream conditions and reconstructed downstream boundary condition satisfies the internal value condition. This work has important applications for estimation in flow networks with unknown capacity reductions. It is applied to urban traffic, to reconstruct signal timings and temporary capacity reductions at intersections, using Lagrangian sensing such as GPS devices onboard vehicles.
Boundary conditions for the gravitational field
Winicour, Jeffrey
2012-06-01
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain. Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, ‘Theories of Everything’)
Stokes equations with penalised slip boundary conditions
Dione, Ibrahima; Tibirna, Cristian; Urquiza, José
2013-07-01
We consider the finite-element approximation of Stokes equations with slip boundary conditions imposed with the penalty method. In the case of a smooth curved boundary, our numerical results suggest that curved finite elements, regularised normal vectors or reduced integration techniques can be used to avoid a Babuska's-type paradox and ensure the convergence of finite-element approximations to the exact solution. Convergence orders with these remedies are also compared.
Boundary conditions in CO5BOLD
Freytag, Bernd
The declaration of boundary conditions is a crucial step in the setup of a CO5BOLD simulation (and many others) due to the physical nature of the problem, that is reflected in the mathematical description by partial differential equations, discrete versions of which are integrated by the numerical solver(s). While parameters controlling the flux of energy through the computational box are most important for all simulations of convective flows, the detailed specifications describing the behavior of energy, gas and dust densities, velocities, and magnetic fields at or just beyond the boundaries influence the flow, dynamics, and stratification within the box. Recent refinements of the treatment of boundary conditions in CO5BOLD resulted in reliably working implementations of open and closed versions for top, bottom, and ``inner'' boundaries even under conditions with strong velocity fields (waves, shocks, or downdrafts). They are implemented and available in the current version of CO5BOLD - but have to be activated properly with parameters adapted to the type of the star under consideration (by defining for instance the depth of the damping layers for the closed-bottom boundary or by specifying the damping constants for the open-bottom boundary).
Antireflective Boundary Conditions for Deblurring Problems
Directory of Open Access Journals (Sweden)
Marco Donatelli
2010-01-01
Full Text Available This survey paper deals with the use of antireflective boundary conditions for deblurring problems where the issues that we consider are the precision of the reconstruction when the noise is not present, the linear algebra related to these boundary conditions, the iterative and noniterative regularization solvers when the noise is considered, both from the viewpoint of the computational cost and from the viewpoint of the quality of the reconstruction. In the latter case, we consider a reblurring approach that replaces the transposition operation with correlation. For many of the considered items, the anti-reflective algebra coming from the given boundary conditions is the optimal choice. Numerical experiments corroborating the previous statement and a conclusion section end the paper.
parabolic equation with integral boundary condition
Directory of Open Access Journals (Sweden)
M. Denche
2001-01-01
Full Text Available In this paper we study the problem of control by the initial conditions of the heat equation with an integral boundary condition. This problem is ill-posed. Perturbing the final condition we obtain an approximate nonlocal problem depending on a small parameter. We show that the approximate problems are well posed. We also obtain estimates of the solutions of the approximate problems and a convergence result of these solutions. Finally, we give explicit convergence rates.
Functional differential inclusions with integral boundary conditions
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2007-07-01
Full Text Available In this paper, we investigate the existence of solutions for a class of second order functional differential inclusions with integral boundary conditions. By using suitable fixed point theorems, we study the case when the right hand side has convex as well as nonconvex values.
An h-principle with boundary condition
DEFF Research Database (Denmark)
Dotto, Emanuele
2010-01-01
We prove an h-principle with boundary condition for a certain class of topological spaces valued sheaves. The techniques used in the proof come from the study of the homotopy type of the cobordism categories, and they are of simplicial and categorical nature. Applying the main result of this paper...
Restructuring surface tessellation with irregular boundary conditions
Directory of Open Access Journals (Sweden)
Tsung-Hsien Wang
2014-12-01
Full Text Available In this paper, the surface tessellation problem is explored, in particular, the task of meshing a surface with the added consideration of incorporating constructible building components. When a surface is tessellated into discrete counterparts, certain unexpected conditions usually occur at the boundary of the surface, in particular, when the surface is being trimmed. For example, irregularly shaped panels form at the trimmed edges. To reduce the number of irregular panels that may form during the tessellation process, this paper presents an algorithmic approach to restructuring the surface tessellation by investigating irregular boundary conditions. The objective of this approach is to provide an alternative way for freeform surface manifestation from a well-structured discrete model of the given surface.
Absorbing boundary conditions for inertial random processes
Energy Technology Data Exchange (ETDEWEB)
Masoliver, J.; Porra, J.M. [Departament de Fisica Fonamental, Universitat de Barcelona, Diagonal, 647, 08028-Barcelona (Spain); Lindenberg, K. [Department of Chemistry and Biochemistry and Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0340 (United States)
1996-12-01
A recent paper by J. Heinrichs [Phys. Rev. E {bold 48}, 2397 (1993)] presents analytic expressions for the first-passage times and the survival probability for a particle moving in a field of random correlated forces. We believe that the analysis there is flawed due to an improper use of boundary conditions. We compare that result, in the white noise limit, with the known exact expression of the mean exit time. {copyright} {ital 1996 The American Physical Society.}
Boundary conditions in conformal and integrable theories
Petkova, V B
2000-01-01
The study of boundary conditions in rational conformal field theories is not only physically important. It also reveals a lot on the structure of the theory ``in the bulk''. The same graphs classify both the torus and the cylinder partition functions and provide data on their hidden ``quantum symmetry''. The Ocneanu triangular cells -- the 3j-symbols of these symmetries, admit various interpretations and make a link between different problems.
Thermal explosion in oscillating ambient conditions
Novozhilov, Vasily
2016-01-01
Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is considered. This is a new problem in thermal explosion theory, not previously considered in a distributed system formulation, but important for combustion and fire science. It describes autoignition of wide range of fires (such as but not limited to piles of biosolids and other organic matter; storages of munitions, explosives, propellants) subjected to temperature variations, such as seasonal or day/night variation. The problem is considered in formulation adopted in classical studies of thermal explosion. Critical conditions are determined by frequency and amplitude of ambient temperature oscillations, as well as by a number of other parameters. Effects of all the parameters on critical conditions are quantified. Results are presented for the case of planar symmetry. Development of thermal explosion in time is also considered, and a new type of unsteady thermal explosion development is discovered where thermal runaway occurs after several periods of temperature oscillations within the medium. PMID:27443235
Open Boundary Conditions for Dissipative MHD
Energy Technology Data Exchange (ETDEWEB)
Meier, E T
2011-11-10
In modeling magnetic confinement, astrophysics, and plasma propulsion, representing the entire physical domain is often difficult or impossible, and artificial, or 'open' boundaries are appropriate. A novel open boundary condition (BC) for dissipative MHD, called Lacuna-based open BC (LOBC), is presented. LOBC, based on the idea of lacuna-based truncation originally presented by V.S. Ryaben'kii and S.V. Tsynkov, provide truncation with low numerical noise and minimal reflections. For hyperbolic systems, characteristic-based BC (CBC) exist for separating the solution into outgoing and incoming parts. In the hyperbolic-parabolic dissipative MHD system, such separation is not possible, and CBC are numerically unstable. LOBC are applied in dissipative MHD test problems including a translating FRC, and coaxial-electrode plasma acceleration. Solution quality is compared to solutions using CBC and zero-normal derivative BC. LOBC are a promising new open BC option for dissipative MHD.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2016-01-06
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Bayesian Inference for Linear Parabolic PDEs with Noisy Boundary Conditions
Ruggeri, Fabrizio
2015-01-07
In this work we develop a hierarchical Bayesian setting to infer unknown parameters in initial-boundary value problems (IBVPs) for one-dimensional linear parabolic partial differential equations. Noisy boundary data and known initial condition are assumed. We derive the likelihood function associated with the forward problem, given some measurements of the solution field subject to Gaussian noise. Such function is then analytically marginalized using the linearity of the equation. Gaussian priors have been assumed for the time-dependent Dirichlet boundary values. Our approach is applied to synthetic data for the one-dimensional heat equation model, where the thermal diffusivity is the unknown parameter. We show how to infer the thermal diffusivity parameter when its prior distribution is lognormal or modeled by means of a space-dependent stationary lognormal random field. We use the Laplace method to provide approximated Gaussian posterior distributions for the thermal diffusivity. Expected information gains and predictive posterior densities for observable quantities are numerically estimated for different experimental setups.
Canonical group quantization and boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Characteristic Boundary Conditions for ARO-1
1983-05-01
8217--’--’~,oc=~ AEDC-TR-82-28 Characteristic Boundary Conditions for ARO-1 Karl R. Kneile and Donald C. Todd Sverdrup Technology, Inc. and James...REPORT DOCUMENTATION PAGE I i I R E P O R T NUMBER 12 GOVT ACCESSION NO. 3 I AEDC-TR-82-28 4. T I T L E (and Subtitle:, CHARACTERISTIC BOU~DARY...ARO-I program 20. A B S T R A C T ( C ~ t i n ~ ~ reverme side tf n e c o s e a ~ and I d e n t l ~ ~ b lock n u m b o ~ Characteristic
Scalar boundary conditions in hyperscaling violating geometry
Directory of Open Access Journals (Sweden)
Jian-Pin Wu
2016-02-01
Full Text Available We study the possible boundary conditions of scalar field modes in a hyperscaling violation (HV geometry with Lifshitz dynamical exponent z (z≥1 and hyperscaling violation exponent θ (θ≠0. For the case with θ>0, we show that in the parameter range 1≤z≤2, −z+d−12, −z+d−10, which has been addressed in Ref. [1]. Meanwhile, we also carry out the parallel investigation in the case with θ0, only one type is available.
DEFF Research Database (Denmark)
Sarhadi, Ali; Hattel, Jesper Henri; Hansen, Hans Nørgaard
2012-01-01
of the heating system in the glass moulding process considering detailed heating mechanisms therefore plays an important part in optimizing the heating system and the subsequent pressing stage in the lens manufacturing process.The current paper deals with three-dimensional transient thermal modelling...... pressures. Finally, the three-dimensional modelling of the multi-stage heating system in the wafer based glass moulding process is simulated with the FEM software ABAQUS for a particular industrial application for mobile phone camera lenses to obtain the temperature distribution in the glass wafer...
Energy Technology Data Exchange (ETDEWEB)
Rosa, Cinara Ewerling da, E-mail: cinara@pb.ifarroupilha.edu.br [Universidade Federal do Rio Grande do Sul (IFF/UFRS), Porto Alegre, RS (Brazil); Instituto Federal Farroupilha, Panambi, RS (Brazil); Knackfuss, Rosenei Felippe, E-mail: knackfuss@smail.ufsm.br [Universidade Federal de Santa Maria (UFSM), Santa Maria, RS (Brazil)
2013-07-01
In this work is presented a series of numerical results and graphical comparisons of the physical quantities of interest such as: the velocity profile and the heat on profile. This formulation is developed for the problem of Thermal Creep, where the gas is moving between two parallel plates with different chemical constitutions (heterogeneous plates) due to a temperature gradient. The flow of a rarefied gas, is investigated with special attention to the gas-surface interaction, modeled by the Cercignani-Lampis kernel, that unlike Maxwell's scattering kernel, is defined in terms of two accommodation coefficients (normal and tangential) to represent the physical properties of the gas. The kinetic theory for rarefied gas dynamics, derived from the linearized Boltzmann equation, is developed in an unified approach, to the BGK model, S model, GJ model and MRS model. In the search for solutions to solve the problem of Thermal Creep with kernel of the Cercignani-Lampis, we used a analytical version of the discrete ordinates method (ADO) based on an arbitrary quadrature scheme, under which is determined a problem of eigenvalues and their respective separation constants. Numerical results are developed by the computer program FORTRAN. (author)
Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Lotoreichik, Vladimir; Rohleder, Jonathan
2017-07-01
Inequalities for the eigenvalues of the (negative) Laplacian subject to mixed boundary conditions on polyhedral and more general bounded domains are established. The eigenvalues subject to a Dirichlet boundary condition on a part of the boundary and a Neumann boundary condition on the remainder of the boundary are estimated in terms of either Dirichlet or Neumann eigenvalues. The results complement several classical inequalities between Dirichlet and Neumann eigenvalues due to Pólya, Payne, Levine and Weinberger, Friedlander, and others.
Study of the blowing impact on a hot turbulent boundary layer using Thermal Large Eddy Simulation
Energy Technology Data Exchange (ETDEWEB)
Brillant, G. [CEA/Grenoble DEN/DER/SSTH/LMDL, 17 rue des Martyrs 38054, Grenoble Cedex 9 (France); INSA/Centre de Thermique de Lyon (UMR CNRS 5008), Bat. Sadi Carnot 69621, Villeurbanne Cedex (France); Husson, S. [INSA/Centre de Thermique de Lyon (UMR CNRS 5008), Bat. Sadi Carnot 69621, Villeurbanne Cedex (France); Bataille, F. [INSA/Centre de Thermique de Lyon (UMR CNRS 5008), Bat. Sadi Carnot 69621, Villeurbanne Cedex (France)], E-mail: Francoise.Daumas-Bataille@univ-perp.fr; Ducros, F. [CEA/Grenoble DEN/DER/SSTH/LMDL, 17 rue des Martyrs 38054, Grenoble Cedex 9 (France)
2008-12-15
We investigate Thermal Large Eddy Simulation in a complex case using Trio U. We develop a thermal turbulent inflow condition based on parallel flows in order to simulate a turbulent thermal boundary layer. This inflow condition is tested with a turbulent channel flow. We show that it produces fine profiles for velocity and temperature. Later, this inlet condition is used in the case of blowing through a porous plate. Two different blowing regimes are studied: the classical turbulent boundary layer and the blown off boundary layer. Comparisons show that we obtain similar experimental and numerical profiles (Brillant, G., Husson, S., Bataille, F., 2008. Experimental study of the blowing impact on a hot turbulent boundary layer. International Journal of Heat and Mass Transfer 51 (7-8), 1996-2005.). We finish with additional results obtained only through numerical simulations.
Interactions between the thermal internal boundary layer and sea breezes
Energy Technology Data Exchange (ETDEWEB)
Steyn, D.G. [The Univ. of British Columbia, Dept. of Geography, Atmospheric Science Programme, Vancouver (Canada)
1997-10-01
In the absence of complex terrain, strongly curved coastline or strongly varying mean wind direction, the Thermal Internal Boundary Layer (TIBL) has well known square root behaviour with inland fetch. Existing slab modeling approaches to this phenomenon indicate no inland fetch limit at which this behaviour must cease. It is obvious however that the TIBL cannot continue to grow in depth with increasing fetch, since the typical continental Mixed Layer Depths (MLD) of 1500 to 2000 m must be reached between 100 and 200 km from the shoreline. The anticyclonic conditions with attendant strong convection and light winds which drive the TIBL, also drive daytime Sea Breeze Circulations (SBC) in the coastal zone. The onshore winds driving mesoscale advection of cool air are at the core of TIBL mechanisms, and are invariably part of a SBC. It is to be expected that TIBL and SBC be intimately linked through common mechanisms, as well as external conditions. (au)
Motion of particles in a thermal boundary layer
Energy Technology Data Exchange (ETDEWEB)
Schefer, R.W.; Agrawal, Y.; Cheng, R.K.; Robben, F.; Talbot, L.
1978-06-15
In the course of using laser Doppler velocimetry to study combustion in a thermal boundary layer, the particle count rate was found to decrease abruptly to zero inside the boundary layer. Experimental and theoretical investigation of this phenomenon was carried out. The motion of the particles may be due to the combined effects of thermophoresis and radiative heating.
Thermal propagation of normal-superconductor boundaries
Energy Technology Data Exchange (ETDEWEB)
Gray, K.E.; Zasadzinski, J.; Kampwirth, R.T.
1981-01-01
The model of Newhouse for thermal propagation of long normal regions in thin superconducting films on good thermal conducting substrates has been verified. Measurements show much slower velocities for short regions, but the dependence is compatible with a new model calculation. Stable hot spots are found which agree semi-quantitatively with a modified hot-spot calculation.
Variable Thermal Conductivity on Compressible Boundary Layer ...
African Journals Online (AJOL)
In this paper, variable thermal conductivity on heat transfer over a circular cylinder is presented. The concept of assuming constant thermal conductivity on materials is however not efficient. Hence, the governing partial differential equation is reduced using non-dimensionless variables into a system of coupled non-linear ...
A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Colli, Pierluigi, E-mail: pierluigi.colli@unipv.it; Gilardi, Gianni, E-mail: gianni.gilardi@unipv.it [Universitá di Pavia and Research Associate at the IMATI – C.N.R. PAVIA, Dipartimento di Matematica “F. Casorati” (Italy); Sprekels, Jürgen, E-mail: juergen.sprekels@wias-berlin.de [Weierstrass Institute (Germany)
2016-04-15
A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.
Monitoring Thermal Conditions in Footwear
Silva-Moreno, Alejandra. A.; Lopez Vela, Martín; Alcalá Ochoa, Noe
2006-09-01
Thermal conditions inside the foot were evaluated on a volunteer subject. We have designed and constructed an electronic system which can monitors temperature and humidity of the foot inside the shoe. The data is stored in a battery-powered device for later uploading to a host computer for data analysis. The apparatus potentially can be used to provide feedback to patients who are prone to having skin breakdowns.
On domain wall boundary conditions for the XXZ spin Hamiltonian
DEFF Research Database (Denmark)
Orlando, Domenico; Reffert, Susanne; Reshetikhin, Nicolai
In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions.......In this note, we derive the spectrum of the infinite quantum XXZ spin chain with domain wall boundary conditions. The eigenstates are constructed as limits of Bethe states for the finite XXZ spin chain with quantum sl(2) invariant boundary conditions....
On Hydroelastic Body-Boundary Condition of Floating Structures
DEFF Research Database (Denmark)
Xia, Jinzhu
1996-01-01
A general linear body boundary condition of hydroelastic analysis of arbitrary shaped floating structures generalizes the classic kinematic rigid-body (Timman-Newman) boundary condition for seakeeping problems. The new boundary condition is consistent with the existing theories under certain...
Influence of anisotropy on thermal boundary conductance at solid interfaces
Hopkins, Patrick E.; Beechem, Thomas; Duda, John C.; Hattar, Khalid; Ihlefeld, Jon F.; Rodriguez, Mark A.; Piekos, Edward S.
2011-09-01
We investigate the role of anisotropy on interfacial transport across solid interfaces by measuring the thermal boundary conductance from 100 to 500 K across Al/Si and Al/sapphire interfaces with different substrate orientations. The measured thermal boundary conductances show a dependency on substrate crystallographic orientation in the sapphire samples (trigonal conventional cell) but not in the silicon samples (diamond cubic conventional cell). The change in interface conductance in the sapphire samples is ascribed to anisotropy in the Brillouin zone along the principal directions defining the conventional cell. This leads to resultant phonon velocities in the direction of thermal transport that vary nearly 40% based on crystallographic direction.
The Stochastic Ising Model with the Mixed Boundary Conditions
Directory of Open Access Journals (Sweden)
Wang Jun
2009-01-01
Full Text Available Abstract We estimate the spectral gap of the two-dimensional stochastic Ising model for four classes of mixed boundary conditions. On a finite square, in the absence of an external field, two-sided estimates on the spectral gap for the first class of (weak positive boundary conditions are given. Further, at inverse temperatures , we will show lower bounds of the spectral gap of the Ising model for the other three classes mixed boundary conditions.
Boundary Conditions, Data Assimilation, and Predictability in Coastal Ocean Models
National Research Council Canada - National Science Library
Samelson, Roger M; Allen, John S; Egbert, Gary D; Kindle, John C; Snyder, Chris
2007-01-01
...: The specific objectives of this research are to determine the impact on coastal ocean circulation models of open ocean boundary conditions from Global Ocean Data Assimilation Experiment (GODAE...
Thermal Internal Boundary Layer characteristics at a tropical coastal ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
examined with the help of measurements carried out with a mini-SODAR (SOund Detection And ..... moisture upwards and periodic intrusion of mar- ..... Ocean System 2. 351–362. Kunhikrishnan P K, Gupta K S, Ramachandran R, Prakash. J W, Nair K N 1993 Study on thermal internal boundary layer structure over Thumba, ...
Quantum “violation” of Dirichlet boundary condition
Directory of Open Access Journals (Sweden)
I.Y. Park
2017-02-01
Full Text Available Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Quantum “violation” of Dirichlet boundary condition
Energy Technology Data Exchange (ETDEWEB)
Park, I.Y., E-mail: inyongpark05@gmail.com
2017-02-10
Dirichlet boundary conditions have been widely used in general relativity. They seem at odds with the holographic property of gravity simply because a boundary configuration can be varying and dynamic instead of dying out as required by the conditions. In this work we report what should be a tension between the Dirichlet boundary conditions and quantum gravitational effects, and show that a quantum-corrected black hole solution of the 1PI action no longer obeys, in the naive manner one may expect, the Dirichlet boundary conditions imposed at the classical level. We attribute the ‘violation’ of the Dirichlet boundary conditions to a certain mechanism of the information storage on the boundary.
Directory of Open Access Journals (Sweden)
Rai Nath Kabindra Rajeev
2009-01-01
Full Text Available In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.
Simulation of Thermal Flow Problems via a Hybrid Immersed Boundary-Lattice Boltzmann Method
Directory of Open Access Journals (Sweden)
J. Wu
2012-01-01
Full Text Available A hybrid immersed boundary-lattice Boltzmann method (IB-LBM is presented in this work to simulate the thermal flow problems. In current approach, the flow field is resolved by using our recently developed boundary condition-enforced IB-LBM (Wu and Shu, (2009. The nonslip boundary condition on the solid boundary is enforced in simulation. At the same time, to capture the temperature development, the conventional energy equation is resolved. To model the effect of immersed boundary on temperature field, the heat source term is introduced. Different from previous studies, the heat source term is set as unknown rather than predetermined. Inspired by the idea in (Wu and Shu, (2009, the unknown is calculated in such a way that the temperature at the boundary interpolated from the corrected temperature field accurately satisfies the thermal boundary condition. In addition, based on the resolved temperature correction, an efficient way to compute the local and average Nusselt numbers is also proposed in this work. As compared with traditional implementation, no approximation for temperature gradients is required. To validate the present method, the numerical simulations of forced convection are carried out. The obtained results show good agreement with data in the literature.
Thermal conductivity and thermal boundary resistance of nanostructures
Directory of Open Access Journals (Sweden)
Merabia Samy
2011-01-01
Full Text Available Abstract We present a fabrication process of low-cost superlattices and simulations related with the heat dissipation on them. The influence of the interfacial roughness on the thermal conductivity of semiconductor/semiconductor superlattices was studied by equilibrium and non-equilibrium molecular dynamics and on the Kapitza resistance of superlattice's interfaces by equilibrium molecular dynamics. The non-equilibrium method was the tool used for the prediction of the Kapitza resistance for a binary semiconductor/metal system. Physical explanations are provided for rationalizing the simulation results. PACS 68.65.Cd, 66.70.Df, 81.16.-c, 65.80.-g, 31.12.xv
Stationary solutions and Neumann boundary conditions in the Sivashinsky equation.
Denet, Bruno
2006-09-01
New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. With these boundary conditions, the time evolution of the Sivashinsky equation in the presence of a moderate white noise is controlled by jumps between stationary solutions.
Performance of Numerical Boundary Condition based on Active Wave Absorption
DEFF Research Database (Denmark)
Troch, Peter; De Rouck, Julien; Frigaard, Peter
2001-01-01
The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented.......The performance of a new active wave generating-absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented....
Boundary Conditions and Predictions of Quantum Cosmology
Page, Don N.
2008-09-01
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum cosmology, item (1) is often called a 'theory of everything,' and item (2) is the quantum state of the cosmos. Hartle and Hawking have made the 'no-boundary' proposal, that the wavefunction of the universe is given by a path integral over all compact Euclidean 4-dimensional geometries and matter fields that have the 3-dimensional argument of the wavefunction on their one and only boundary. This proposal has had several partial successes, mainly when one takes the zero-loop approximation of summing over a small number of complex extrema of the action. However, it has also been severely challenged by an argument by Susskind.
GenCade Lateral Boundary Conditions
2017-01-01
from marine corals, algae , and other organisms. ................... 18 Figure 5. The Complementary Error Function...Eckstein was Deputy Director of CHL, and José E. Sánchez was Director of CHL. COL Bryan S. Green was ERDC Commander. Dr. Jeffery P. Holland was ERDC... benefit of producing perfect agreement at this boundary during model calibration. However, it would be serendipitous if this procedure also produced
Stress boundary conditions with the staggered grid: a numerical investigation
Duretz, Thibault; May, Dave
2014-05-01
In this study, we investigate the numerical properties of the finite-difference method employing dynamic boundary conditions (BC). Stress BC's are gaining popularity in the geodynamic modelling community since the use of a free surface (stress-free BC) is required to model the dynamic evolution of topography. Additionnaly, normal stress BC's might also be used to prescribe known lithospheric rheological models as a dynamic forcing. Under this constraints, boundary velocities are not fixed, they thus vary through time in reaction to stress equilibria within the domain. Dynamic BC's were implemented on a regular Cartesian mesh using a standart staggered grid discretisation. The numerical properties of the scheme were quantified by means of a convergence study and error analysis. Integrated errors owing to the numerical method were evaluated using analytical and manufactured full flow-field solutions and associated convergence rates were derived. Finally, we present two lithospheric-scale applications. The first model depicts the topographic evolution of a linear-viscous lithosphere subjected to the rise of a mantle plume, employing a staircase type free surface. The second model shows the pattern of strain localisation in a thermally activated power law crust subjected to normal stress loading.
Qu, Zhechao; Werhahn, Olav; Ebert, Volker
2018-01-01
The effects of thermal boundary layers on tunable diode laser absorption spectroscopy (TDLAS) measurement results must be quantified when using the line-of-sight (LOS) TDLAS under conditions with spatial temperature gradient. In this paper, a new methodology based on spectral simulation is presented quantifying the LOS TDLAS measurement deviation under conditions with thermal boundary layers. The effects of different temperature gradients and thermal boundary layer thickness on spectral collisional widths and gas concentration measurements are quantified. A CO 2 TDLAS spectrometer, which has two gas cells to generate the spatial temperature gradients, was employed to validate the simulation results. The measured deviations and LOS averaged collisional widths are in very good agreement with the simulated results for conditions with different temperature gradients. We demonstrate quantification of thermal boundary layers' thickness with proposed method by exploitation of the LOS averaged the collisional width of the path-integrated spectrum.
A Thermal Plume Model for the Martian Convective Boundary Layer
Colaïtis, Arnaud; Hourdin, Frédéric; Rio, Catherine; Forget, François; Millour, Ehouarn
2013-01-01
The Martian Planetary Boundary Layer [PBL] is a crucial component of the Martian climate system. Global Climate Models [GCMs] and Mesoscale Models [MMs] lack the resolution to predict PBL mixing which is therefore parameterized. Here we propose to adapt the "thermal plume" model, recently developed for Earth climate modeling, to Martian GCMs, MMs, and single-column models. The aim of this physically-based parameterization is to represent the effect of organized turbulent structures (updrafts and downdrafts) on the daytime PBL transport, as it is resolved in Large-Eddy Simulations [LESs]. We find that the terrestrial thermal plume model needs to be modified to satisfyingly account for deep turbulent plumes found in the Martian convective PBL. Our Martian thermal plume model qualitatively and quantitatively reproduces the thermal structure of the daytime PBL on Mars: superadiabatic near-surface layer, mixing layer, and overshoot region at PBL top. This model is coupled to surface layer parameterizations taking ...
Chiral boundary conditions for singletons and W-branes
Raeymaekers, Joris; Van den Bleeken, Dieter
2017-07-01
We revisit the holographic dictionary for a free massless scalar in AdS3, focusing on the `singleton' solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Compère-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.
Zhou, Guofeng; Wang, Limin; Wang, Xiaowei; Ge, Wei
2011-12-01
Many investigators have coupled the Lees-Edwards boundary conditions (LEBCs) and suspension methods in the framework of the lattice Boltzmann method to study the pure bulk properties of particle-fluid suspensions. However, these suspension methods are all link-based and are more or less exposed to the disadvantages of violating Galilean invariance. In this paper, we have coupled LEBCs with a node-based suspension method, which is demonstrated to be Galilean invariant in benchmark simulations. We use the coupled algorithm to predict the viscosity of a particle-fluid suspension at very low Reynolds number, and the simulation results are in good agreement with the semiempirical Krieger-Dougherty formula.
Yusop, Nur Syaza Mohd; Mohamed, Nurul Akmal
2017-05-01
Boundary Element Method (BEM) is a numerical way to approximate the solutions of a Boundary Value Problem (BVP). The potential problem which involves the Laplace's equation on the square shape domain will be considered where the boundary is divided into four sets of linear boundary elements. We study the derivation system of equation for mixed BVP with one Dirichlet Boundary Condition (BC) is prescribed on one element of the boundary and Neumann BC on the other three elements. The mixed BVP will be reduced to a Boundary Integral Equation (BIE) by using a direct method which involves Green's second identity representation formula. Then, linear interpolation is used where the boundary will be discretized into some linear elements. As the result, we then obtain the system of linear equations. In conclusion, the specific element in the mixed BVP will have the specific prescribe value depends on the type of boundary condition. For Dirichlet BC, it has only one value at each node but for the Neumann BC, there will be different values at the corner nodes due to outward normal. Therefore, the assembly process for the system of equations related to the mixed BVP may not be as straight forward as Dirichlet BVP and Neumann BVP. For the future research, we will consider the different shape domains for mixed BVP with different prescribed boundary conditions.
Exponential reduction of finite volume effects with twisted boundary conditions
Cherman, Aleksey; Sen, Srimoyee; Wagman, Michael L.; Yaffe, Laurence G.
2017-04-01
Flavor-twisted boundary conditions can be used for exponential reduction of finite volume artifacts in flavor-averaged observables in lattice QCD calculations with S U (Nf) light quark flavor symmetry. Finite volume artifact reduction arises from destructive interference effects in a manner closely related to the phase averaging which leads to large Nc volume independence. With a particular choice of flavor-twisted boundary conditions, finite volume artifacts for flavor-singlet observables in a hypercubic spacetime volume are reduced to the size of finite volume artifacts in a spacetime volume with periodic boundary conditions that is four times larger.
Boundary conditions for potentials at a plane interface
Energy Technology Data Exchange (ETDEWEB)
Tsai, W.Y.; DeRaad, L.L. Jr.
1985-01-01
For the case of plane interfaces, it is shown that Maxwell's equations can be solved by use of potentials that satisfy a set of decoupled boundary conditions. This is accomplished by exploiting the gauge freedom that is intrinsic to potentials. It is shown that it is always possible to choose a special Lorentz gauge such that the boundary conditions can be restated as the continuity of the vector and scalar potentials as well as the normal derivative of the tangential components of the vector potential. The advantages of this new set of decoupled boundary conditions are demonstrated by three simple examples.
Facilitating conditions for boundary-spanning behavior in governance networks
I.F. van Meerkerk (Ingmar); J. Edelenbos (Jurian)
2017-01-01
textabstractThis article examines the impact of two facilitating conditions for boundary-spanning behaviour in urban governance networks. While research on boundary spanning is growing, there is little attention for antecedents. Combining governance network literature on project management and
Directory of Open Access Journals (Sweden)
Nieto JuanJ
2009-01-01
Full Text Available This paper deals with some existence results for a boundary value problem involving a nonlinear integrodifferential equation of fractional order with integral boundary conditions. Our results are based on contraction mapping principle and Krasnosel'skiĭ's fixed point theorem.
Directory of Open Access Journals (Sweden)
John Graef
2013-09-01
Full Text Available The authors consider a nonlinear fractional boundary value problem with the Dirichlet boundary condition. An associated Green's function is constructed as a series of functions by applying spectral theory. Criteria for the existence and uniqueness of solutions are obtained based on it.
Refined impedance boundary conditions on a semitransparent periodically loaded structure
Tereshin, O. N.; Dvurechenskii, V. D.
1987-09-01
Improved impedance boundary conditions are presented for a semitransparent periodically loaded structure, i.e., a periodic array of conductors in which reactive loads are inserted. Structures of this sort find application in antenna-feed devices.
Directory of Open Access Journals (Sweden)
Guotao Wang
2012-01-01
Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.
Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions
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Binbin Pei
2017-01-01
Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.
Time-domain boundary conditions for outdoor ground surfaces
Collier, Sandra L.; Ostashev, Vladimir E.; Wilson, D. Keith; Marlin, David H.
2003-10-01
Finite-difference time-domain techniques are promising for detailed dynamic simulations of sound propagation in complex atmospheric environments. Success of such simulations requires the development of new techniques to accurately handle the reflective and absorptive properties of a porous ground. One method of treating the ground boundary condition in the time domain [Salomons et al., Acta Acust. 88, 483-492 (2002)] is to use modified fluid dynamic equations, where the ground is considered as a porous medium described by its physical properties. However, this approach significantly increases computation time, as the domain must be extended into the ground and a large number of grid points are needed. Standard impedance models for the ground boundary condition are frequency-domain models, which generally are non-causal [Y. H. Berthelot, J. Acoust. Soc. Am. 109, 1736-1739 (2001)]. The development of a time-domain boundary condition from these models requires removing the singularity from the impedance equation when transforming from the frequency domain to the time domain. Alternatively, as the impedance boundary condition is a flux equation, a time-domain boundary condition can be derived from first principles, using the physical properties of the ground. We report on our development of a time-domain ground boundary condition.
Two Baryons with Twisted Boundary Conditions
Energy Technology Data Exchange (ETDEWEB)
Briceno, Raul [Thomas Jefferson National Accelerator Facility, Newport News, VA (United States); Davoudi, Zohreh [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States); Luu, Thomas [Lawrence Livermore National Laboratory, Livermore, CA (United States); Savage, Martin [Univ. of Washington, Seattle, WA (United States) and Institute for Nuclear Theory, Seattle, WA (United States)
2014-04-01
The quantization condition for two particle systems with arbitrary number of two-body open coupled-channels, spin and masses in a finite cubic volume is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is fully relativistic and holds for all momenta below inelastic thresholds and is exact up to exponential volume corrections that are governed by m{sub {pi}} L, where m{sub {pi}} is the pion mass and L is the spatial extent of my box. Its implication for the studies of coupled-channel baryon-baryon systems is discussed, and the necessary tools for implementing the formalism are review.
Cai, Shuang; Zhao, Weiwei; Zafar, Amina; Wu, Zhangting; Tao, Yi; Bi, Kedong; Wei, Zhiyong; Ni, Zhenhua; Chen, Yunfei
2017-10-01
Monolayer transition metal dichalcogenides (TMDs) such as MoS2 and WS2 have been considered as promising candidate materials in nanophotonic applications. However, the structure stability of TMDs based optoelectronic devices is highly sensitive to the working environment. Here we present a successive photoluminescence study of the thermal stability characterization of grain boundary in chemical vapor deposition grown monolayer WS2. Results show that PL intensity enhancement in grain boundaries can be significantly weakened during the annealing process. Transformation temperature starts around 210 °C, substantially lower than the surrounding non-grain-boundary area. First-principle calculations results show that the PL quenching of grain boundaries is caused by the increased structural defects induced by annealing process, which makes the transition of electrons more difficult. Our results provide a route for characterizing the structure stability of two dimensional (2D) semiconductors, calling for extra attention to nanophotonic device working condition.
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson
2012-05-01
The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.
Boundary conditions for gas flow problems from anisotropic scattering kernels
To, Quy-Dong; Vu, Van-Huyen; Lauriat, Guy; Léonard, Céline
2015-10-01
The paper presents an interface model for gas flowing through a channel constituted of anisotropic wall surfaces. Using anisotropic scattering kernels and Chapman Enskog phase density, the boundary conditions (BCs) for velocity, temperature, and discontinuities including velocity slip and temperature jump at the wall are obtained. Two scattering kernels, Dadzie and Méolans (DM) kernel, and generalized anisotropic Cercignani-Lampis (ACL) are examined in the present paper, yielding simple BCs at the wall fluid interface. With these two kernels, we rigorously recover the analytical expression for orientation dependent slip shown in our previous works [Pham et al., Phys. Rev. E 86, 051201 (2012) and To et al., J. Heat Transfer 137, 091002 (2015)] which is in good agreement with molecular dynamics simulation results. More important, our models include both thermal transpiration effect and new equations for the temperature jump. While the same expression depending on the two tangential accommodation coefficients is obtained for slip velocity, the DM and ACL temperature equations are significantly different. The derived BC equations associated with these two kernels are of interest for the gas simulations since they are able to capture the direction dependent slip behavior of anisotropic interfaces.
Studies of planetary boundary layer by infrared thermal imagery
Energy Technology Data Exchange (ETDEWEB)
Albina, Bogdan; Dimitriu, Dan Gheorghe, E-mail: dimitriu@uaic.ro; Gurlui, Silviu Octavian, E-mail: dimitriu@uaic.ro [Alexandru Ioan Cuza University of Iasi, Faculty of Physics, Atmosphere Optics, Spectroscopy and Lasers Laboratory, 11 Carol I Blvd., 700506 Iasi (Romania); Cazacu, Marius Mihai [Alexandru Ioan Cuza University of Iasi, Faculty of Physics, Atmosphere Optics, Spectroscopy and Lasers Laboratory, 11 Carol I Blvd., 700506 Iasi, Romania and Department of Physics, Gheorghe Asachi Technical University of Iasi, 59A Mangeron Blvd., 700 (Romania); Timofte, Adrian [Alexandru Ioan Cuza University of Iasi, Faculty of Physics, Atmosphere Optics, Spectroscopy and Lasers Laboratory, 11 Carol I Blvd., 700506 Iasi, Romania and National Meteorological Administration, Regional Forecast Center Bacau, 1 Cuza Voda Str., 60 (Romania)
2014-11-24
The IR camera is a relatively novel device for remote sensing of atmospheric thermal processes from the Planetary Boundary Layer (PBL) based on measurements of the infrared radiation. Infrared radiation is energy radiated by the motion of atoms and molecules on the surface of aerosols, when their temperature is more than absolute zero. The IR camera measures directly the intensity of radiation emitted by aerosols which is converted by an imaging sensor into an electric signal, resulting a thermal image. Every image pixel that corresponds to a specific radiance is pre-processed to identify the brightness temperature. The thermal infrared imaging radiometer used in this study, NicAir, is a precision radiometer developed by Prata et al. The device was calibrated for the temperature range of 270–320 K and using a calibration table along with image processing software, important information about variations in temperature can be extracted from acquired IR images. The PBL is the lowest layer of the troposphere where the atmosphere interacts with the ground surfaces. The importance of PBL lies in the fact that it provides a finite but varying volume in which pollutants can disperse. The aim of this paper is to analyze the PBL altitude and thickness variations over Iasi region using the IR imaging camera as well as its behavior from day to night and thermal processes occurring in PBL.
DNS of Turbulent Boundary Layers under Highenthalpy Conditions
Duan, Lian; Martín, Pino
2010-11-01
To study real-gas effects and turbulence-chemistry interaction, direct numerical simulations (DNS) of hypersonic boundary layers are conducted under typical hypersonic conditions. We consider the boundary layer on a lifting-body consisting of a flat plate at an angle of attack, which flies at altitude 30km with a Mach number 21. Two different inclined angles, 35^o and 8^o, are considered,representing blunt and slender bodies. Both noncatalytic and supercatalytic wall conditions are considered. The DNS data are studied to assess the validity of Morkovin's hypothesis, the strong Reynolds analogy, as well as the behaviors of turbulence structures under high-enthalpy conditions.Relative to low-enthalpy conditions [1], significant differences in typical scalings are observed. [4pt] [1] L. Duan and I. Beekman and M. P. Mart'in, Direct numerical simulation of hypersonic turbulent boundary layers. Part 2: Effect of temperature, J. Fluid Mech. 655 (2010), 419-445.
Directory of Open Access Journals (Sweden)
Hussein A. H. Salem
2013-01-01
Full Text Available The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.
Boundary-value problems for second-order differential operators with nonlocal boundary conditions
Directory of Open Access Journals (Sweden)
Mohamed Denche
2007-04-01
Full Text Available In this paper, we study a second-order differential operator combining weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions, called regular and non regular cases, we prove that the resolvent decreases with respect to the spectral parameter in $L^{p}(0,1$, but there is no maximal decrease at infinity for $p>1$. Furthermore, the studied operator generates in $L^{p}(0,1 $, an analytic semi group for $p=1$ in the regular case, and an analytic semi group with singularities for $p>1$, in both cases, and for $p=1$, in the non regular case only. The obtained results are then used to show the correct solvability of a mixed problem for parabolic partial differential equation with non regular boundary conditions.
Equilibrium limit of thermal conduction and boundary scattering in nanostructures.
Haskins, Justin B; Kınacı, Alper; Sevik, Cem; Çağın, Tahir
2014-06-28
Determining the lattice thermal conductivity (κ) of nanostructures is especially challenging in that, aside from the phonon-phonon scattering present in large systems, the scattering of phonons from the system boundary greatly influences heat transport, particularly when system length (L) is less than the average phonon mean free path (MFP). One possible route to modeling κ in these systems is through molecular dynamics (MD) simulations, inherently including both phonon-phonon and phonon-boundary scattering effects in the classical limit. Here, we compare current MD methods for computing κ in nanostructures with both L ⩽ MFP and L ≫ MFP, referred to as mean free path constrained (cMFP) and unconstrained (uMFP), respectively. Using a (10,0) CNT (carbon nanotube) as a benchmark case, we find that while the uMFP limit of κ is well-defined through the use of equilibrium MD and the time-correlation formalism, the standard equilibrium procedure for κ is not appropriate for the treatment of the cMFP limit because of the large influence of boundary scattering. To address this issue, we define an appropriate equilibrium procedure for cMFP systems that, through comparison to high-fidelity non-equilibrium methods, is shown to be the low thermal gradient limit to non-equilibrium results. Further, as a means of predicting κ in systems having L ≫ MFP from cMFP results, we employ an extrapolation procedure based on the phenomenological, boundary scattering inclusive expression of Callaway [Phys. Rev. 113, 1046 (1959)]. Using κ from systems with L ⩽ 3 μm in the extrapolation, we find that the equilibrium uMFP κ of a (10,0) CNT can be predicted within 5%. The equilibrium procedure is then applied to a variety of carbon-based nanostructures, such as graphene flakes (GF), graphene nanoribbons (GNRs), CNTs, and icosahedral fullerenes, to determine the influence of size and environment (suspended versus supported) on κ. Concerning the GF and GNR systems, we find that
Mahmood, Asif; Aziz, Asim; Jamshed, Wasim; Hussain, Sajid
Solar energy is the cleanest, renewable and most abundant source of energy available on earth. The main use of solar energy is to heat and cool buildings, heat water and to generate electricity. There are two types of solar energy collection system, the photovoltaic systems and the solar thermal collectors. The efficiency of any solar thermal system depend on the thermophysical properties of the operating fluids and the geometry/length of the system in which fluid is flowing. In the present research a simplified mathematical model for the solar thermal collectors is considered in the form of non-uniform unsteady stretching surface. The flow is induced by a non-uniform stretching of the porous sheet and the uniform magnetic field is applied in the transverse direction to the flow. The non-Newtonian Maxwell fluid model is utilized for the working fluid along with slip boundary conditions. Moreover the high temperature effect of thermal radiation and temperature dependent thermal conductivity are also included in the present model. The mathematical formulation is carried out through a boundary layer approach and the numerical computations are carried out for cu-water and TiO2 -water nanofluids. Results are presented for the velocity and temperature profiles as well as the skin friction coefficient and Nusselt number and the discussion is concluded on the effect of various governing parameters on the motion, temperature variation, velocity gradient and the rate of heat transfer at the boundary.
Reduction in thermal boundary conductance due to proton implantation in silicon and sapphire
Hopkins, Patrick E.; Hattar, Khalid; Beechem, Thomas; Ihlefeld, Jon F.; Medlin, Douglas L.; Piekos, Edward S.
2011-06-01
We measure the thermal boundary conductance across Al/Si and Al/Al2O3 interfaces that are subjected to varying doses of proton ion implantation with time domain thermoreflectance. The proton irradiation creates a major reduction in the thermal boundary conductance that is much greater than the corresponding decrease in the thermal conductivities of both the Si and Al2O3 substrates into which the ions were implanted. Specifically, the thermal boundary conductances decrease by over an order of magnitude, indicating that proton irradiation presents a unique method to systematically decrease the thermal boundary conductance at solid interfaces.
Transport synthetic acceleration with opposing reflecting boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Zika, M.R.; Adams, M.L.
2000-02-01
The transport synthetic acceleration (TSA) scheme is extended to problems with opposing reflecting boundary conditions. This synthetic method employs a simplified transport operator as its low-order approximation. A procedure is developed that allows the use of the conjugate gradient (CG) method to solve the resulting low-order system of equations. Several well-known transport iteration algorithms are cast in a linear algebraic form to show their equivalence to standard iterative techniques. Source iteration in the presence of opposing reflecting boundary conditions is shown to be equivalent to a (poorly) preconditioned stationary Richardson iteration, with the preconditioner defined by the method of iterating on the incident fluxes on the reflecting boundaries. The TSA method (and any synthetic method) amounts to a further preconditioning of the Richardson iteration. The presence of opposing reflecting boundary conditions requires special consideration when developing a procedure to realize the CG method for the proposed system of equations. The CG iteration may be applied only to symmetric positive definite matrices; this condition requires the algebraic elimination of the boundary angular corrections from the low-order equations. As a consequence of this elimination, evaluating the action of the resulting matrix on an arbitrary vector involves two transport sweeps and a transmission iteration. Results of applying the acceleration scheme to a simple test problem are presented.
Superradiance in the BTZ black hole with Robin boundary conditions
Dappiaggi, Claudio; Ferreira, Hugo R. C.; Herdeiro, Carlos A. R.
2018-03-01
We show the existence of superradiant modes of massive scalar fields propagating in BTZ black holes when certain Robin boundary conditions, which never include the commonly considered Dirichlet boundary conditions, are imposed at spatial infinity. These superradiant modes are defined as those solutions whose energy flux across the horizon is towards the exterior region. Differently from rotating, asymptotically flat black holes, we obtain that not all modes which grow up exponentially in time are superradiant; for some of these, the growth is sourced by a bulk instability of AdS3, triggered by the scalar field with Robin boundary conditions, rather than by energy extraction from the BTZ black hole. Thus, this setup provides an example wherein Bosonic modes with low frequency are pumping energy into, rather than extracting energy from, a rotating black hole.
Vibration Analysis of Annular Sector Plates under Different Boundary Conditions
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Dongyan Shi
2014-01-01
Full Text Available An analytical framework is developed for the vibration analysis of annular sector plates with general elastic restraints along each edge of plates. Regardless of boundary conditions, the displacement solution is invariably expressed as a new form of trigonometric expansion with accelerated convergence. The expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling annular sector plates under a variety of boundary conditions and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. Of equal importance, the proposed approach is universally applicable to annular sector plates of any inclusion angles up to 2π. The reliability and accuracy of the current method are adequately validated through numerical examples.
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
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Ciprian G. Gal
2017-01-01
Full Text Available Given a bounded domain Ω⊂RN with a Lipschitz boundary ∂Ω and p,q∈(1,+∞, we consider the quasilinear elliptic equation -Δpu+α1u=f in Ω complemented with the generalized Wentzell-Robin type boundary conditions of the form bx∇up-2∂nu-ρbxΔq,Γu+α2u=g on ∂Ω. In the first part of the article, we give necessary and sufficient conditions in terms of the given functions f, g and the nonlinearities α1, α2, for the solvability of the above nonlinear elliptic boundary value problems with the nonlinear boundary conditions. In other words, we establish a sort of “nonlinear Fredholm alternative” for our problem which extends the corresponding Landesman and Lazer result for elliptic problems with linear homogeneous boundary conditions. In the second part, we give some additional results on existence and uniqueness and we study the regularity of the weak solutions for these classes of nonlinear problems. More precisely, we show some global a priori estimates for these weak solutions in an L∞-setting.
Directory of Open Access Journals (Sweden)
Paul Eloe
2002-01-01
Full Text Available The method of quasilinearization for nonlinear impulsive differential equations with linear boundary conditions is studied. The boundary conditions include periodic boundary conditions. It is proved the convergence is quadratic.
Function Substitution in Partial Differential Equations: Nonhomogeneous Boundary Conditions
Directory of Open Access Journals (Sweden)
T. V. Oblakova
2017-01-01
Full Text Available The paper considers a mixed initial-boundary value problem for a parabolic equation with nonhomogeneous boundary conditions. The classical approach to search for analytical solution of such problems in the first phase involves variable substitution, leading to a problem with homogeneous boundary conditions. Reference materials [1] give, as a rule, the simplest types of variable substitutions where new and old unknown functions differ by a term, linear in the spatial variable. The form of this additive term depends on the type of the boundary conditions, but is in no way related to the equation under consideration. Moreover, in the case of the second boundary-value problem, it is necessary to use a quadratic additive, since a linear substitution for this type of conditions may be unavailable. The courseware [2] - [4], usually, ends only with the first boundary-value problem generally formulated.The paper considers a substitution that takes into account, in principle, the form of a linear differential operator. Namely, as an additive term, it is proposed to use the parametrically time-dependent solution of the boundary value problem for an ordinary differential equation obtained from the original partial differential equation by the method of separation of the Fourier variables.The existence of the proposed substitution for boundary conditions of any type is proved by the example of a non-stationary heat-transfer equation with the heat exchange available with the surrounding medium. In this case, the additive term is a linear combination of hyperbolic functions. It is shown that, in addition to the "insensitivity" to the type of boundary conditions, the advantages of a new substitution in comparison with the traditional linear (or quadratic one include a much simpler structure of the solution obtained. Just the described approach allows us to obtain a solution with a clearly distinguished stationary component, in case a stationarity occurs, for
Boundary conditions for hyperbolic systems of partial differentials equations.
Guaily, Amr G; Epstein, Marcelo
2013-07-01
An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.
Optimal control problems for impulsive systems with integral boundary conditions
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Allaberen Ashyralyev
2013-03-01
Full Text Available In this article, the optimal control problem is considered when the state of the system is described by the impulsive differential equations with integral boundary conditions. Applying the Banach contraction principle the existence and uniqueness of the solution is proved for the corresponding boundary problem by the fixed admissible control. The first and second variation of the functional is calculated. Various necessary conditions of optimality of the first and second order are obtained by the help of the variation of the controls.
Non-local boundary conditions and internal gravity wave generation
Bulatov, Vitaly V
2010-01-01
This work focuses on the mathematical modeling of wave dynamics in a stratified medium. Non-local absorbing boundary conditions are considered based on the two following assumptions: (i) a linear theory can be applied at large distances from perturbation sources; and (ii) there are no other sources of wave disturbance outside the mixing zone in the stratified medium. The boundary conditions considered in this paper allowed us to describe the diverging internal gravity waves generated by the mixing region in a stratified medium.
Weak imposition of the slip boundary condition on curved boundaries for Stokes flow
Urquiza, José M.; Garon, André; Farinas, Marie-Isabelle
2014-01-01
We study the finite element approximation of two methods to weakly impose a slip boundary condition for incompressible fluid flows: the Lagrange multiplier method and Nitsche's method. For each method, we can distinguish several formulations depending on the values of some real parameters. In the case of a spatial domain with a polygonal or polyhedral boundary, we prove convergence results of their finite element approximations, extending previous results of Verfürth [33] and we show numerical results confirming them. In the case of a spatial domain with a smooth curved boundary, numerical results show that approximations computed on polygonal domains approximating the original domain may not converge to the exact solution, depending on the values of the aforementioned parameters and on the finite element discretization. These negative results seem to highlight Babuska's like paradox, due to the approximation of the boundary by polygonal ones. In particular, they seem to contradict some of Verfürth's theoretical convergence results.
Thermal conductivity at different humidity conditions
DEFF Research Database (Denmark)
Kristiansen, Finn Harken; Rode, Carsten
1999-01-01
The thermal conductivity (the l-value) of several alternative insulation products and a traditional product is determined under different humidity conditions in a specially constructed hot plate apparatus.The hot plate apparatus is constructed with an air gap on each side of the test specimen where...... of the thermal conductivity is 3-8% because of the hygroscopic uptake of humidity from the ambient air....
A New Parallel Boundary Condition for Turbulence Simulations in Stellarators
Martin, Mike F.; Landreman, Matt; Dorland, William; Xanthopoulos, Pavlos
2017-10-01
For gyrokinetic simulations of core turbulence, the ``twist-and-shift'' parallel boundary condition (Beer et al., PoP, 1995), which involves a shift in radial wavenumber proportional to the global shear and a quantization of the simulation domain's aspect ratio, is the standard choice. But as this condition was derived under the assumption of axisymmetry, ``twist-and-shift'' as it stands is formally incorrect for turbulence simulations in stellarators. Moreover, for low-shear stellarators like W7X and HSX, the use of a global shear in the traditional boundary condition places an inflexible constraint on the aspect ratio of the domain, requiring more grid points to fully resolve its extent. Here, we present a parallel boundary condition for ``stellarator-symmetric'' simulations that relies on the local shear along a field line. This boundary condition is similar to ``twist-and-shift'', but has an added flexibility in choosing the parallel length of the domain based on local shear consideration in order to optimize certain parameters such as the aspect ratio of the simulation domain.
Gorham, Caroline S.; Hattar, Khalid; Cheaito, Ramez; Duda, John C.; Gaskins, John T.; Beechem, Thomas E.; Ihlefeld, Jon F.; Biedermann, Laura B.; Piekos, Edward S.; Medlin, Douglas L.; Hopkins, Patrick E.
2014-07-01
The thermal boundary conductance across solid-solid interfaces can be affected by the physical properties of the solid boundary. Atomic composition, disorder, and bonding between materials can result in large deviations in the phonon scattering mechanisms contributing to thermal boundary conductance. Theoretical and computational studies have suggested that the mixing of atoms around an interface can lead to an increase in thermal boundary conductance by creating a region with an average vibrational spectra of the two materials forming the interface. In this paper, we experimentally demonstrate that ion irradiation and subsequent modification of atoms at solid surfaces can increase the thermal boundary conductance across solid interfaces due to a change in the acoustic impedance of the surface. We measure the thermal boundary conductance between thin aluminum films and silicon substrates with native silicon dioxide layers that have been subjected to proton irradiation and post-irradiation surface cleaning procedures. The thermal boundary conductance across the Al/native oxide/Si interfacial region increases with an increase in proton dose. Supported with statistical simulations, we hypothesize that ion beam mixing of the native oxide and silicon substrate within ˜2.2nm of the silicon surface results in the observed increase in thermal boundary conductance. This ion mixing leads to the spatial gradation of the silicon native oxide into the silicon substrate, which alters the acoustic impedance and vibrational characteristics at the interface of the aluminum film and native oxide/silicon substrate. We confirm this assertion with picosecond acoustic analyses. Our results demonstrate that under specific conditions, a "more disordered and defected" interfacial region can have a lower resistance than a more "perfect" interface.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 4. The No-Slip Boundary Condition in Fluid Mechanics - 1.The Riddle of Fluid Sticking to the Wall in Flow. Sandeep Prabhakara M D Deshpande. General Article Volume 9 Issue 4 April 2004 pp 50-60 ...
Stress and mixed boundary conditions for two-dimensional ...
Indian Academy of Sciences (India)
For plate bending and stretching problems in two-dimensional (2D) dodecagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory and Wan is ...
Validation of Boundary Conditions for CFD Simulations on Ventilated Rooms
DEFF Research Database (Denmark)
Topp, Claus; Jensen, Rasmus Lund; Pedersen, D.N.
2001-01-01
The application of Computational Fluid Dynamics (CFD) for ventilation research and design of ventilation systems has increased during the recent years. This paper provides an investigation of direct description of boundary conditions for a complex inlet diffuser and a heated surface. A series...
"Missing" boundary conditions? Discretize first, substitute next, and combine later
Veldman, Arthur E.P.
1990-01-01
A simple approach exists to prevent the need for constructing boundary conditions in situations where they are not explicitly supplied by the original analytical formulation of the problem. An example is the Poisson equation for the pressure in calculations of incompressible flow. Other examples are
Stokes flow with slip and Kuwabara boundary conditions
Indian Academy of Sciences (India)
... distributed parallel circular cylinder or spheres in uniform viscous flow are investigated with slip boundary condition under Stokes approximation using particle-in-cell model technique and the result compared with the no-slip case. The corresponding problem of streaming flow past spheroidal particles departing but little in ...
Existence of solutions for fractional differential inclusions with boundary conditions
Directory of Open Access Journals (Sweden)
Dandan Yang
2010-07-01
Full Text Available This article concerns the existence of solutions for fractional-order differential inclusions with boundary-value conditions. The main tools are based on fixed point theorems due to Bohnerblust-Karlin and Leray-Schauder together with a continuous selection theorem for upper semi-continuous multi-valued maps.
Stress and mixed boundary conditions for two-dimensional ...
Indian Academy of Sciences (India)
Abstract. For plate bending and stretching problems in two-dimensional (2D) do- decagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for. QCs are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all order. The method developed by Gregory ...
Mesoscopic Modelling of Heterogeneous Boundary Conditions for Microchannel Flows
Benzi, R.; Biferale, L.; Sbragaglia, M.; Succi, S.; Toschi, F.
2006-01-01
We present a mesoscopic model of the fluid–wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single-phase fluid. We distinguish different slippage
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 9; Issue 5. The No-Slip Boundary Condition in Fluid Mechanics - Solution of the Sticky Problem. Sandeep Prabhakara M D Deshpande. General Article Volume 9 Issue 5 May 2004 pp 61-71 ...
On a stochastic Burgers equation with Dirichlet boundary conditions
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Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
Salesperson improvisation: Antecedents, performance outcomes, and boundary conditions
Yeboah Banin, A.; Boso, N.; Hultman, M.; Souchon, A. L.; Hughes, P; Nemkova, E.
2016-01-01
The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Premised on the idea that not all salesperson behaviors can be pre-scripted and that, increasingly, salespersons must find ways to respond to unexpected but urgent market conditions, this study theorizes the drivers, outcomes and boundary conditions of salesperson improvisation. Using primary data from industrial salespersons, the study examine...
Thermal boundary conductance of hydrophilic and hydrophobic ionic liquids
Oyake, Takafumi; Sakata, Masanori; Yada, Susumu; Shiomi, Junichiro
2015-03-01
A solid/liquid interface plays a critical role for understanding mechanisms of biological and physical science. Moreover, carrier density of the surface is dramatically enhanced by electric double layer with ionic liquid, salt in the liquid state. Here, we have measured the thermal boundary conductance (TBC) across an interface of gold thin film and ionic liquid by using time-domain thermoreflectance technique. Following the prior researches, we have identified the TBC of two interfaces. One is gold and hydrophilic ionic liquid, N,N-Diethyl-N-methyl-N-(2-methoxyethyl) ammonium tetrafluoroborate (DEME-BF4), which is a hydrophilic ionic liquid, and the other is N,N-Diethyl-N-methyl-N-(2-methoxyethyl) ammonium bis (trifluoromethanesulfonyl) imide (DEME-TFSI), which is a hydrophobic ionic liquid. We found that the TBC between gold and DEME-TFIS (19 MWm-2K-1) is surprisingly lower than the interface between gold and DEME-BF4 (45 MWm-2K-1). With these data, the importance of the wetting angle and ion concentration for the thermal transport at the solid/ionic liquid interface is discussed. Part of this work is financially supported by Japan Society for the Promotion of Science (JSPS) and Japan Science and Technology Agency. The author is financially supported by JSPS Fellowship.
The boundary conditions for point transformed electromagnetic invisibility cloaks
Energy Technology Data Exchange (ETDEWEB)
Weder, Ricardo [Departamento de Metodos Matematicos y Numericos, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)], E-mail: weder@servidor.unam.mx
2008-10-17
In this paper we study point transformed electromagnetic invisibility cloaks in transformation media that are obtained by transformation from general anisotropic media. We assume that there are several point transformed electromagnetic cloaks located in different points in space. Our results apply in particular to the first-order invisibility cloaks introduced by Pendry et al and to the high-order invisibility cloaks introduced by Hendi et al and by Cai et al. We identify the appropriate cloaking boundary conditions that the solutions of Maxwell equations have to satisfy at the outside, {partial_derivative}K{sub +}, and at the inside, {partial_derivative}K{sub -}, of the boundary of the cloaked object K in the case where the permittivity and the permeability are bounded below and above in K. Namely, that the tangential components of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub +}-which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at {partial_derivative}K{sub -}. These results are proven requiring that energy be conserved. In the case of one spherical cloak with a spherically stratified K and a radial current at {partial_derivative}K we verify by an explicit calculation that our cloaking boundary conditions are satisfied and that cloaking of active devices holds, even if the current is at the boundary of the cloaked object. As we prove our results for media that are obtained by transformation from general anisotropic media, our results apply to the cloaking of objects with passive and active devices contained in general anisotropic media, in particular to objects with passive and active devices contained inside general crystals. Our results suggest a method to enhance cloaking in the approximate transformation media that are used in practice. Namely, to coat the boundary of the cloaked object (the inner boundary of the cloak) with a material that imposes the
Boundary Conditions for a New Type of Design Task
DEFF Research Database (Denmark)
McAloone, Tim C.
2011-01-01
-teresting to understand the shifting focus and identification of boundary conditions that manufacturing organisations must undergo, in order to develop just as systematic an approach to the service-related aspects of their business development, as they have in place for their product development. This chapter...... and knowledge associated with the use of the product is increasingly perceived to be the new design object. But how to organise the design of combined products and services, over expanded time domains and new stakeholder boundaries? The design research community is paying increasing attention to this new design...
Directory of Open Access Journals (Sweden)
Boričić Aleksandar Z.
2016-01-01
Full Text Available The unsteady 2-D dynamic, thermal, and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal cylinder of incompressible and electrical conductivity fluid, in mixed convection in the presence of heat source or sink and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that induction of outer magnetic field is a function of longitudinal co-ordinate outer electric field is neglected and magnetic Reynolds number is significantly lower than one, i. e. considered the problem is in approximation without induction. Fluid electrical conductivity is constant. Free stream velocity, temperature, and concentration on the body are functions of longitudinal co-ordinate. The developed governing boundary layer equations and associated boundary conditions are made dimensionless using a suitable similarity transformation and similarity parameters. System of non-dimensionless equations is solved using the implicit finite difference three-diagonal and iteration method. Numerical results are obtained and presented for different Prandtl, Eckart, and Schmidt numbers, and values: magnetic parameter, temperature, and diffusion parameters, buoyancy temperature parameters, thermal parameter, and chemical reaction parameter. Variation of velocity profiles, temperature and diffusion distributions, and many integral and differential characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.
On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics
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Thomas Hochrainer
2017-07-01
Full Text Available Continuum dislocation dynamics (CDD is a single crystal strain gradient plasticity theory based exclusively on the evolution of the dislocation state. Recently, we derived a constitutive theory for the average dislocation velocity in CDD in a phase field-type description for an infinite domain. In the current work, so-called rational thermodynamics is employed to obtain thermodynamically consistent boundary conditions for the dislocation density variables of CDD. We find that rational thermodynamics reproduces the bulk constitutive equations as obtained from irreversible thermodynamics. The boundary conditions we find display strong parallels to the microscopic traction conditions derived by Gurtin and Needleman (M.E. Gurtin and A. Needleman, J. Mech. Phys. Solids 53 (2005 1–31 for strain gradient theories based on the Kröner–Nye tensor.
Modeling Groundwater Flow using both Neumann and Dirichlet Boundary Conditions
Zijl, Wouter; El-Rawy, Mustafa; Batelaan, Okke
2013-04-01
In groundwater flow models it is customary to use the recharge rate, obtained from measured precipitation minus run off and evapotranspiration, as the top boundary condition (a Neumann boundary condition). However, as has been emphasized by Tóth (1962; 2009), the topography of the water table offers a better boundary condition (a Dirichlet boundary condition), because it leads to the delineation of flow systems and stagnation zones. However, in practical modeling studies the recharge rates obtained when using the Dirichlet boundary condition may turn out to be unrealistically small or large. To remediate this we have developed an unconventional modeling procedure that is based on both the Neumann and the Dirichlet boundary condition on the phreatic surface. Such a model does not only calculate the heads and fluxes, but also an update of the initially perceived hydraulic conductivities, in such a way that the initially perceived conductivity model is preserved as much as possible. For given grid block conductivities, numerical groundwater models (e.g. MODFLOW) are linear in the heads. However, for given heads the numerical models are not linear in the grid block conductivities. Mohammed et al. (2009) have developed a MODFLOW-compatible numerical model that is linear in the stream functions for given grid block conductivities, while it is also linear in the grid block resistivities (inverse of conductivities) if the heads are given. Unconventional modeling is based on this bi-linearity. Assume we specify a reasonable perception of the hydraulic conductivities and determine the numerical solution with Neumann boundary conditions. The resulting fluxes are then substituted into the stream function model, together with Dirichlet boundary conditions, and the grid block resistivities can then be determined by a standard routine for solving systems of linear algebraic equations. The thus calibrated grid block conductivities do not deviate much from the initially perceived
Directory of Open Access Journals (Sweden)
Swati Mukhopadhyay
2013-09-01
Full Text Available The boundary layer flow and heat transfer towards a porous exponential stretching sheet in presence of a magnetic field is presented in this analysis. Velocity slip and thermal slip are considered instead of no-slip conditions at the boundary. Thermal radiation term is incorporated in the temperature equation. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and energy equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter as well as with the increasing magnetic parameter. Temperature increases with the increasing values of magnetic parameter. Temperature is found to decrease with an increase of thermal slip parameter. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.
SOLUTION TO THE PROBLEM OF THERMOELASTIC VIBRATION OF A PLATE IN SPECIAL BOUNDARY CONDITIONS
Directory of Open Access Journals (Sweden)
Egorychev Oleg Aleksandrovich
2012-10-01
Full Text Available Operating conditions of uneven non-stationary heating can cause changes in physical and mechanical properties of materials. The awareness of the value and nature of thermal stresses is needed to perform a comprehensive analysis of structural strength. The authors provide their solution to the problem of identification of natural frequencies of vibrations of rectangular plates, whenever a thermal factor is taken into account. In the introductory section of the paper, the authors provide the equation describing the thermoelastic vibration of a plate and set the initial and boundary conditions. Furthermore, the authors provide a frequency equation derivation for the problem that has an analytical solution available (if all edges are simply supported at zero temperature. The equation derived by the authors has no analytical solution and can be solved only numerically. In the middle of the paper, the authors describe a method of frequency equation derivation for plates exposed to special boundary conditions, if the two opposite edges are simply supported at zero temperature, while the two other edges have arbitrary types of fixation and arbitrary thermal modes. For this boundary condition derived as a general solution, varying fixation of the two edges makes it possible to obtain transcendental trigonometric equations reducible to algebraic frequency equations by using expending in series. Thus, the obtaining frequency equations different from the general solution becomes possible for different types of boundary conditions. The final section of the paper covers the practical testing of the described method for the problem that has an analytical solution (all edges are simply supported at zero temperature as solved above. An approximate equation provided in the research leads to the analytical solution that is already available.
Effects of thermal aging on the microstructure of Type-II boundaries in dissimilar metal weld joints
Energy Technology Data Exchange (ETDEWEB)
Yoo, Seung Chang; Choi, Kyoung Joon [School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 100 Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan 689-798 (Korea, Republic of); Bahn, Chi Bum [School of Mechanical Engineering, Pusan National University, 63-gil, Geumjeong-Gu, Pusan 609-735 (Korea, Republic of); Kim, Si Hoon; Kim, Ju Young [School of Materials Science and Engineering, Ulsan National Institute of Science and Technology (UNIST), 100 Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan 689-798 (Korea, Republic of); Kim, Ji Hyun, E-mail: kimjh@unist.ac.kr [School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 100 Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan 689-798 (Korea, Republic of)
2015-04-15
In order to investigate the effects of long-term thermal aging on the microstructural evolution of Type-II boundary regions in the weld metal of Alloy 152, a representative dissimilar metal weld was fabricated from Alloy 690, Alloy 152, and A533 Gr.B. This mock-up was thermally aged at 450 °C to accelerate the effects of thermal aging in a nuclear power plant operation condition (320 °C). The microstructure of the Type-II boundary region of the weld root, which is parallel to and within 100 μm of the fusion boundary and known to be more susceptible to material degradation, was then characterized after different aging times using a scanning electron microscope equipped with an energy dispersive X-ray spectroscope for micro-compositional analysis, electron backscattered diffraction detector for grain and grain boundary orientation analysis, and a nanoindenter for measurement of mechanical properties. Through this, it was found that a steep compositional gradient and high grain average misorientation is created in the narrow zone between the Type-II and fusion boundaries, while the concentration of chromium and number of low-angle grain boundaries increases with aging time. A high average hardness was also observed in the same region of the dissimilar metal welds, with hardness peaking with thermal aging simulating an operational time of 15 years.
Effects of thermal aging on the microstructure of Type-II boundaries in dissimilar metal weld joints
Yoo, Seung Chang; Choi, Kyoung Joon; Bahn, Chi Bum; Kim, Si Hoon; Kim, Ju Young; Kim, Ji Hyun
2015-04-01
In order to investigate the effects of long-term thermal aging on the microstructural evolution of Type-II boundary regions in the weld metal of Alloy 152, a representative dissimilar metal weld was fabricated from Alloy 690, Alloy 152, and A533 Gr.B. This mock-up was thermally aged at 450 °C to accelerate the effects of thermal aging in a nuclear power plant operation condition (320 °C). The microstructure of the Type-II boundary region of the weld root, which is parallel to and within 100 μm of the fusion boundary and known to be more susceptible to material degradation, was then characterized after different aging times using a scanning electron microscope equipped with an energy dispersive X-ray spectroscope for micro-compositional analysis, electron backscattered diffraction detector for grain and grain boundary orientation analysis, and a nanoindenter for measurement of mechanical properties. Through this, it was found that a steep compositional gradient and high grain average misorientation is created in the narrow zone between the Type-II and fusion boundaries, while the concentration of chromium and number of low-angle grain boundaries increases with aging time. A high average hardness was also observed in the same region of the dissimilar metal welds, with hardness peaking with thermal aging simulating an operational time of 15 years.
Directory of Open Access Journals (Sweden)
Syahira Mansur
2014-01-01
Full Text Available The magnetohydrodynamic (MHD boundary layer flow of a nanofluid past a stretching/shrinking sheet with velocity, thermal, and solutal slip boundary conditions is studied. Numerical solutions to the governing equations were obtained using a shooting method. The skin friction coefficient and the local Sherwood number increase as the stretching/shrinking parameter increases. However, the local Nusselt number decreases with increasing the stretching/shrinking parameter. The range of the stretching/shrinking parameter for which the solution exists increases as the velocity slip parameter and the magnetic parameter increase. For the shrinking sheet, the skin friction coefficient increases as the velocity slip parameter and the magnetic parameter increase. For the stretching sheet, it decreases when the velocity slip parameter and the magnetic parameter increase. The local Nusselt number diminishes as the thermal slip parameter increases while the local Sherwood number decreases with increasing the solutal slip parameter. The local Nusselt number is lower for higher values of Lewis number, Brownian motion parameter, and thermophoresis parameter.
Revisiting Johnson and Jackson boundary conditions for granular flows
Energy Technology Data Exchange (ETDEWEB)
Li, Tingwen; Benyahia, Sofiane
2012-07-01
In this article, we revisit Johnson and Jackson boundary conditions for granular flows. The oblique collision between a particle and a flat wall is analyzed by adopting the classic rigid-body theory and a more realistic semianalytical model. Based on the kinetic granular theory, the input parameter for the partial-slip boundary conditions, specularity coefficient, which is not measurable in experiments, is then interpreted as a function of the particle-wall restitution coefficient, the frictional coefficient, and the normalized slip velocity at the wall. An analytical expression for the specularity coefficient is suggested for a flat, frictional surface with a low frictional coefficient. The procedure for determining the specularity coefficient for a more general problem is outlined, and a working approximation is provided.
Ullah, Imran; Bhattacharyya, Krishnendu; Shafie, Sharidan; Khan, Ilyas
2016-01-01
Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
Directory of Open Access Journals (Sweden)
Imran Ullah
Full Text Available Numerical results are presented for the effect of first order chemical reaction and thermal radiation on mixed convection flow of Casson fluid in the presence of magnetic field. The flow is generated due to unsteady nonlinearly stretching sheet placed inside a porous medium. Convective conditions on wall temperature and wall concentration are also employed in the investigation. The governing partial differential equations are converted to ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. It is noticed that fluid velocity rises with increase in radiation parameter in the case of assisting flow and is opposite in the case of opposing fluid while radiation parameter has no effect on fluid velocity in the forced convection. It is also seen that fluid velocity and concentration enhances in the case of generative chemical reaction whereas both profiles reduces in the case of destructive chemical reaction. Further, increase in local unsteadiness parameter reduces fluid velocity, temperature and concentration. Over all the effects of physical parameters on fluid velocity, temperature and concentration distribution as well as on the wall shear stress, heat and mass transfer rates are discussed in detail.
Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions
Grunau, H.-Ch.; Sweers, G.
1996-01-01
Cranston, Fabes and Zhao ([26], [5]) established the uniform bound sup x; y 2 x 6= y R G1;n (x; z)G1;n (z; y) dz G1;n (x; y) M < 1; (1) where G1;n (x; y) is the Green function for the Laplacian - with Dirichlet boundary conditions on a Lipschitz domain - Rn with n 3 (see [27] for n = 2).
Boundary conditions for simulating large SAW devices using ANSYS.
Peng, Dasong; Yu, Fengqi; Hu, Jian; Li, Peng
2010-08-01
In this report, we propose improved substrate left and right boundary conditions for simulating SAW devices using ANSYS. Compared with the previous methods, the proposed method can greatly reduce computation time. Furthermore, the longer the distance from the first reflector to the last one, the more computation time can be reduced. To verify the proposed method, a design example is presented with device center frequency 971.14 MHz.
Scattering of wedges and cones with impedance boundary conditions
Lyalinov, Mikhail
2012-01-01
This book is a systematic and detailed exposition of different analytical techniques used in studying two of the canonical problems, the wave scattering by wedges or cones with impedance boundary conditions. It is the first reference on novel, highly efficient analytical-numerical approaches for wave diffraction by impedance wedges or cones. The applicability of the reported solution procedures and formulae to existing software packages designed for real-world high-frequency problems encountered in antenna, wave propagation, and radar cross section.
On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2008-01-01
are suppressed by using a very high artificial hardening modulus. Through numerical studies of pure bending under plane strain conditions, it is shown that this method predicts the build-up of higher order stresses in the pseudo-elastic regime. This has the effect of delaying the onset of incipient yield......A computational method for dealing with higher order boundary conditions on moving elastic-plastic boundaries in strain gradient plasticity is proposed. The basic idea is to skip the notion of a purely elastic regime, and instead introduce a pseudo-elastic regime, where plastic deformations......, as well as extending the plastic zone further toward the neutral axis of the beam, when compared to conventional models. Arguments supporting the present method are presented that rest on both mathematical and physical grounds. The results obtained are compared with other methods for dealing with higher...
The Impact of Local Microclimate Boundary Conditions on Building Energy Performance
Directory of Open Access Journals (Sweden)
Anna Laura Pisello
2015-07-01
Full Text Available Local environmental boundaries play an important role in determining microclimate conditions affecting thermal-energy behavior of buildings. In this scenario, the purpose of the present work is to investigate how residential buildings are affected by different local microclimate conditions. To this aim, the continuous microclimate monitoring of (i a rural area; (ii a suburban area; and (iii an urban area is carried out, and the comparative analysis of the different boundary conditions is performed. In particular, the effect of the presence of a large lake in the rural area on building energy demand for heating and cooling is evaluated, both in winter and summer. Coupled degree hour method and numerical analysis are performed in order to predict the energy requirement of buildings subject to local microclimate boundary conditions. The main results show higher air temperature and relative humidity values for the rural area. No significant mitigation effect due to the lake presence is found in urban and suburban areas because of the peculiar wind regime of the region. Additionally, the dynamic thermal-energy simulation shows a decrease of 14% and 25% in the heating consumption and an increase of 58% and 194% in cooling requirements of buildings situated in the rural area around the lake compared to the urban and suburban areas, respectively.
Implementation of a Phase-Lagged Boundary Condition for Turbomachinery
Wouden, Alex; Cimbala, John; Lewis, Bryan
2012-11-01
One factor that contributes significantly to the cost of a time-dependent CFD simulation is the size and scope of the computational domain. Common approximations, such as periodic and symmetric boundary conditions, have the advantage of reducing the domain proportional to its periodicity or symmetry. However, turbomachinery applications featuring multiple blade rows render the periodic boundary condition unphysical because the adjacent blade rows are designed with dissimilar blade counts. Though the meshes of adjacent blade rows can be modeled independently and data can be interpolated across a grid interface, applying the standard periodic definition to the coupled faces leads to an over-constrained situation: a failure to reconcile two governing relations imposed on the same cell. A phase-lagged boundary condition (PLBC) relaxes the over-constraint problem and provides a more correct assumption for the resulting flow field. PLBC is available in a limited number of private CFD codes and is only briefly documented in the literature. The present work expands upon its development by implementing PLBC in OpenFOAM®, an open-source CFD software package. Its performance is demonstrated for basic turbomachinery applications through comparisons with full-wheel simulation. This research is funded by a grant from the DOE.
Danoyan Z.N.; Atoyan L.H.
2010-01-01
In the paper reflection problem of an incident bulk ferromagnetic spin-wave is solved. The wave reflects from the ferromagnetic medium surface, when on the surface are given the generalized boundary conditions for magnetization density [4]. Solution of the problem provides a foundation to confirm, that in ferromagnetic medium appears two non-homogeneous accompanying surface waves, besides of the mirror reflected wave. The two surface waves propagation velocities are the same, but coefficients...
Energy Technology Data Exchange (ETDEWEB)
Novikov, I.A.
1979-01-01
A mathematical solution is worked out for solving direct and inverse linear boundary problems on thermal conductivity where the heat transfer process is assumed to occur at a finite velocity. Three-dimensional potentials for a simple and binary layers and volume are introduced for the telegrapher's equation. Within the limiting cases of a parabolic and wave equation, they transfer to the corresponding heat and wave potentials. The introduced potentials make it possible to reduce the internal boundary problems of thermal conductivity to second order integral-differential equations. In addition, the potentials of the telegrapher's equation are used to reduce a linear three-dimensional boundary inverse problem on thermal conductivity to a system composed of integral-differential equations of the second order and a certain integral condition for two coordinate and time functions. 9 references.
Phonon thermal transport through tilt grain boundaries in strontium titanate
Energy Technology Data Exchange (ETDEWEB)
Zheng, Zexi; Chen, Xiang; Yang, Shengfeng; Xiong, Liming; Chen, Youping [Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611 (United States); Deng, Bowen; Chernatynskiy, Aleksandr [Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611 (United States)
2014-08-21
In this work, we perform nonequilibrium molecular dynamics simulations to study phonon scattering at two tilt grain boundaries (GBs) in SrTiO{sub 3}. Mode-wise energy transmission coefficients are obtained based on phonon wave-packet dynamics simulations. The Kapitza conductance is then quantified using a lattice dynamics approach. The obtained results of the Kapitza conductance of both GBs compare well with those obtained by the direct method, except for the temperature dependence. Contrary to common belief, the results of this work show that the optical modes in SrTiO{sub 3} contribute significantly to phonon thermal transport, accounting for over 50% of the Kapitza conductance. To understand the effect of the GB structural disorder on phonon transport, we compare the local phonon density of states of the atoms in the GB region with that in the single crystalline grain region. Our results show that the excess vibrational modes introduced by the structural disorder do not have a significant effect on phonon scattering at the GBs, but the absence of certain modes in the GB region appears to be responsible for phonon reflections at GBs. This work has also demonstrated phonon mode conversion and simultaneous generation of new modes. Some of the new modes have the same frequency as the initial wave packet, while some have the same wave vector but lower frequencies.
On the nonlinear Schrodinger equation with nonzero boundary conditions
Fagerstrom, Emily
integral, provided the initial condition satisfies further conditions. Modulational instability (focusing NLS with symmetric nonzero boundary conditions at infinity.) The focusing NLS equation is considered with potentials that are "box-like" piecewise constant functions. Several results are obtained. In particular, it is shown that there are conditions on the parameters of the potential for which there are no discrete eigenvalues. Thus there is a class of potentials for which the corresponding solutions of the NLS equation have no solitons. Hence, solitons cannot be the medium for the modulational instability. This contradicts a recent conjecture by Zakharov. On the other hand, it is shown for a different class of potentials the scattering problem always has a discrete eigenvalue along the imaginary axis. Thus, there exist arbitrarily small perturbations of the constant potential for which solitons exist, so no area theorem is possible. The existence, number and location of discrete eigenvalues in other situations are studied numerically. Finally, the small-deviation limit of the IST is computed and compared with the direct linearization of the NLS equation around a constant background. From this it is shown that there is an interval of the continuous spectrum on which the eigenvalue is imaginary and the scattering parameter is imaginary. The Jost eigenfunctions corresponding to this interval are the nonlinear analogue of the unstable Fourier modes. Defocusing NLS equation with asymmetric boundary conditions at infinity. The defocusing NLS equation with asymmetric boundary conditions is considered. To do so, first the case of symmetric boundary conditions is revisited. While the IST for this case has been formulated in the literature, it is usually done through the use of a uniformization variable. This was done because the eigenvalues of the scattering problem have branching; the uniformization variable allows one to move from a 2-sheeted Riemann surface to the complex
Dual reciprocity boundary element method for solving thermal wave model of bioheat transfer.
Liu, J; Lu, W
1997-12-01
The newly developed dual reciprocity boundary element method (DRBEM) was extended to solve the thermal wave model of bioheat transfer (TWMBT) and a practical algorithm was established. A preliminary simulation of the temperature evolution in a two dimensional zone under certain boundary conditions and micro wave heating was conducted as a numerical illustration for the method and some meaningful conclusions were drawn. The validity of DRBEM was testified through a comparison with finite difference method (FDM) under one-dimensional calculation. Owing to its unique advantages like not confined by the complex shape of biological bodies, no need of discretization of the inner domain, save vast CPU time and easy to deal with different bioheat models, DRBEM may become an important approach for predicting and controlling the transient temperature field of biological bodies under hyperthermia or hypothermia.
Unexpectedly high thermal boundary resistance of Cr/graphene/SiO2 structure
Zhan, Tianzhuo; Wang, Haidong; Xu, Yibin
2017-05-01
We measured the thermal resistances of the Au/graphene/SiO2, Au/Ti/graphene/SiO2, and Au/Cr/graphene/SiO2 structures. The thermal resistances of the three structures were found to be significantly higher than those of the corresponding graphene-free structures, indicating that even monolayer graphene can greatly increase the thermal boundary resistance at metal/SiO2 interfaces. Furthermore, the thermal resistance of the Au/Cr/graphene/SiO2 structure is unexpectedly significantly higher than those of the other two structures, indicating that the diffusion mismatch model (DMM) fails to predict the thermal boundary resistance at metal/graphene interfaces. The poly(methyl methacrylate) (PMMA) residue contamination layer on the graphene surface may play an important role in increasing the thermal resistances of metal/graphene/SiO2 structures. Also, transition metal/graphene and transition metal/PMMA interactions may also affect the thermal boundary resistance.
Thompson, Stephen C; LoPresti, Janice L
2008-03-01
Expressions are derived for the acoustical impedance of a rectangular enclosure and of a finite annular cylindrical enclosure. The derivation is valid throughout the frequency range in which all dimensions of the enclosure are much less than the wavelength. The results are valid throughout the range from adiabatic to isothermal conditions in the enclosure. The effect is equivalent to placing an additional, frequency-dependent complex impedance in parallel with the adiabatic compliance. As the thermal boundary layer grows to fill the cavity, the reactive part of the impedance varies smoothly from the adiabatic value to the isothermal value. In some microphones, this change in cavity stiffness is sufficient to modify the sensitivity. The resistive part of the additional cavity impedance varies as the inverse square root of frequency at high frequencies where the boundary layer has not grown to fill the enclosure. The thermal modification gives rise to a thermal noise whose spectral density varies asymptotically as l/f(3/2) above the isothermal transition frequency.
Ruggeri, Fabrizio
2016-05-12
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given prescribed initial condition. We show how to derive the joint likelihood function for the forward problem, given some measurements of the solution field subject to Gaussian noise. Given Gaussian priors for the time-dependent Dirichlet boundary values, we analytically marginalize the joint likelihood using the linearity of the equation. Our hierarchical Bayesian approach is fully implemented in an example that involves the heat equation. In this example, the thermal diffusivity is the unknown parameter. We assume that the thermal diffusivity parameter can be modeled a priori through a lognormal random variable or by means of a space-dependent stationary lognormal random field. Synthetic data are used to test the inference. We exploit the behavior of the non-normalized log posterior distribution of the thermal diffusivity. Then, we use the Laplace method to obtain an approximated Gaussian posterior and therefore avoid costly Markov Chain Monte Carlo computations. Expected information gains and predictive posterior densities for observable quantities are numerically estimated using Laplace approximation for different experimental setups.
Reddy, M. Gnaneswara
2015-01-01
The unsteady two-dimensional flow of a non-Newtonian fluid over a stretching surface with the effects of thermal radiation and variable thermal conductivity is investigated. The Casson fluid model is used to characterize the non-Newtonian fluid behavior. First, using a similarity transformation, the governing time-dependent partial differential equations are transformed into coupled nonlinear ordinary differential equations with variable coefficients. Then the transformed equations are solved numerically under appropriate boundary conditions by the shooting method. An exact solution corresponding to the momentum equation for a steady case is found. The obtained numerical results are analyzed as to the effect of the pertinent parameters on the flow and heat transfer characteristics.
MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate
Directory of Open Access Journals (Sweden)
Mohammad M. Rashidi
2014-01-01
Full Text Available We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to (x--1/2 where x- is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.
Influence of boundary conditions on fluid flow on hydrophobic surfaces
Simona, Fialová; František, Pochylý; Michal, Havlásek; Jiři, Malík
2017-09-01
The work is focused on the shape of velocity profiles of viscous liquid (water) in contact with hydrophobic surface. A demonstration is done on an example of liquid flow between two parallel plates. The solution is carried out at both the constant and variable viscosity of the liquid near the wall. The slip boundary condition of the liquid on the wall is expressed by the coefficient of adhesion and the shear stress on the wall. As a result, presented are the shapes of the velocity profiles in dependence on the coefficient of adhesion and the slip velocity on the wall. This solution is for laminar flow.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Magnetospheric conditions near the equatorial footpoints of proton isotropy boundaries
Directory of Open Access Journals (Sweden)
V. A. Sergeev
2015-12-01
Full Text Available Data from a cluster of three THEMIS (Time History of Events and Macroscale Interactions during Substorms spacecraft during February–March 2009 frequently provide an opportunity to construct local data-adaptive magnetospheric models, which are suitable for the accurate mapping along the magnetic field lines at distances of 6–9 Re in the nightside magnetosphere. This allows us to map the isotropy boundaries (IBs of 30 and 80 keV protons observed by low-altitude NOAA POES (Polar Orbiting Environmental Satellites to the equatorial magnetosphere (to find the projected isotropy boundary, PIB and study the magnetospheric conditions, particularly to evaluate the ratio KIB (Rc/rc; the magnetic field curvature radius to the particle gyroradius in the neutral sheet at that point. Special care is taken to control the factors which influence the accuracy of the adaptive models and mapping. Data indicate that better accuracy of an adaptive model is achieved when the PIB distance from the closest spacecraft is as small as 1–2 Re. For this group of most accurate predictions, the spread of KIB values is still large (from 4 to 32, with the median value KIB ~13 being larger than the critical value Kcr ~ 8 expected at the inner boundary of nonadiabatic angular scattering in the current sheet. It appears that two different mechanisms may contribute to form the isotropy boundary. The group with K ~ [4,12] is most likely formed by current sheet scattering, whereas the group having KIB ~ [12,32] could be formed by the resonant scattering of low-energy protons by the electromagnetic ion-cyclotron (EMIC waves. The energy dependence of the upper K limit and close proximity of the latter event to the plasmapause locations support this conclusion. We also discuss other reasons why the K ~ 8 criterion for isotropization may fail to work, as well as a possible relationship between the two scattering mechanisms.
Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle
Broeze, J.; Broeze, Jan; van Daalen, Edwin F.G.; van Daalen, E.F.G.
1992-01-01
A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary
Development of a Discrete Mass Inflow Boundary Condition for MFIX
Directory of Open Access Journals (Sweden)
Jordan Musser
2011-02-01
Full Text Available MFIX (Multiphase Flow with Interphase eXchanges is an open source software package developed by the National Energy Technology Laboratory (NETL used for modeling the chemical reactions, heat transfer, and hydrodynamics of fluid-solid systems. Currently, the stable publically available release of MFIX does not include a discrete mass inflow boundary condition (DMIBC for its discrete element method (DEM package. Inflow boundary conditions are useful for simulating systems where particles are consumed through chemical reactions and an incoming feed is necessary to sustain the reaction. To implement the DMIBC an inlet staging area is designated outside the computational domain and particles are passed through the wall region associated with the inlet. Forces incurred on entering particles, generated from collisions with particles already in the system, are ignored whereas, particles already in the system respond to contact forces and react accordingly, moving away from the inlet. This approach prevents any unphysical overlap between new and existing particles. It also ensures that particles entering the system will enter the computational domain regardless of opposing forces. Once an incoming particle is fully within the domain, it reacts appropriately to any and all contact force. This approach for a DMIBC has been implemented and is available within the current development version of MFIX.
Nonlinear Vibrations of Multiwalled Carbon Nanotubes under Various Boundary Conditions
Directory of Open Access Journals (Sweden)
Hossein Aminikhah
2011-01-01
Full Text Available The present work deals with applying the homotopy perturbation method to the problem of the nonlinear oscillations of multiwalled carbon nanotubes embedded in an elastic medium under various boundary conditions. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals interlayer forces. The amplitude-frequency curves for large-amplitude vibrations of single-walled, double-walled, and triple-walled carbon nanotubes are obtained. The influences of some commonly used boundary conditions, changes in material constant of the surrounding elastic medium, and variations of the nanotubes geometrical parameters on the vibration characteristics of multiwalled carbon nanotubes are discussed. The comparison of the generated results with those from the open literature illustrates that the solutions obtained are of very high accuracy and clarifies the capability and the simplicity of the present method. It is worthwhile to say that the results generated are new and can be served as a benchmark for future works.
Directory of Open Access Journals (Sweden)
Jianwei Dong
2005-11-01
Full Text Available We show the existence of solutions for mixed boundary-value problems that model quantum hydrodynamics in thermal equilibrium. Also we find the semi-classical limit of the solutions.
Uniqueness for a boundary identification problem in thermal imaging
Directory of Open Access Journals (Sweden)
Kurt Bryan
1998-11-01
Full Text Available An inverse problem for an initial-boundary value problem is considered. The goal is to determine an unknown portion of the boundary of a region in ${mathbb R}^n$ from measurements of Cauchy data on a known portion of the boundary. The dynamics in the interior of the region are governed by a differential operator of parabolic type. Utilizing a unique continuation result for evolution operators, along with the method of eigenfunction expansions, it is shown that uniqueness holds for a large and physically reasonable class of Cauchy data pairs.
Influence of Spanwise Boundary Conditions on Slat Noise Simulations
Lockard, David P.; Choudhari, Meelan M.; Buning, Pieter G.
2015-01-01
The slat noise from the 30P/30N high-lift system is being investigated through computational fluid dynamics simulations with the OVERFLOW code in conjunction with a Ffowcs Williams-Hawkings acoustics solver. In the present study, two different spanwise grids are being used to investigate the effect of the spanwise extent and periodicity on the near-field unsteady structures and radiated noise. The baseline grid with periodic boundary conditions has a short span equal to 1/9th of the stowed chord, whereas the other, longer span grid adds stretched grids on both sides of the core, baseline grid to allow inviscid surface boundary conditions at both ends. The results indicate that the near-field mean statistics obtained using the two grids are similar to each other, as are the directivity and spectral shapes of the radiated noise. However, periodicity forces all acoustic waves with less than one wavelength across the span to be two-dimensional, without any variation in the span. The spanwise coherence of the acoustic waves is what is needed to make estimates of the noise that would be radiated from realistic span lengths. Simulations with periodic conditions need spans of at least six slat chords to allow spanwise variation in the low-frequencies associated with the peak of broadband slat noise. Even then, the full influence of the periodicity is unclear, so employing grids with a fine, central region and highly stretched meshes that go to slip walls may be a more efficient means of capturing the spanwise decorrelation of low-frequency acoustic phenomena.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses ar...
Sarna, Neeraj; Torrilhon, Manuel
2017-11-01
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
A Structural Based Thermal Model Description for Vertical SiC Power MOSFETs under Fault Conditions
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Andreas Maerz
2016-01-01
Full Text Available The accurate prediction of the SiC MOSFET withstanding time for single fault events greatly influences the requirements for device protection circuits for these devices in power converter applications, like voltage source inverters or power electronic transformers. For this reason, a thermal model, based on the structural design and the physical dimensions of the chip as well as material properties of 4H-SiC, is proposed. This article gives a general description of the thermal behaviour of vertical SiC MOSFET under various driving and boundary conditions in case of a short-circuit event. The thermal model substitutes destructive tests of a device for an individual set of boundary conditions of an occurring fault event. The validity of the analytically parametrised thermal model is verified by experimental short-circuit tests of state-of-the-art vertical SiC MOSFETs for a set of various boundary conditions. The investigated thermal model can furthermore be used to standardise different gate-oxide degradation values from the literature for means of lifetime prediction of the gate oxide for an individual application under repetitive occurring fault or overload conditions. These manufacturer specific reported values measured with no standardised testing procedures can be translated into a maximum junction temperature, which is repeatedly reached. The thermal model therefore provides a unifying parameter for the gate-oxide lifetime calculation for an individual chip and application.
Importance of boundary conditions for fluctuation-induced forces between colloids at interfaces.
Lehle, Hartwig; Oettel, Martin
2007-01-01
We calculate the effective fluctuation-induced force between spherical or disklike colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir-type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation-induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. Separating the colloid fluctuations from the fluctuations of the capillary wave field leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on a multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.
Baroclinic Planetary Boundary Layer Model: Neutral and Stable Stratification Conditions
Yordanov, D.; Djolov, G.; Syrakov, D.
1998-01-01
The temperature and wind profiles in a baroclinic Planetary Boundary Layer (PBL) are investigated. Assuming stationarity, the turbulent state in the PBL at stable and neutral conditions is uniquely determined by the Rossby number, the external stratification parameter and two external baroclinic parameters. A simple two-layer baroclinic model is developed. It consists of a Surface Layer (SL) and overlying Ekman type layer. The system of dynamic and heat transfer equations is close using the K-theory. In SL the turbulent exchange coefficient is consistent with the results of similarity theory while in the Ekman layer it is constant. The universal functions in the resistance, heat and humidity transfer laws can be deduced from the model. The internal PBL characteristics, necessary for the model calculations, are presented in terms of the external parameters. Favourable agreement of model results with experimental data is demonstrated.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
cost than e.g. using large-eddy simulations. The developed ABL model is successfully validated using a range of different test cases with increasing complexity. Data from several large scale field campaigns, wind tunnel experiments, and previous numerical simulations is presented and compared against...... model results. A method is developed how to simulate the time-dependant non-neutral ABL flow over complex terrain: a precursor simulation is used to specify unsteady inlet boundary conditions on complex terrain domains. The advantage of the developed RANS model framework is its general applicability....... All implementations in the ABL model are tuning free, and except for standard site specific input parameters, no additional model coefficients need to be specified before the simulation. In summary the results show that the implemented modifications are applicable and reproduce the main flow...
Atom-partitioned multipole expansions for electrostatic potential boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Lee, M., E-mail: michael.s.lee131.civ@mail.mil [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Leiter, K. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Eisner, C. [Secure Mission Solutions, a Parsons Company (United States); Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States); Knap, J. [Simulation Sciences Branch, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005 (United States)
2017-01-01
Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.
Boundary conditions for free surface inlet and outlet problems
Taroni, M.
2012-08-10
We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.
Path-integral quantum Monte Carlo simulation with open-boundary conditions
Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Neven, Hartmut
2017-10-01
The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path-integral quantum Monte Carlo (QMC) [Isakov et al., Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402]. This is because the exponential scaling with the number of spins of the thermally assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang et al., Phys. Rev. A 95, 012322 (2017), 10.1103/PhysRevA.95.012322], a result of a dominant instantonic tunneling path. In Isakov et al., it was also conjectured that the escape rate in open-boundary QMC is quadratically larger than that of conventional periodic-boundary QMC; therefore, open-boundary QMC might be used as a powerful tool to solve combinatorial optimization problems. The intuition behind this conjecture is that the action of the instanton in open-boundary QMC is a half of that in periodic-boundary QMC. Here, we show that this simple intuition—although very useful in interpreting some numerical results—deviates from the actual situation in several ways. Using a fully connected quantum spin model, we derive a set of conditions on the positions and momenta of the end points of the instanton, which remove the extra degrees of freedom due to open boundaries. In comparison, the half-instanton conjecture incorrectly sets the momenta at the end points to zero. We also found that the instantons in open-boundary QMC correspond to quantum tunneling events in the symmetric subspace (maximum total angular momentum) at all temperatures, whereas the instantons in periodic-boundary QMC typically lie in subspaces with lower total angular momenta at finite temperatures. This leads to a lesser-than-quadratic speedup at finite temperatures. The results provide useful insights in utilizing open-boundary QMC to solve hard optimization problems. We also outline the generalization of the instantonic tunneling method to many-qubit systems without permutation
Thermal activated grain boundary creep in polycrystalline copper ...
African Journals Online (AJOL)
Creep deformation in metals and alloys at intermediate temperatures and low stresses are attributed to power-law and diffusion mechanisms. ... By superposition of the rate equations, the net strain rate is determined as the sum of three independent creep mechanisms of Cobble diffusion creep, gra-in boundary sliding and ...
Thermal Internal Boundary Layer characteristics at a tropical coastal ...
Indian Academy of Sciences (India)
... Prabha1 R Venkatesan2 Erich Mursch-Radlgruber3 G Rengarajan3 N Jayanthi4. Crop and Soil Sciences, University of Georgia, GA, USA. Health and Safety Division, SHINE Group, IGCAR, Kalpakkam, India 603 102. Boundary Layer Meteorology Division, Institut fuer Meteorologie und Physik (IMP-BOKU), Wien, Austria.
Influence of boundary conditions on the solution of a hyperbolic thermoelasticity problem
Vitokhin, Evgeniy Yu.; Babenkov, Mikhail B.
2017-03-01
We consider a series of problems with a short laser impact on a thin metal layer accounting various boundary conditions of the first and second kind. The behavior of the material is modeled by the hyperbolic thermoelasticity of Lord-Shulman type. We obtain analytical solutions of the problems in the semi-coupled formulation and numerical solutions in the coupled formulation. Numerical solutions are compared with the analytical ones. The analytical solutions of the semi-coupled problems and numerical solutions of the coupled problems show qualitative match. The solutions of hyperbolic thermoelasticity problems are compared with those obtained in the frame of the classical thermoelasticity. It was determined that the most prominent difference between the classical and hyperbolic solutions arises in the problem with fixed boundaries and constant temperature on them. The smallest differences were observed in the problem with unconstrained, thermally insulated edges. It was shown that a cooling zone is observed if the boundary conditions of the first kind are given for the temperature. Analytical expressions for the velocities of the quasiacoustic and quasithermal fronts as well as the critical value for the attenuation coefficient of the excitation impulse are verified numerically.
Directory of Open Access Journals (Sweden)
Nahed S. Hussein
2014-01-01
Full Text Available A numerical boundary integral scheme is proposed for the solution to the system of eld equations of plane. The stresses are prescribed on one-half of the circle, while the displacements are given. The considered problem with mixed boundary conditions in the circle is replaced by two problems with homogeneous boundary conditions, one of each type, having a common solution. The equations are reduced to a system of boundary integral equations, which is then discretized in the usual way, and the problem at this stage is reduced to the solution to a rectangular linear system of algebraic equations. The unknowns in this system of equations are the boundary values of four harmonic functions which define the full elastic solution and the unknown boundary values of stresses or displacements on proper parts of the boundary. On the basis of the obtained results, it is inferred that a stress component has a singularity at each of the two separation points, thought to be of logarithmic type. The results are discussed and boundary plots are given. We have also calculated the unknown functions in the bulk directly from the given boundary conditions using the boundary collocation method. The obtained results in the bulk are discussed and three-dimensional plots are given. A tentative form for the singular solution is proposed and the corresponding singular stresses and displacements are plotted in the bulk. The form of the singular tangential stress is seen to be compatible with the boundary values obtained earlier. The efficiency of the used numerical schemes is discussed.
Thermal convection in a spherical shell with melting/freezing at either or both of its boundaries
Deguen, Renaud
2013-01-01
In a number of geophysical or planetological settings (Earth's inner core, a silicate mantle crystallizing from a magma ocean, or an ice shell surrounding a deep water ocean) a convecting crystalline layer is in contact with a layer of its melt. Allowing for melting/freezing at one or both of the boundaries of the solid layer is likely to affect the pattern of convection in the layer. We study here the onset of thermal convection in a viscous spherical shell with dynamically induced melting/freezing at either or both of its boundaries. It is shown that the behavior of each interface depends on the value of a dimensional number P, which is the ratio of a melting/freezing timescale over a viscous relaxation timescale. A small value of P corresponds to permeable boundary conditions, while a large value of P corresponds to impermeable boundary conditions. The linear stability analysis predicts a significant effect of semi-permeable boundaries when the number P characterizing either of the boundary is small enough...
A Two-Dimensional Transverse Magnetic Propagation Model of a Sine Wave Using Mur Boundary Conditions
National Research Council Canada - National Science Library
Korjack, T
1997-01-01
.... The nonreflecting boundary conditions due to Mur were used at the boundary surfaces. Electric field intensity distributions resulted over a progressive time expansion to illustrate the propagation effect over the entire 2-D mesh...
Modelling of Edge Insulation Depending on Boundary Conditions for the Ground Level
Stolarska, Agata; Strzałkowski, Jarosław
2017-10-01
The article presents results of CFD software aided simulations of a thermal bridge, existing at the wall–slab on ground connection. Calculations were made for different variants of the edge insulation location. Schemes without any edge insulation, with some vertical insulation, horizontal, diagonal, and diagonal combined with insulation used as formwork under the slab on ground were analysed. Each variant was differentiated with boundary conditions for the ground. Vertical borders of the model in the ground, as well as the lower border were described in the first solution as adiabatic, while in the second case, a variable temperature value, depending on the ground depth, was set. For comparison, additional calculations were conducted for non-stationary conditions, in which the initial temperature of the ground was set to the average annual temperature of air. The calculations were based on the location of Szczecin, for which the outside air temperature was set to -16.0°C. Results obtained from the simulation were then used to determine the thermal bridge parameters, in particular, thermal coupling coefficient and linear thermal transmittance. The effect of the set of boundary conditions is clearly seen. In general, for all the five variants, lower values of heat fluxes and linear thermal transmittances were obtained, when variable temperature in the ground was assumed. From the point of view of energy balance, it is more favourable to use the values of ψg obtained when the ground temperature is taken into account. The data breakdown shows that application of the actual temperature distribution in the ground to a model has a strong effect on distribution of the 0.0°C isotherm. The adiabatic model indicates that the ground under the slab freezes, while the model, which takes into account the temperature of the ground, shows that the ground under the floor has positive temperatures and the 0.0°C isotherm reaches only the edge of the outer wall. Moreover, the
Thermal boundary resistance at Si/Ge interfaces by molecular dynamics simulation
Directory of Open Access Journals (Sweden)
Tianzhuo Zhan
2015-04-01
Full Text Available In this study, we investigated the temperature dependence and size effect of the thermal boundary resistance at Si/Ge interfaces by non-equilibrium molecular dynamics (MD simulations using the direct method with the Stillinger-Weber potential. The simulations were performed at four temperatures for two simulation cells of different sizes. The resulting thermal boundary resistance decreased with increasing temperature. The thermal boundary resistance was smaller for the large cell than for the small cell. Furthermore, the MD-predicted values were lower than the diffusion mismatch model (DMM-predicted values. The phonon density of states (DOS was calculated for all the cases to examine the underlying nature of the temperature dependence and size effect of thermal boundary resistance. We found that the phonon DOS was modified in the interface regions. The phonon DOS better matched between Si and Ge in the interface region than in the bulk region. Furthermore, in interface Si, the population of low-frequency phonons was found to increase with increasing temperature and cell size. We suggest that the increasing population of low-frequency phonons increased the phonon transmission coefficient at the interface, leading to the temperature dependence and size effect on thermal boundary resistance.
Directory of Open Access Journals (Sweden)
Masood Khan
Full Text Available In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Boundary conditions in the Ginzburg Landau Formulation in heavy ...
African Journals Online (AJOL)
The linearized gap equation is the basis for the microscopic derivation of the second order terms in the Ginzburg-Landau free energy expansion. However, close to the boundary these second order terms do not have the same form, since the kernel is changed due to quasi-particle scattering. In addition, these boundary ...
Haskins, Justin; Kinaci, Alper; Sevik, Cem; Cagin, Tahir
2012-01-01
It is widely known that graphene and many of its derivative nanostructures have exceedingly high reported thermal conductivities (up to 4000 W/mK at 300 K). Such attractive thermal properties beg the use of these structures in practical devices; however, to implement these materials while preserving transport quality, the influence of structure on thermal conductivity should be thoroughly understood. For graphene nanostructures, having average phonon mean free paths on the order of one micron, a primary concern is how size influences the potential for heat conduction. To investigate this, we employ a novel technique to evaluate the lattice thermal conductivity from the Green-Kubo relations and equilibrium molecular dynamics in systems where phonon-boundary scattering dominates heat flow. Specifically, the thermal conductivities of graphene nanoribbons and carbon nanotubes are calculated in sizes up to 3 microns, and the relative influence of boundary scattering on thermal transport is determined to be dominant at sizes less than 1 micron, after which the thermal transport largely depends on the quality of the nanostructure interface. The method is also extended to carbon nanostructures (fullerenes) where phonon confinement, as opposed to boundary scattering, dominates, and general trends related to the influence of curvature on thermal transport in these materials are discussed.
Thermal boundary effects on a GT liner structure
Salvatore, M.; Laget, H.; Vanderhaegen, E.; Altunlu, A.C.; Tufano, S.; Daumantas, Ciplys
2012-01-01
GT combustor liners are subjected to mechanical and thermal loads that damage the structure and reduce their operational life. Among those, the thermo-acoustic instabilities develop, generating pressure oscillations because of the interaction between heat release, acoustic waves and structure
CT image segmentation using FEM with optimized boundary condition.
Directory of Open Access Journals (Sweden)
Hiroyuki Hishida
Full Text Available The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM, as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery.
Calculation of the radial electric field with RF sheath boundary conditions in divertor geometry
Gui, B.; Xia, T. Y.; Xu, X. Q.; Myra, J. R.; Xiao, X. T.
2018-02-01
The equilibrium electric field that results from an imposed DC bias potential, such as that driven by a radio frequency (RF) sheath, is calculated using a new minimal two-field model in the BOUT++ framework. Biasing, using an RF-modified sheath boundary condition, is applied to an axisymmetric limiter, and a thermal sheath boundary is applied to the divertor plates. The penetration of the bias potential into the plasma is studied with a minimal self-consistent model that includes the physics of vorticity (charge balance), ion polarization currents, force balance with E× B , ion diamagnetic flow (ion pressure gradient) and parallel electron charge loss to the thermal and biased sheaths. It is found that a positive radial electric field forms in the scrape-off layer and it smoothly connects across the separatrix to the force-balanced radial electric field in the closed flux surface region. The results are in qualitative agreement with the experiments. Plasma convection related to the E× B net flow in front of the limiter is also obtained from the calculation.
Srivastava, R.; Rosner, D. E.
1979-01-01
A rational approach to the correlation of boundary layer mass transport rates, applicable to many commonly encountered laminar flow conditions with thermal diffusion and/or variable properties, is outlined. The correlation scheme builds upon already available constant property blowing/suction solutions by introducing appropriate correction factors to account for the additional ('pseudo' blowing and source) effects identified with variable properties and thermal diffusion. Applications of the scheme to the particular laminar boundary layer mass transfer problems considered herein (alkali and transition metal compound vapor transport) indicates satisfactory accuracy up to effective blowing factors equivalent to about one third of the 'blow off' value. As a useful by-product of the variable property correlation, we extend the heat-mass transfer analogy, for a wide range of Lewis numbers, to include variable property effects.
Boundary Layer Separation and Reattachment Detection on Airfoils by Thermal Flow Sensors
Directory of Open Access Journals (Sweden)
Peter Busche
2012-10-01
Full Text Available A sensor concept for detection of boundary layer separation (flow separation, stall and reattachment on airfoils is introduced in this paper. Boundary layer separation and reattachment are phenomena of fluid mechanics showing characteristics of extinction and even inversion of the flow velocity on an overflowed surface. The flow sensor used in this work is able to measure the flow velocity in terms of direction and quantity at the sensor’s position and expected to determine those specific flow conditions. Therefore, an array of thermal flow sensors has been integrated (flush-mounted on an airfoil and placed in a wind tunnel for measurement. Sensor signals have been recorded at different wind speeds and angles of attack for different positions on the airfoil. The sensors used here are based on the change of temperature distribution on a membrane (calorimetric principle. Thermopiles are used as temperature sensors in this approach offering a baseline free sensor signal, which is favorable for measurements at zero flow. Measurement results show clear separation points (zero flow and even negative flow values (back flow for all sensor positions. In addition to standard silicon-based flow sensors, a polymer-based flexible approach has been tested showing similar results.
Modeling Interfacial Thermal Boundary Conductance of Engineered Interfaces
2014-08-31
interface between materials 1 & 2 with an impurity mass mint , the energy transmission of all phonon frequencies is maximized when mint = (m1 +m2)/2...properties of the source and sink. Figure 5: Phonon transmission spectra, with curves corresponding to different impurity masses, mint (left plot) or...substrate [2, 34]. The thermal decay of each sample, measured by TDTR, was compared to a multilayer solution of the heat diffusion equation to extract
Kushwaha, Hari Mohan; Sahu, Santosh Kumar
2017-10-01
This paper reports the hydrodynamically and thermally fully developed, laminar, incompressible, forced convective heat transfer characteristics of gaseous flows through a parallel plate microchannel with different constant heat flux boundary conditions. The first order velocity slip and viscous dissipation effects are considered in the analysis. Here, three different thermal boundary conditions such as: both plates kept at different constant heat fluxes, both plates kept at equal constant heat fluxes and one plate kept at constant heat flux and other one insulated are considered for the analysis. The deviation in Nusselt number between the model that considers both first order velocity slip and temperature jump and the one that considers only velocity slip is reported. Also, the effect of various heat flux ratios on the Nusselt number is reported in this analysis. In addition, the deviation in Nusselt number between first and second order slip model is discussed in this study.
A simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations
Directory of Open Access Journals (Sweden)
Yibao Li
2017-01-01
Full Text Available Many researchers have proposed special treatments for outlet boundary conditions owing to lack of information at the outlet. Among them, the simplest method requires a large enough computational domain to prevent or reduce numerical errors at the boundaries. However, an efficient method generally requires special treatment to overcome the problems raised by the outlet boundary condition used. For example, mass flux is not conserved and the fluid field is not divergence-free at the outlet boundary. Overcoming these problems requires additional computational cost. In this paper, we present a simple and efficient outflow boundary condition for the incompressible Navier–Stokes equations, aiming to reduce the computational domain for simulating flow inside a long channel in the streamwise direction. The proposed outflow boundary condition is based on the transparent equation, where a weak formulation is used. The pressure boundary condition is derived by using the Navier–Stokes equations and the outlet flow boundary condition. In the numerical algorithm, a staggered marker-and-cell grid is used and temporal discretization is based on a projection method. The intermediate velocity boundary condition is consistently adopted to handle the velocity–pressure coupling. Characteristic numerical experiments are presented to demonstrate the robustness and accuracy of the proposed numerical scheme. Furthermore, the agreement of computational results from small and large domains suggests that our proposed outflow boundary condition can significantly reduce computational domain sizes.
Revisit boundary conditions for the self-adjoint angular flux formulation
Energy Technology Data Exchange (ETDEWEB)
Wang, Yaqi [Idaho National Lab. (INL), Idaho Falls, ID (United States); Gleicher, Frederick N. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-03-01
We revisit the boundary conditions for SAAF. We derived the equivalent parity variational form ready for coding up. The more rigorous approach of evaluating odd parity should be solving the odd parity equation coupled with the even parity. We proposed a symmetric reflecting boundary condition although neither positive definiteness nor even-odd decoupling is achieved. A simple numerical test verifies the validity of these boundary conditions.
Solution to the one-dimensional telegrapher's equation subject to a backreaction boundary condition
Prüstel, Thorsten; Meier-Schellersheim, Martin
2013-01-01
We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function. Furthermore, we formulate a backreaction boundary condition, which has been widely used in the context of diffusion-controlled reversible reactions, for a one-dimensional telegrapher's equation and derive the corresponding Green's function.
Directory of Open Access Journals (Sweden)
Sulym Heorhiy
2016-03-01
Full Text Available This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.
Finite-temperature effective boundary theory of the quantized thermal Hall effect
Nakai, Ryota; Ryu, Shinsei; Nomura, Kentaro
2015-01-01
A finite-temperature effective free energy of the boundary of a quantized thermal Hall system is derived microscopically from the bulk two-dimensional Dirac fermion coupled with a gravitational field. In two spatial dimensions, the thermal Hall conductivity of fully gapped insulators and superconductors is quantized and given by the bulk Chern number, in analogy to the quantized electric Hall conductivity in quantum Hall systems. From the perspective of effective action functionals, two disti...
Effective nonlinear Neumann boundary conditions for 1D nonconvex Hamilton-Jacobi equations
Guerand, Jessica
2017-09-01
We study Hamilton-Jacobi equations in [ 0 , + ∞) of evolution type with nonlinear Neumann boundary conditions in the case where the Hamiltonian is not necessarily convex with respect to the gradient variable. In this paper, we give two main results. First, we prove for a nonconvex and coercive Hamiltonian that general boundary conditions in a relaxed sense are equivalent to effective ones in a strong sense. Here, we exhibit the effective boundary conditions while for a quasi-convex Hamiltonian, we already know them (Imbert and Monneau, 2016). Second, we give a comparison principle for a nonconvex and nonnecessarily coercive Hamiltonian where the boundary condition can have constant parts.
Method Suitable for Updating the Boundary Condition of Continuous Beam Bridges
Cao, JianXin; Zheng, Honglan; Liu, Yang
2017-10-01
The boundary support conditions of continuous beam bridges play the great influence on the results of the structural analysis, but it is difficult to accurately model the boundaries owing to the complexity structure of constraint conditions. To address this issue, a parameterized method is proposed to update the boundary support conditions in this study. First, the connection stiffness at boundary is considered as the optimization variable, and then the optimization problem of updating the boundary conditions are described in detail based on the theory of finite element model updating. Second, for verifying the proposed method, a loading test was conducted on an actual three-span continuous beam bridge. With the proposed method, the discrepancy between the measured modal parameters and the analytical results are greatly reduced; therefore, it is shown that the proposed method is effective for updating the boundary support conditions of actual continuous beam bridges.
Chiruta, Daniel; Linares, Jorge; Miyashita, Seiji; Boukheddaden, Kamel
2014-05-01
In order to explain clearly the role of the open boundary conditions (OBCs) on phase transition in one dimensional system, we consider an Ising model with both short-range (J) and long-range (G) interactions, which has allowed us to study the cooperative nature of spin-crossover (SCO) materials at the nanometer scale. At this end, we developed a transfer-matrix method for one-dimensional (1D) SCO system with free boundary conditions, and we give numerical evidences for how the thermal spin transition curves vary as a function of the physical parameters (J, G) or an applied pressure. Moreover for OBCs case, we have derived the bulk, surface and finite-size contributions to the free energy and we have investigated the variation of these energies as function of J and system size. We have found that the surface free energy behaves like J⟨σ⟩2, where ⟨σ⟩ is the average magnetization per site. Since the properties of the nanometric scale are dramatically influenced by the system's size (N), our analytical outcomes for the size dependence represent a step to achieve new characteristic of the future devices and also a way to find various novel properties which are absent in the bulk materials.
Directory of Open Access Journals (Sweden)
Korobkina Dariya V.
2014-01-01
Full Text Available The problem of an estimation of thermal defeats at influence of affected factors of fire has great value for various areas of technics, industry and medicine. Results of mathematical simulation of heat transfer in layered structure of human skin influenced by the radiant thermal flux of the set value are presented in the work. The three-layer system of skin is considered. Research according to the various boundary conditions exposed in human tissue is carried out. Temperature distribution on thickness of skin is presented.
Energy Technology Data Exchange (ETDEWEB)
Osanyintola, O. F.; Talukdar, P.; Simonson, C. J. [Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Sask. (China)
2006-07-01
In this paper, the moisture buffering capacity of spruce plywood is measured by recording the change in mass of a test specimen when the air relative humidity (RH) is changed between 33% RH and 75% RH. The aim is to represent diurnal cycles in indoor humidity with 33% RH maintained for 16 h and 75% RH maintained for 8 h. Measurements are taken using two different apparatuses, which provide different convective transfer coefficients between the air and the plywood, and the results are compared to a numerical model for validation. The validated numerical model is then used to investigate the effect of initial conditions, boundary conditions and thickness on the moisture buffering capacity of plywood. The results show that the buffering capacity of plywood depends on the initial conditions and thickness of the plywood as well as the surface film coefficient and humidity cycle. (author)
Thermo-mechanical Analysis of the Dry Clutches under Different Boundary Conditions
Directory of Open Access Journals (Sweden)
O.I. Abdullah
2014-06-01
Full Text Available The high thermal stresses, generated between the contacting surfaces of the clutch system (pressure plate, clutch disc and flywheel due to the frictional heating during the slipping, are considered to be one of the main reasons of clutch failure. A finite element technique has been used to study the transient thermoelastic phenomena of a dry clutch. The effect of the boundary conditions on the contact pressure distribution, the temperature field and the heat flux generated along the frictional surfaces are investigated. Analysis has been completed using two dimensional axisymmetric model that was used to simulate the clutch elements. ANSYS software has been used to perform the numerical calculation in this paper.
Questions on solvability of exterior boundary value problems with fractional boundary conditions
Directory of Open Access Journals (Sweden)
Berikbol Torebek
2016-05-01
Full Text Available In this paper we study questions on solvability of some boundary value problems for the Laplace equation with boundary integro-differential operators in the exterior of a unit ball. We study properties of the given integral - differential operators of fractional order in a class of functions which are harmonic outside a ball. We prove theorems about existence and uniqueness of a solution of the problem. We construct explicit form of the solution of the problem in integral form, by solving the Dirichlet problem.
Experimental verification of free-space singular boundary conditions in an invisibility cloak
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile
2016-04-01
A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.
Absorption and impedance boundary conditions for phased geometrical-acoustics methods
DEFF Research Database (Denmark)
Jeong, Cheol-Ho
2012-01-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been...... developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated...... with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce...
Absorption and impedance boundary conditions for phased geometrical-acoustics methods.
Jeong, Cheol-Ho
2012-10-01
Defining accurate acoustical boundary conditions is of crucial importance for room acoustic simulations. In predicting sound fields using phased geometrical acoustics methods, both absorption coefficients and surface impedances of the boundary surfaces can be used, but no guideline has been developed on which boundary condition produces accurate results. In this study, various boundary conditions in terms of normal, random, and field incidence absorption coefficients and normal incidence surface impedance are used in a phased beam tracing model, and the simulated results are validated with boundary element solutions. Two rectangular rooms with uniform and non-uniform absorption distributions are tested. Effects of the neglect of reflection phase shift are also investigated. It is concluded that the impedance, random incidence, and field incidence absorption boundary conditions produce reasonable results with some exceptions at low frequencies for acoustically soft materials.
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2015-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations
Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.
2014-01-01
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.
On one method for solving transient heat conduction problems with asymmetric boundary conditions
Directory of Open Access Journals (Sweden)
Igor V. Kudinov
2016-06-01
Full Text Available Using additional boundary conditions and additional required function in integral method of heat-transfer we obtain approximate analytical solution of transient heat conduction problem for an infinite plate with asymmetric boundary conditions of the first kind. This solution has a simple form of trigonometric polynomial with coefficients exponentially stabilizing in time. With the increase in the count of terms of a polynomial the obtained solution is approaching the exact solution. The introduction of a time-dependent additional required function, setting in the one (point of the boundary points, allows to reduce solving of differential equation in partial derivatives to integration of ordinary differential equation. The additional boundary conditions are found in the form that the required solution would implement the additional boundary conditions and that implementation would be equivalent to executing the original differential equation in boundary points. In this article it is noted that the execution of the original equation at the boundaries of the area only (via the implementation of the additional boundary conditions leads to the execution of the original equation also inside that area. The absence of direct integration of the original equation on the spatial variable allows to apply this method to solving the nonlinear boundary value problems with variable initial conditions and variable physical properties of the environment, etc.
Evaluation of outflow boundary conditions for two-phase lattice Boltzmann equation.
Lou, Qin; Guo, Zhaoli; Shi, Baochang
2013-06-01
Outflow boundary condition (OBC) is a critical issue in computational fluid dynamics. As a type of numerical method for fluid flows, the lattice Boltzmann equation (LBE) method has gained much success in a variety of complex flows, and certain OBCs have been suggested for the LBE in simulating simple single-phase flows. However, very few discussions on the OBCs have been made for the two-phase LBE method. In this work, three types of OBCs that are widely used in the LBE for single-phase flows, i.e., the Neumann boundary condition, the convective boundary condition, and the extrapolation boundary condition, are extended to a two-phase LBE method and their performances are investigated. The comprehensive results of several two-phase flows show that these boundary conditions behave quite differently in the simulations of two-phase flows. Specifically, it is found that the Neumann boundary condition and the extrapolation boundary condition give rather poor predictions, while the type of convective boundary conditions work well, although the choice of the convection velocity has some slight influences on the results. We also apply these OBC schemes to some other two-phase models, and similar observations are found.
Sman, van der R.G.M.
2013-01-01
We have investigated the performance of an alternative wetting boundary condition for complex geometries in a phase field Lattice Boltzmann scheme, which is an alternative to the commonly used formulation by Yeomans and coworkers. Though our boundary condition is much simpler in its implementation,
Eigenstates of a particle in an array of hexagons with periodic boundary condition
Directory of Open Access Journals (Sweden)
A Nemati
2013-10-01
Full Text Available In this paper the problem of a particle in an array of hexagons with periodic boundary condition is solved. Using the projection operators, we categorize eigenfunctions corresponding to each of the irreducible representations of the symmetry group . Based on these results, the Dirichlet and Neumann boundary conditions are discussed.
DEFF Research Database (Denmark)
Jha, Abhinav K.; Zhu, Yansong; Kang, Jin U.
2016-01-01
An integral Neumann-series implementation of the Radiative Transfer Equation that accounts for boundary conditions is proposed to simulate photon transport through tissue for transcranial optical imaging.......An integral Neumann-series implementation of the Radiative Transfer Equation that accounts for boundary conditions is proposed to simulate photon transport through tissue for transcranial optical imaging....
Cheaito, Ramez; Gaskins, John T.; Caplan, Matthew E.; Donovan, Brian F.; Foley, Brian M.; Giri, Ashutosh; Duda, John C.; Szwejkowski, Chester J.; Constantin, Costel; Brown-Shaklee, Harlan J.; Ihlefeld, Jon F.; Hopkins, Patrick E.
2015-01-01
The advances in phonon spectroscopy in homogeneous solids have unveiled extremely useful physics regarding the contribution of phonon energies and mean-free paths to the thermal transport in solids. However, as material systems decrease to length scales less than the phonon mean-free paths, thermal transport can become much more impacted by scattering and transmission across interfaces between two materials than the intrinsic relaxation in the homogeneous solid. To elucidate the fundamental interactions driving this thermally limiting interfacial phonon scattering process, we analytically derive and experimentally measure a thermal boundary conductance accumulation function. We develop a semiclassical theory to calculate the thermal boundary conductance accumulation function across interfaces using the diffuse mismatch model, and validate this derivation by measuring the interface conductance between eight different metals on native oxide/silicon substrates and four different metals on sapphire substrates. Measurements were performed at room temperature using time-domain thermoreflectance and represent the first-reported values for interface conductance across several metal/native oxide/silicon and metal/sapphire interfaces. The various metal films provide a variable bandwidth of phonons incident on the metal/substrate interface. This method of varying phonons' cutoff frequency in the film while keeping the same substrate allows us to mimic the accumulation of thermal boundary conductance and thus provides a direct method to experimentally validate our theory. We show that the accumulation function can be written as the product of a weighted average of the interfacial phonon transmission function and the accumulation of the temperature derivative of the phonon flux incident on the interface; this provides the framework to extract an average, spectrally dependent phonon transmissivity from a series of thermal boundary conductance measurements. Our approach provides
Conditions affecting boundary response to messages out of awareness.
Fisher, S
1976-05-01
Multiple studies evaluated the role of the following parameters in mediating the effects of auditory subliminal inputs upon the body boundary: being made aware that exposure to subliminal stimuli is occurring, nature of the priming preliminary to the input, length of exposure, competing sensory input, use of specialized content messages, tolerance for unrealistic experience, and masculinity-feminity. A test-retest design was typically employed that involved measuring the baseline Barrier score with the Holtzman bolts and then ascertaining the Barrier change when responding to a second series of Holtzman blots at the same time that subliminal input was occurring. Complex results emerged that defined in considerably new detail what facilitates and blocks the boundary-disrupting effects of subliminal messages in men and to a lesser degree in women.
General Considerations of the Electrostatic Boundary Conditions in Oxide Heterostructures
Energy Technology Data Exchange (ETDEWEB)
Higuchi, Takuya
2011-08-19
When the size of materials is comparable to the characteristic length scale of their physical properties, novel functionalities can emerge. For semiconductors, this is exemplified by the 'superlattice' concept of Esaki and Tsu, where the width of the repeated stacking of different semiconductors is comparable to the 'size' of the electrons, resulting in novel confined states now routinely used in opto-electronics. For metals, a good example is magnetic/non-magnetic multilayer films that are thinner than the spin-scattering length, from which giant magnetoresistance (GMR) emerged, used in the read heads of hard disk drives. For transition metal oxides, a similar research program is currently underway, broadly motivated by the vast array of physical properties that they host. This long-standing notion has been recently invigorated by the development of atomic-scale growth and probe techniques, which enables the study of complex oxide heterostructures approaching the precision idealized in Fig. 1(a). Taking the subset of oxides derived from the perovskite crystal structure, the close lattice match across many transition metal oxides presents the opportunity, in principle, to develop a 'universal' heteroepitaxial materials system. Hand-in-hand with the continual improvements in materials control, an increasingly relevant challenge is to understand the consequences of the electrostatic boundary conditions which arise in these structures. The essence of this issue can be seen in Fig. 1(b), where the charge sequence of the sublayer 'stacks' for various representative perovskites is shown in the ionic limit, in the (001) direction. To truly 'universally' incorporate different properties using different materials components, be it magnetism, ferroelectricity, superconductivity, etc., it is necessary to access and join different charge sequences, labelled here in analogy to the designations 'group IV, III-V, II
Fluid/Solid Boundary Conditions in Non-Isothermal Systems
Rosner, Daniel E.
1999-01-01
The existing theoretical research concerned with thermal creep at fluid/solid interfaces is briefly reviewed, and the importance of microgravity-based experimental data is then discussed. It is noted that the ultimate goal of this research is a rational molecular level theory that predicts the dependence of a dimensionless thermal creep coefficient, Ctc, on relevant dimensionless parameters describing the way fluid molecules interact with the solid surface and how they interact among themselves. The discussion covers thermophoresis of isolated solid spheres and aggregates in gases; solid sphere thermophoresis in liquids and dense vapors; thermophoresis of small immiscible liquid droplets; and applications of the direct simulation Monte Carlo method.
The Ritz Method for Boundary Problems with Essential Conditions as Constraints
Directory of Open Access Journals (Sweden)
Vojin Jovanovic
2016-01-01
Full Text Available We give an elementary derivation of an extension of the Ritz method to trial functions that do not satisfy essential boundary conditions. As in the Babuška-Brezzi approach boundary conditions are treated as variational constraints and Lagrange multipliers are used to remove them. However, we avoid the saddle point reformulation of the problem and therefore do not have to deal with the Babuška-Brezzi inf-sup condition. In higher dimensions boundary weights are used to approximate the boundary conditions, and the assumptions in our convergence proof are stated in terms of completeness of the trial functions and of the boundary weights. These assumptions are much more straightforward to verify than the Babuška-Brezzi condition. We also discuss limitations of the method and implementation issues that follow from our analysis and examine a number of examples, both analytic and numerical.
Exact finite-size corrections for the spanning-tree model under different boundary conditions
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
Johnson, Anthony N; Hromadka, T V
2015-01-01
The Laplace equation that results from specifying either the normal or tangential force equilibrium equation in terms of the warping functions or its conjugate can be modeled as a complex variable boundary element method or CVBEM mixed boundary problem. The CVBEM is a well-known numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy Integral in complex analysis. This paper highlights three customizations to the technique.•A least squares approach to modeling the complex-valued approximation function will be compared and analyzed to determine if modeling error on the boundary can be reduced without the need to find and evaluated additional linearly independent complex functions.•The nodal point locations will be moved outside the problem domain.•Contour and streamline plots representing the warping function and its complementary conjugate are generated simultaneously from the complex-valued approximating function.
Transition to geostrophic convection: the role of the boundary conditions
Kunnen, R.P.J.; Ostilla-Monico, Rodolfo; van der Poel, Erwin; Verzicco, Roberto; Lohse, Detlef
2016-01-01
Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system
Energy Technology Data Exchange (ETDEWEB)
Lopez, J. Gonzalez [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Jansen, K. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Renner, D.B. [Jefferson Lab, Newport News, VA (United States); Shindler, A. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2012-08-23
The use of chirally rotated boundary conditions provides a formulation of the Schroedinger functional that is compatible with automatic O(a) improvement of Wilson fermions up to O(a) boundary contributions. The elimination of bulk O(a) effects requires the non-perturbative tuning of the critical mass and one additional boundary counterterm. We present the results of such a tuning in a quenched setup for several values of the renormalized gauge coupling, from perturbative to nonperturbative regimes, and for a range of lattice spacings. We also check that the correct boundary conditions and symmetries are restored in the continuum limit. (orig.)
Large time behavior of solutions to parabolic equations with Neumann boundary conditions
da Lio, Francesca
2008-03-01
In this paper we are interested in the large time behavior as t-->+[infinity] of the viscosity solutions of parabolic equations with nonlinear Neumann type boundary conditions in connection with ergodic boundary problems which have been recently studied by Barles and the author in [G. Barles, F. Da Lio, On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions, Ann. Inst. H. Poincaré Anal. Non Linèaire 22 (5) (2005) 521-541].
Half-Space Temperature Field with a Movable Thermally Thin-Coated Boundary Under External Heat Flux
Directory of Open Access Journals (Sweden)
P. A. Vlasov
2014-01-01
Full Text Available In engineering practice analytical methods of the mathematical theory of heat conduction hold a special place. This is due to many reasons, in particular, because of the fact that the solutions of the relevant problems represented in analytically closed form, can be used not only for a parametric analysis of the studied temperature field and to explore the specific features of its formation, but also to test the developed computational algorithms, which are aimed at solving real-world application heat and mass transfer problems. Difficulties arising when using the analytical mathematical theory methods of heat conduction in practice are well known. Also they are significantly exacerbated if the boundaries of the system under study are movable, even in the simplest case, when the law of motion is known.The main goal of the conducted research is to have an analytically closed-form problem solution for finding the orthotropic half-space temperature field, a boundary of which has thermally thin coating exposed to extremely concentrated stationary external heat flux and uniformly moves parallel to itself.The assumption that the covering of the boundary is thermally thin, allowed to realize the idea of \\concentrated capacity", that is to accept the hypothesis that the mean-thickness coating temperature is equal to the temperature of its boundaries. This assumption allowed us to reduce the problem under consideration to a mixed problem for a parabolic equation with a specific boundary condition.The Hankel integral transform of zero order with respect to the radial variable and the Laplace transform with respect to the temporal variable were used to solve the reduced problem. These techniques have allowed us to submit the required solution as an iterated integral.
Uddin, Mohammed J.; Khan, Waqar A.; Ismail, Ahmed I.
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement. PMID:23166688
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Directory of Open Access Journals (Sweden)
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Effects of flow and colony morphology on the thermal boundary layer of corals
Jimenez, Isabel M.; Kühl, Michael; Larkum, Anthony W. D.; Ralph, Peter J.
2011-01-01
The thermal microenvironment of corals and the thermal effects of changing flow and radiation are critical to understanding heat-induced coral bleaching, a stress response resulting from the destruction of the symbiosis between corals and their photosynthetic microalgae. Temperature microsensor measurements at the surface of illuminated stony corals with uneven surface topography (Leptastrea purpurea and Platygyra sinensis) revealed millimetre-scale variations in surface temperature and thermal boundary layer (TBL) that may help understand the patchy nature of coral bleaching within single colonies. The effect of water flow on the thermal microenvironment was investigated in hemispherical and branching corals (Porites lobata and Stylophora pistillata, respectively) in a flow chamber experiment. For both coral types, the thickness of the TBL decreased exponentially from 2.5 mm at quasi-stagnant flow (0.3 cm s−1), to 1 mm at 5 cm s−1, with an exponent approximately 0.5 consistent with predictions from the heat transfer theory for simple geometrical objects and typical of laminar boundary layer processes. Measurements of mass transfer across the diffusive boundary layer using O2 microelectrodes revealed a greater exponent for mass transfer when compared with heat transfer, indicating that heat and mass transfer at the surface of corals are not exactly analogous processes. PMID:21602322
Luce, Charles H.; Tonina, Daniele; Applebee, Ralph; DeWeese, Timothy
2017-11-01
Two common refrains about using the one-dimensional advection diffusion equation to estimate fluid fluxes and thermal conductivity from temperature time series in streambeds are that the solution assumes that (1) the surface boundary condition is a sine wave or nearly so, and (2) there is no gradient in mean temperature with depth. Although the mathematical posing of the problem in the original solution to the problem might lead one to believe these constraints exist, the perception that they are a source of error is a fallacy. Here we develop a mathematical proof demonstrating the equivalence of the solution as developed based on an arbitrary (Fourier integral) surface temperature forcing when evaluated at a single given frequency versus that derived considering a single frequency from the beginning. The implication is that any single frequency can be used in the frequency-domain solutions to estimate thermal diffusivity and 1-D fluid flux in streambeds, even if the forcing has multiple frequencies. This means that diurnal variations with asymmetric shapes or gradients in the mean temperature with depth are not actually assumptions, and deviations from them should not cause errors in estimates. Given this clarification, we further explore the potential for using information at multiple frequencies to augment the information derived from time series of temperature.
Scudeler, C.; Paniconi, C.; Pasetto, D.; Putti, M.
2017-03-01
A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand-in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models.
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Bona, C
2010-01-01
Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a test-bed for constraint-preserving boundary conditions in the non-linear regime. As an illustration, energy-constraint preservation is separately tested in the Z4 framework. Both algebraic conditions, derived from energy estimates, and derivative conditions, deduced from the constraint-propagation system, are considered. The numerical errors at the boundary are of the same order than those at the interior points.
Livshits, Gideon I
2014-01-01
Superpotentials offer a direct means of calculating conserved charges associated with the asymptotic symmetries of space-time. Yet superpotentials have been plagued with inconsistencies, resulting in nonphysical or incongruent values for the mass, angular momentum and energy loss due to radiation. The approach of Regge and Teitelboim, aimed at a clear Hamiltonian formulation with a boundary, and its extension to the Lagrangian formulation by Julia and Silva have resolved these issues, and have resulted in a consistent, well-defined and unique variational equation for the superpotential, thereby placing it on a firm footing. A hallmark solution of this equation is the KBL superpotential obtained from the first-order Lovelock Lagrangian. Nevertheless, here we show that these formulations are still insufficient for Lovelock Lagrangians of higher orders. We present a paradox, whereby the choice of fields affects the superpotential for equivalent on-shell dynamics. We offer two solutions to this paradox: either th...
Holographic Thermalization in Gauss-Bonnet Gravity with de Sitter Boundary
Zhang, Shao-Jun; Abdalla, Elcio; Papantonopoulos, Eleftherios
2015-01-01
We introduce higher-derivative Gauss-Bonnet correction terms in the gravity sector and we relate the modified gravity theory in the bulk to the strongly coupled quantum field theory on a de Sitter boundary. We study the process of holographic thermalization by examining three non-local observables, the two-point function, the Wilson loop and the holographic entanglement entropy. We study the time evolution of these three observables and we find that the modification of the gravity side with the Gauss-Bonnet correction terms influences the saturation time to reach thermal equilibrium with the dominant effect given by the holographic entanglement entropy since it contains more bulk information.
Elo, Teemu; Lähteenmäki, Pasi; Golubev, Dmitri; Savin, Alexander; Arutyunov, Konstantin; Hakonen, Pertti
2017-11-01
We have employed noise thermometry for investigations of thermal relaxation between the electrons and the substrate in nanowires patterned from 40-nm-thick titanium film on top of silicon wafers covered by a native oxide. By controlling the electronic temperature T_e by Joule heating at the base temperature of a dilution refrigerator, we probe the electron-phonon coupling and the thermal boundary resistance at temperatures T_e= 0.5-3 K. Using a regular T^5-dependent electron-phonon coupling of clean metals and a T^4-dependent interfacial heat flow, we deduce a small contribution for the direct energy transfer from the titanium electrons to the substrate phonons due to inelastic electron-boundary scattering.
Exploring the Boundary Conditions of the Redundancy Principle
McCrudden, Matthew T.; Hushman, Carolyn J.; Marley, Scott C.
2014-01-01
This experiment investigated whether study of a scientific text and a visual display that contained redundant text segments would affect memory and transfer. The authors randomly assigned 42 students from a university in the southwestern United States in equal numbers to 1 of 2 conditions: (a) a redundant condition, in which participants studied a…
How to determine a boundary condition for diffusion at a thin membrane from experimental data
Kosztołowicz, Tadeusz; WÄ sik, Sławomir; Lewandowska, Katarzyna D.
2017-07-01
We present a method of deriving a boundary condition for diffusion at a thin membrane from experimental data. Based on experimental results obtained for normal diffusion of ethanol in water, we show that the derived boundary condition at a membrane contains a term with a Riemann-Liouville fractional time derivative of order 1/2 . Such a form of the boundary condition shows that a transfer of particles through a thin membrane is a "long-memory process." The presented method is an example that an important part of the mathematical model of physical processes may be derived directly from experimental data.
First-principle proof of the modified collision boundary conditions for the hard-sphere system
Tessarotto, Massimo; Cremaschini, Claudio
2014-05-01
A fundamental issue lying at the foundation of classical statistical mechanics is the determination of the collision boundary conditions that characterize the dynamical evolution of multi-particle probability density functions (PDF) and are applicable to systems of hard-spheres undergoing multiple elastic collisions. In this paper it is proved that, when the deterministic N-body PDF is included in the class of admissible solutions of the Liouville equation, the customary form of collision boundary conditions adopted in previous literature becomes physically inconsistent and must actually be replaced by suitably modified collision boundary conditions.
Simulations of QCD and QED with C* boundary conditions arXiv
Hansen, Martin; Patella, Agostino; Tantalo, Nazario
We present exploratory results from dynamical simulations of QCD in isolation, as well as QCD coupled to QED, with C* boundary conditions. In finite volume, the use of C* boundary conditions allows for a gauge invariant and local formulation of QED without zero modes. In particular we show that the simulations reproduce known results and that masses of charged mesons can be extracted in a completely gauge invariant way. For the simulations we use a modified version of the HiRep code. The primary features of the simulation code are presented and we discuss some details regarding the implementation of C* boundary conditions and the simulated lattice action.
Chemical boundary conditions are a key input to regional-scale photochemical models. In this study, performed during the third phase of the Air Quality Model Evaluation International Initiative (AQMEII3), we perform annual simulations over North America with chemical boundary con...
Crossing the boundary: numerical investigation of water entry conditions
Angelidis, Dionysios; Sotiropoulos, Fotis
2017-11-01
Several engineering and scientific applications involve water impact problems. To accurately capture the dynamics of the cavity formation and the water ejected as a body hits the water, the formidable range of temporal and spatial scales should accurately be resolved with affordable computational cost. We have enhanced the potential of the two-phase flow version of the immersed-boundary adaptive mesh refinement flow solver, developed by our group, to perform high-fidelity two-phase flow calculations on locally refined grids. We employ a level-set method and tackle the computational challenges arise during the explicit solution of a mass-conserving reinitialization equation. In contrast to conventional approaches, we propose a convergence criterion which enables the number of iterations to be self-adjusted based on the values of the distance function. The efficiency of our method is demonstrated by performing two-phase flow calculations including the high-speed water entry of a V-shaped wedge. Our results are found to be in good agreement with experimental measurements and enable us to gain insight into the instability that arises on the onset of the closure phase of the cavity. This material is based upon work supported by the National Science Foundation (CBET-1509071).
High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions
Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake
2017-03-01
We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.
Yang, Man; Chen, Xianfeng; Wang, Yujie; Yuan, Bihe; Niu, Yi; Zhang, Ying; Liao, Ruoyu; Zhang, Zumin
2017-09-05
In order to analyze the thermal decomposition characteristics of ammonium nitrate (AN), its thermal behavior and stability under different conditions are studied, including different atmospheres, heating rates and gas flow rates. The evolved decomposition gases of AN in air and nitrogen are analyzed with a quadrupole mass spectrometer. Thermal stability of AN at different heating rates and gas flow rates are studied by differential scanning calorimetry, thermogravimetric analysis, paired comparison method and safety parameter evaluation. Experimental results show that the major evolved decomposition gases in air are H2O, NH3, N2O, NO, NO2 and HNO3, while in nitrogen, H2O, NH3, NO and HNO3 are major components. Compared with nitrogen atmosphere, lower initial and end temperatures, higher heat flux and broader reaction temperature range are obtained in air. Meanwhile, higher air gas flow rate tends to achieve lower reaction temperature and to reduce thermal stability of AN. Self-accelerating decomposition temperature of AN in air is much lower than that in nitrogen. It is considered that thermostability of AN is influenced by atmosphere, heating rate and gas flow rate, thus changes of boundary conditions will influence its thermostability, which is helpful to its safe production, storage, transportation and utilization. Copyright © 2017 Elsevier B.V. All rights reserved.
Wu, S. T.; Wang, A. H.; Cassibry, J.
2010-09-01
We discuss the self-consistent time-dependent numerical boundary conditions for magnetohydrodynamic (MHD) simulation to study the solar and laboratory plasma dynamics. It is well known that these plasma flows cover from the sub-sonic and sub-Alfvénic to super-sonic and super-Alfvénic region. Mathematically, the set of governing differential equations is transited from elliptical to hyperbolic type. In order to assure self-consistency, characteristic boundary conditions need to be used because the information propagating according to these characteristics will affect the solutions inside the computational domain. To illustrate the importance of the characteristic boundary conditions, two examples are given; one for solar plasma which is to study the energy and magnetic flux from the sub-photosphere to the corona, and the other one concerns laboratory plasma flow for the investigation of sub-Alfvénic inlet boundary conditions of an MHD nozzle flow.
On the symmetry of the boundary conditions of the volume potential
Kal'menov, Tynysbek Sh.; Arepova, Gaukhar; Suragan, Durvudkhan
2017-09-01
It is well known that the volume potential determines the mass or the charge distributed over the domain with density f. The volume potential is extensively used in function theory and embedding theorems. It is also well known that the volume potential gives a solution to an inhomogeneous equation. And it generates a linear self-adjoint operator. It is known that self-adjoint differential operators are generated by boundary conditions. In our previous papers for an arbitrary domain a boundary condition on the volume potential is given. In the past, it was not possible to prove the self-adjointness of these obtained boundary conditions. In the present paper, we prove the symmetry of boundary condition for the volume potential.
Existence of arbitrarily smooth solutions of the LLG equation in 3D with natural boundary conditions
Feischl, Michael; Tran, Thanh
2016-01-01
We prove that the Landau-Lifshitz-Gilbert equation in three space dimensions with homogeneous Neumann boundary conditions admits arbitrarily smooth solutions, given that the initial data is sufficiently close to a constant function.
Directory of Open Access Journals (Sweden)
Yelda Aygar
2012-01-01
Full Text Available Let denote the operator generated in by , , , and the boundary condition , where , , , and , are complex sequences, , , and is an eigenparameter. In this paper we investigated the principal functions corresponding to the eigenvalues and the spectral singularities of .
Effect of a boundary condition on the cylindrical Couette flow of a rarefied gas
Kosuge, Shingo
2014-12-01
The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated on the basis of kinetic theory. We perform a numerical analysis of the (BGK model) Boltzmann equation for a wide range of the Knudsen number and an asymptotic analysis for small Knudsen numbers employing two kinds of kinetic boundary conditions on the cylinders. One is the modified Maxwell-type boundary condition (proposed by S. K. Dadzie and J. G. Méolans) and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. Our main interest is in the effect of those boundary conditions on the inverted velocity profile. The results show that the onset of the inversion is practically controlled by the tangential accommodation only.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.
Evaluation of wall boundary condition parameters for gas-solids fluidized bed simulations
Energy Technology Data Exchange (ETDEWEB)
Li, Tingwen [URS Corporation; Morgantown, WV (United States); National Energy Technology Lab. (NETL), Morgantown, WV (United States); Benyahia, Sofiane [National Energy Technology Lab. (NETL), Morgantown, WV (United States)
2013-10-01
Wall boundary conditions for the solids phase have significant effects on numerical predictions of various gas-solids fluidized beds. Several models for the granular flow wall boundary condition are available in the open literature for numerical modeling of gas-solids flow. In this study, a model for specularity coefficient used in Johnson and Jackson boundary conditions by Li and Benyahia (AIChE Journal, 2012, 58, 2058-2068) is implemented in the open-source CFD code-MFIX. The variable specularity coefficient model provides a physical way to calculate the specularity coefficient needed by the partial-slip boundary conditions for the solids phase. Through a series of 2-D numerical simulations of bubbling fluidized bed and circulating fluidized bed riser, the model predicts qualitatively consistent trends to the previous studies. Furthermore, a quantitative comparison is conducted between numerical results of variable and constant specularity coefficients to investigate the effect of spatial and temporal variations in specularity coefficient.
Applying the method of fundamental solutions to harmonic problems with singular boundary conditions
Valtchev, Svilen S.; Alves, Carlos J. S.
2017-07-01
The method of fundamental solutions (MFS) is known to produce highly accurate numerical results for elliptic boundary value problems (BVP) with smooth boundary conditions, posed in analytic domains. However, due to the analyticity of the shape functions in its approximation basis, the MFS is usually disregarded when the boundary functions possess singularities. In this work we present a modification of the classical MFS which can be applied for the numerical solution of the Laplace BVP with Dirichlet boundary conditions exhibiting jump discontinuities. In particular, a set of harmonic functions with discontinuous boundary traces is added to the MFS basis. The accuracy of the proposed method is compared with the results form the classical MFS.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
gradient near a wall have to satisfy the no-slip condition at every instant. ... The well known Bernoulli equation giving a relation .... resistance being proportional to the slip velocity itself. leads to infinite stress. But this model was proposed before the. N-S equations were known. The third hypothesis was due to Navier himself.
A Boundary Mixture Approach to Violations of Conditional Independence
Braeken, Johan
2011-01-01
Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of…
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Ern, Rasmus; Johansen, Jacob L; Rummer, Jodie L; Esbaugh, Andrew J
2017-07-01
Rising ocean temperatures are predicted to cause a poleward shift in the distribution of marine fishes occupying the extent of latitudes tolerable within their thermal range boundaries. A prevailing theory suggests that the upper thermal limits of fishes are constrained by hypoxia and ocean acidification. However, some eurythermal fish species do not conform to this theory, and maintain their upper thermal limits in hypoxia. Here we determine if the same is true for stenothermal species. In three coral reef fish species we tested the effect of hypoxia on upper thermal limits, measured as critical thermal maximum (CT max ). In one of these species we also quantified the effect of hypoxia on oxygen supply capacity, measured as aerobic scope (AS). In this species we also tested the effect of elevated CO 2 (simulated ocean acidification) on the hypoxia sensitivity of CT max We found that CT max was unaffected by progressive hypoxia down to approximately 35 mmHg, despite a substantial hypoxia-induced reduction in AS. Below approximately 35 mmHg, CT max declined sharply with water oxygen tension ( P w O 2 ). Furthermore, the hypoxia sensitivity of CT max was unaffected by elevated CO 2 Our findings show that moderate hypoxia and ocean acidification do not constrain the upper thermal limits of these tropical, stenothermal fishes. © 2017 The Author(s).
Evaluation of thermal conditions inside a vehicle cabin
Directory of Open Access Journals (Sweden)
Orzechowski Tadeusz
2016-01-01
Full Text Available There are several important factors influencing road accidents. Temperature inside the vehicle is ranked third after alcohol and seat belts. For this reason, maintaining thermal comfort in the passenger compartment is essential. Thermal comfort is provided by the air conditioning system, which consumes much energy. In the case of electrically powered vehicles, this results in a shorter range. Optimization of such systems is therefore required. This paper proposes a set of equations describing the thermal conditions inside the vehicle, which are the result of appropriate energy balances for air, interior elements, and glass. Variable transmission conditions are included for transparent materials exposed to short and long wave radiation. The study focused on unsteady air-conditioning of the vehicle interior. The measurement data was compared with the results obtained through numerical solutions of the proposed set of equations.
Evaluation of thermal conditions inside a vehicle cabin
Orzechowski, Tadeusz; Skrobacki, Zbigniew
2016-03-01
There are several important factors influencing road accidents. Temperature inside the vehicle is ranked third after alcohol and seat belts. For this reason, maintaining thermal comfort in the passenger compartment is essential. Thermal comfort is provided by the air conditioning system, which consumes much energy. In the case of electrically powered vehicles, this results in a shorter range. Optimization of such systems is therefore required. This paper proposes a set of equations describing the thermal conditions inside the vehicle, which are the result of appropriate energy balances for air, interior elements, and glass. Variable transmission conditions are included for transparent materials exposed to short and long wave radiation. The study focused on unsteady air-conditioning of the vehicle interior. The measurement data was compared with the results obtained through numerical solutions of the proposed set of equations.
Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang
2017-11-01
We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.
Semi-transparent boundary conditions in the worldline formalism
Energy Technology Data Exchange (ETDEWEB)
Vinas, S A Franchino; Pisani, P A G, E-mail: safranchino@fisica.unlp.edu.ar, E-mail: pisani@fisica.unlp.edu.ar [IFLP-CONICET/Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67, (1900) La Plata (Argentina)
2011-07-22
The interaction of a quantum field with a background containing a Dirac delta function with support on a surface of codimension 1 represents a particular kind of matching conditions on that surface for the field. In this paper, we show that the worldline formalism can be applied to this model. We obtain the asymptotic expansion of the heat kernel corresponding to a scalar field on R{sup d+1} in the presence of an arbitrary regular potential and subject to this kind of matching conditions on a flat surface. We also consider two such surfaces and compute their Casimir attraction due to the vacuum fluctuations of a massive scalar field weakly coupled to the corresponding Dirac deltas.
Xu, Xinpeng
2012-01-01
Recently, liquid-gas flows related to droplets, bubbles, and thin films on solid surfaces with thermal and wettability gradients have attracted widespread attention because of the many physical processes involved and their promising potential applications in biology, chemistry, and industry. Various new physical effects have been discovered at fluid-solid interfaces by experiments and molecular dynamics simulations, e.g., fluid velocity slip, temperature slip (Kapitza resistance), mechanical-thermal cross coupling, etc. There have been various models and theories proposed to explain these experimental and numerical observations. However, to the best of our knowledge,a continuum hydrodynamic model capable of predicting the temperature and velocity profiles of liquid-gas flows on non-isothermal, heterogeneous solid substrates is still absent. The purpose of this work is to construct a continuum model for simulating the liquid-gas flows on solid surfaces that are flat and rigid, and may involve wettability gradients and thermal gradients. This model is able to describe fluid velocity slip, temperature slip, and mechanical-thermal coupling that may occur at fluid-solid interfaces. For this purpose, we first employ the diffuse interface modeling to formulate the hydrodynamic equations for one-component liquid-gas flows in the bulk region. This reproduces the dynamic van der Waals theory of Onuki [Phys. Rev. Lett., 94: 054501, 2005]. We then extendWaldmann\\'s method [Z. Naturforsch. A, 22: 1269-1280, 1967] to formulate the boundary conditions at the fluid-solid interface that match the hydrodynamic equations in the bulk. The effects of the solid surface curvature are also briefly discussed in the appendix. The guiding principles of our model derivation are the conservation laws and the positive definiteness of entropy production together with the Onsager reciprocal relation. The derived model is self-consistent in the sense that the boundary conditions are
Rayleigh-Benard convection with time-dependent boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Swift, J.B.; Hohenberg, P.C.
1989-04-15
The 13-mode Lorenz model previously introduced to describe hexagons and rolls in a Rayleigh-Benard cell with periodic modulation of the lower plate is generalized to arbitrary time dependence of both upper and lower plates. Earlier results of Krishnamurti (J. Fluid Mech. 33, 445 (1968); 33, 457 (1968)) for the case of a linear ramp with constant temperature difference are recovered. The conditions for observing hexagons are derived analytically for periodic modulation with different frequencies, amplitudes, and phases at the two plates.
Hayat, Tasawar; Ashraf, Muhammad Bilal; Alsulami, Hamed H; Alhuthali, Muhammad Shahab
2014-01-01
The objective of present research is to examine the thermal radiation effect in three-dimensional mixed convection flow of viscoelastic fluid. The boundary layer analysis has been discussed for flow by an exponentially stretching surface with convective conditions. The resulting partial differential equations are reduced into a system of nonlinear ordinary differential equations using appropriate transformations. The series solutions are developed through a modern technique known as the homotopy analysis method. The convergent expressions of velocity components and temperature are derived. The solutions obtained are dependent on seven sundry parameters including the viscoelastic parameter, mixed convection parameter, ratio parameter, temperature exponent, Prandtl number, Biot number and radiation parameter. A systematic study is performed to analyze the impacts of these influential parameters on the velocity and temperature, the skin friction coefficients and the local Nusselt number. It is observed that mixed convection parameter in momentum and thermal boundary layers has opposite role. Thermal boundary layer is found to decrease when ratio parameter, Prandtl number and temperature exponent are increased. Local Nusselt number is increasing function of viscoelastic parameter and Biot number. Radiation parameter on the Nusselt number has opposite effects when compared with viscoelastic parameter.
Jin, Guoyong; Su, Zhu
2015-01-01
This book develops a uniform accurate method which is capable of dealing with vibrations of laminated beams, plates and shells with arbitrary boundary conditions including classical boundaries, elastic supports and their combinations. It also provides numerous solutions for various configurations including various boundary conditions, laminated schemes, geometry and material parameters, which fill certain gaps in this area of reach and may serve as benchmark solutions for the readers. For each case, corresponding fundamental equations in the framework of classical and shear deformation theory are developed. Following the fundamental equations, numerous free vibration results are presented for various configurations including different boundary conditions, laminated sequences and geometry and material properties. The proposed method and corresponding formulations can be readily extended to static analysis.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
DEFF Research Database (Denmark)
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
for uniaxial plane strain compression of a single crystal block and for uniform pure bending of a single crystal foil. The compressed block has loading surfaces that are penetrable or impenetrable to dislocations. This allows for a study of the two types of higher-order boundaries available, and a significant......The finite deformation version of the higher-order gradient crystal plasticity model proposed by the authors is applied to solve plane strain boundary value problems, in order to obtain an understanding of the effect of the higher-order boundary conditions. Numerical solutions are carried out...... effect of higher-order boundary conditions on the overall deformation mode of the block is observed. The bent foil has free surfaces through which dislocations can go out of the material, and we observe a strong size-dependent mechanical response resulting from the surface condition assumed....
An energy absorbing far-field boundary condition for the elastic wave equation
Energy Technology Data Exchange (ETDEWEB)
Petersson, N A; Sjogreen, B
2008-07-15
The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
Nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Ahmet Batal
2016-08-01
Full Text Available In this article, we study the initial boundary value problem for nonlinear Schrodinger equations on the half-line with nonlinear boundary conditions $$ u_x(0,t+\\lambda|u(0,t|^ru(0,t=0,\\quad \\lambda\\in\\mathbb{R}-\\{0\\},\\; r> 0. $$ We discuss the local well-posedness when the initial data $u_0=u(x,0$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\\mathbb{R}_+$ with $s\\in (\\frac{1}{2},\\frac{7}{2}-\\{\\frac{3}{2}\\}$. We deal with the nonlinear boundary condition by first studying the linear Schrodinger equation with a time-dependent inhomogeneous Neumann boundary condition $u_x(0,t=h(t$ where $h\\in H^{\\frac{2s-1}{4}}(0,T$.
Performance of Numerical Boundary Condition based on Active Wave Absorption System
DEFF Research Database (Denmark)
Trouch, P.; Rouck, J. de; Frigaard, Peter
2001-01-01
The implementation and performance of a new active wave generating‐absorbing boundary condition for a numerical model based on the Volume Of Fluid (VOF) method for tracking free surfaces is presented. This numerical boundary condition AWAVOF is based on an active wave absorption system...... that was first developed in the context of physical wave flume experiments, using a wave paddle. The method applies to regular and irregular waves. Velocities are measured at one location inside the computational domain. The reflected wave train is separated from the incident wave field in front of a structure...... by means of digital filtering and subsequent superposition of the measured velocity signals. The incident wave signal is corrected, so that the reflected wave is effectively absorbed at the boundary. The effectiveness of the active wave generating‐absorbing boundary condition is proved using numerical...
Exact solution for the fractional cable equation with nonlocal boundary conditions
Bazhlekova, Emilia; Dimovski, Ivan
2013-10-01
The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the problem to a system of integral equations in any generalized eigenspace. In this way we prove uniqueness of the solution and give an algorithm for constructing the solution in the form of an expansion in terms of the generalized eigenfunctions and three-parameter Mittag-Leffler functions. Explicit representation of the solution is given for the case of double eigenvalues. We consider some examples and as a particular case we recover a recent result. The asymptotic behavior of the solution is also studied.
Phase-space networks of the six-vertex model under different boundary conditions.
Han, Yilong
2010-04-01
The six-vertex model is mapped to three-dimensional sphere stacks and different boundary conditions corresponding to different containers. The shape of the container provides a qualitative visualization of the boundary effect. Based on the sphere-stacking picture, we map the phase spaces of the six-vertex models to discrete networks. A node in the network represents a state of the system, and an edge between two nodes represents a zero-energy spin flip, which corresponds to adding or removing a sphere. The network analysis shows that the phase spaces of systems with different boundary conditions share some common features. We derived a few formulas for the number and the sizes of the disconnected phase-space subnetworks under the periodic boundary conditions. The sphere stacking provides new challenges in combinatorics and may cast light on some two-dimensional models.
A new approach to implement absorbing boundary condition in biomolecular electrostatics.
Goni, Md Osman
2013-01-01
This paper discusses a novel approach to employ the absorbing boundary condition in conjunction with the finite-element method (FEM) in biomolecular electrostatics. The introduction of Bayliss-Turkel absorbing boundary operators in electromagnetic scattering problem has been incorporated by few researchers. However, in the area of biomolecular electrostatics, this boundary condition has not been investigated yet. The objective of this paper is twofold. First, to solve nonlinear Poisson-Boltzmann equation using Newton's method and second, to find an efficient and acceptable solution with minimum number of unknowns. In this work, a Galerkin finite-element formulation is used along with a Bayliss-Turkel absorbing boundary operator that explicitly accounts for the open field problem by mapping the Sommerfeld radiation condition from the far field to near field. While the Bayliss-Turkel condition works well when the artificial boundary is far from the scatterer, an acceptable tolerance of error can be achieved with the second order operator. Numerical results on test case with simple sphere show that the treatment is able to reach the same level of accuracy achieved by the analytical method while using a lower grid density. Bayliss-Turkel absorbing boundary condition (BTABC) combined with the FEM converges to the exact solution of scattering problems to within discretization error.
DEFF Research Database (Denmark)
Svec, Oldrich; Skoček, Jan
2013-01-01
The ability of the Lattice Boltzmann method, as the fluid dynamics solver, to properly simulate macroscopic Navier’s slip boundary condition is investigated. An approximate equation relating the Lattice Boltzmann variable slip boundary condition with the macroscopic Navier’s slip boundary condition...
Directory of Open Access Journals (Sweden)
K. V. Dobrego
2015-01-01
Full Text Available Differential approximation is derived from radiation transfer equation by averaging over the solid angle. It is one of the more effective methods for engineering calculations of radia- tive heat transfer in complex three-dimensional thermal power systems with selective and scattering media. The new method for improvement of accuracy of the differential approximation based on using of auto-adaptable boundary conditions is introduced in the paper. The efficiency of the named method is proved for the test 2D-systems. Self-consistent auto-adaptable boundary conditions taking into consideration the nonorthogonal component of the incident to the boundary radiation flux are formulated. It is demonstrated that taking in- to consideration of the non- orthogonal incident flux in multi-dimensional systems, such as furnaces, boilers, combustion chambers improves the accuracy of the radiant flux simulations and to more extend in the zones adjacent to the edges of the chamber.Test simulations utilizing the differential approximation method with traditional boundary conditions, new self-consistent boundary conditions and “precise” discrete ordinates method were performed. The mean square errors of the resulting radiative fluxes calculated along the boundary of rectangular and triangular test areas were decreased 1.5–2 times by using auto- adaptable boundary conditions. Radiation flux gaps in the corner points of non-symmetric sys- tems are revealed by using auto-adaptable boundary conditions which can not be obtained by using the conventional boundary conditions.
Zhang, Wei; Markfort, Corey; Porté-Agel, Fernando
2014-11-01
Turbulent flows over complex surface topography have been of great interest in the atmospheric science and wind engineering communities. The geometry of the topography, surface roughness and temperature characteristics as well as the atmospheric thermal stability play important roles in determining momentum and scalar flux distribution. Studies of turbulent flow over simplified topography models, under neutrally stratified boundary-layer conditions, have provided insights into fluid dynamics. However, atmospheric thermal stability has rarely been considered in laboratory experiments, e.g., wind-tunnel experiments. Series of wind-tunnel experiments of thermally-stratified boundary-layer flow over a surface-mounted 2-D block, in a well-controlled boundary-layer wind tunnel, will be presented. Measurements using high-resolution PIV, x-wire/cold-wire anemometry and surface heat flux sensors were conducted to quantify the turbulent flow properties, including the size of the recirculation zone, coherent vortex structures and the subsequent boundary layer recovery. Results will be shown to address thermal stability effects on momentum and scalar flux distribution in the wake, as well as dominant mechanism of turbulent kinetic energy generation and consumption. The authors gratefully acknowledge funding from the Swiss National Foundation (Grant 200021-132122), the National Science Foundation (Grant ATM-0854766) and NASA (Grant NNG06GE256).
Pan, Qing; Wang, Ruofan; Reglin, Bettina; Fang, Luping; Pries, Axel R; Ning, Gangmin
2014-01-01
Estimation of the boundary condition is a critical problem in simulating hemodynamics in microvascular networks. This paper proposed a boundary estimation strategy based on a particle swarm optimization (PSO) algorithm, which aims to minimize the number of vessels with inverted flow direction in comparison to the experimental observation. The algorithm took boundary values as the particle swarm and updated the position of the particles iteratively to approach the optimization target. The method was tested in a real rat mesenteric network. With random initial boundary values, the method achieved a minimized 9 segments with an inverted flow direction in the network with 546 vessels. Compared with reported literature, the current work has the advantage of a better fit with experimental observations and is more suitable for the boundary estimation problem in pulsatile hemodynamic models due to the experiment-based optimization target selection.
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson
2012-03-07
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
Xydou, A; Aicheler, M; Djurabekova, F
2016-01-01
By means of molecular dynamic simulations, the stability of cylindrical voids is examined with respect to the diffusion bonding procedure. To do this, the effect of grain boundaries between the grains of different crystallographic orientations on the void closing time was studied at high temperatures from 0.7 up to 0.94 of the bulk melting temperature $(T_m)$. The diameter of the voids varied from 3.5 to 6.5 nm. A thermal instability occurring at high temperatures at the surface of the void placed in a grain boundary triggered the eventual closure of the void at all examined temperatures. The closing time has an exponential dependence on the examined temperature values. A model based on the defect diffusion theory is developed to predict the closing time for voids of macroscopic size. The diffusion coefficient within the grain boundaries is found to be overall higher than the diffusion coefficient in the region around the void surface. The activation energy for the diffusion in the grain boundary is calculate...
An outgoing energy flux boundary condition for finite difference ICRP antenna models
Energy Technology Data Exchange (ETDEWEB)
Batchelor, D.B.; Carter, M.D.
1992-11-01
For antennas at the ion cyclotron range of frequencies (ICRF) modeling in vacuum can now be carried out to a high level of detail such that shaping of the current straps, isolating septa, and discrete Faraday shield structures can be included. An efficient approach would be to solve for the fields in the vacuum region near the antenna in three dimensions by finite methods and to match this solution at the plasma-vacuum interface to a solution obtained in the plasma region in one dimension by Fourier methods. This approach has been difficult to carry out because boundary conditions must be imposed at the edge of the finite difference grid on a point-by-point basis, whereas the condition for outgoing energy flux into the plasma is known only in terms of the Fourier transform of the plasma fields. A technique is presented by which a boundary condition can be imposed on the computational grid of a three-dimensional finite difference, or finite element, code by constraining the discrete Fourier transform of the fields at the boundary points to satisfy an outgoing energy flux condition appropriate for the plasma. The boundary condition at a specific grid point appears as a coupling to other grid points on the boundary, with weighting determined by a kemel calctdated from the plasma surface impedance matrix for the various plasma Fourier modes. This boundary condition has been implemented in a finite difference solution of a simple problem in two dimensions, which can also be solved directly by Fourier transformation. Results are presented, and it is shown that the proposed boundary condition does enforce outgoing energy flux and yields the same solution as is obtained by Fourier methods.
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-06-01
Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.
Implementation aspects of the Boundary Element Method including viscous and thermal losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2014-01-01
The implementation of viscous and thermal losses using the Boundary Element Method (BEM) is based on the Kirchhoff’s dispersion relation and has been tested in previous work using analytical test cases and comparison with measurements. Numerical methods that can simulate sound fields in fluids...... including losses are particularly interesting whenever small cavities and narrow passages are present, as is the case with many acoustic devices such as transducers and small audio appliances. The present paper describes current work aimed at improving the method by addressing some specific issues related...
Effects of air pollution on thermal structure and dispersion in an urban planetary boundary layer
Viskanta, R.; Johnson, R. O.; Bergstrom, R. W.
1977-01-01
The short-term effects of urbanization and air pollution on the transport processes in the urban planetary boundary layer (PBL) are studied. The investigation makes use of an unsteady two-dimensional transport model which has been developed by Viskanta et al., (1976). The model predicts pollutant concentrations and temperature in the PBL. The potential effects of urbanization and air pollution on the thermal structure in the urban PBL are considered, taking into account the results of numerical simulations modeling the St. Louis, Missouri metropolitan area.
Effect of Boundary Conditions on the Back Face Deformations of Flat UHMWPE Panels
2014-12-01
the experimental results in general, and was computationally more expedient. Delamination is a very common failure mode in composite laminates , and... delaminations in the composites . The calculation showed reasonable agreement with the experimental data for the clamped-corners and free boundary condition...cases for the peak BFD, remaining thickness of the composite and the delamination behavior. The model is useful to assess the size-effects and boundary
Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
Directory of Open Access Journals (Sweden)
Lizhi Cui
2014-04-01
Full Text Available In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hilbert Uniqueness Method. Moreover, we shall give the explicit dependence of the controllability time on the speed of the moving endpoint.
Kaufman, L. G., II; Johnson, C. B.
1981-09-01
Empirical anaytic methods are presented for calculating thermal and pressure distributions in three-dimensional, shock-wave turbulent-boundary-layer, interaction-flow regions on the surface of controllable hypersonic aircraft and missiles. The methods, based on several experimental investigations, are useful and reliable for estimating both the extent and magnitude of the increased thermal and pressure loads on the vehicle surfaces.
[Savants and cultutal boundaries. Thermalism in Savoy and the work of Joseph Daquin (1732-1815)].
Carpanetto, Dino
2008-01-01
The essay sets out to explain the general orientation of the studies, the problems, the perspectives and the research that were done by Joseph Daquin (1732-1815), a physician born in Chambéry (Savoy, Kingdom of Sardinia). He had a secular education at the Faculty of Medicine of Turin, where he earned his degree under Ignazio Somis and Vitaliano Donati. The aim of this essay is to give a critical contribution to cultural history and examine the origins of thermalism with particular emphasis on therapy, physics experiments, and its relation to political and social structure. Daquin was a witness of the advancement of science beyond the boundaries of scientific Enlightenment. His overriding intellectual concern was with the meaning and impact of chemistry theories on medical practices. The author has published an interesting Analyse des eaux thermales d'Aix en Savoie (1773), a natural experimental history of mineral waters in Aix-les-Bains.
Modelling of hydrogen thermal desorption spectrum in nonlinear dynamical boundary-value problem
Kostikova, E. K.; Zaika, Yu V.
2016-11-01
One of the technological challenges for hydrogen materials science (including the ITER project) is the currently active search for structural materials with various potential applications that will have predetermined limits of hydrogen permeability. One of the experimental methods is thermal desorption spectrometry (TDS). A hydrogen-saturated sample is degassed under vacuum and monotone heating. The desorption flux is measured by mass spectrometer to determine the character of interactions of hydrogen isotopes with the solid. We are interested in such transfer parameters as the coefficients of diffusion, dissolution, desorption. The paper presents a distributed boundary-value problem of thermal desorption and a numerical method for TDS spectrum simulation, where only integration of a nonlinear system of low order (compared with, e.g., the method of lines) ordinary differential equations (ODE) is required. This work is supported by the Russian Foundation for Basic Research (project 15-01-00744).
Dubail, J.; Santachiara, R.; Emig, T.
2017-03-01
Systems as diverse as binary mixtures and inclusions in biological membranes, and many more, can be described effectively by interacting spins. When the critical fluctuations in these systems are constrained by boundary conditions, critical Casimir forces (CCF) emerge. Here we analyze CCF between boundaries with alternating boundary conditions in two dimensions, employing conformal field theory (CFT). After presenting the concept of boundary changing operators, we specifically consider two different boundary configurations for a strip of critical Ising spins: (I) alternating equi-sized domains of up and down spins on both sides of the strip, with a possible lateral shift, and (II) alternating domains of up and down spins of different size on one side and homogeneously fixed spins on the other side of the strip. Asymptotic results for the CCF at small and large distances are derived. We introduce a novel modified Szegö formula for determinants of real antisymmetric block Toeplitz matrices to obtain the exact CCF and the corresponding scaling functions at all distances. We demonstrate the existence of a surface renormalization group flow between universal force amplitudes of different magnitude and sign. The Casimir force can vanish at a stable equilibrium position that can be controlled by parameters of the boundary conditions. Lateral Casimir forces assume a universal simple cosine form at large separations.
Winkler boundary conditions for three-point bending tests on 1D nanomaterials
Gangadean, D.; McIlroy, David N.; Faulkner, Brian E.; Aston, D. Eric
2010-06-01
Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.
Winkler boundary conditions for three-point bending tests on 1D nanomaterials.
Gangadean, D; McIlroy, David N; Faulkner, Brian E; Aston, D Eric
2010-06-04
Bending tests with atomic force microscopes (AFM) is a common method for elasticity measurements on 1D nanomaterials. Interpretation of the force and deflection data is necessary to determine the Young's modulus of the tested material and has been done assuming either of two classic boundary conditions that represent two extreme possibilities for the rigidity of the sample-anchor interface. The elasticity results from the two boundary conditions differ by a factor of four. Furthermore, both boundary conditions ignore the effects of deflections in the anchors themselves. The Winkler model for beams on elastic foundations is developed here for three-point bending tests to provide a more realistic representation. Equations for computing sample elasticity are derived from two sets of boundary conditions for the Winkler model. Application of this model to interpret the measurement of mechanical stiffness of a silica nanowire at multiple points in a three-point bending is discussed. With the correct choice of boundary conditions, the Winkler model gives a better fit for the observed stiffness profile than the classical beam models while providing a result that differs from both by a factor of two and is comparable to the bulk elasticity.
Thermal Loads on a Domed Protuberance Under a Mach 5.7 Boundary Layer
Ostoich, Christopher; Bodony, Daniel; Geubelle, Philippe
2011-11-01
A high-fidelity, high-accuracy multi-physics computational tool has been developed to make predictions of structural-thermal response in the hypersonic regime. The predicted surface heat flux distribution was compared with measured data taken from a 1986 experiment in the NASA Langley 8-foot high-temperature tunnel in which a flat plate with a domed protuberance was inserted into a Mach 6.59 flow. The solution from the fluid and thermal domains obtained from the coupled simulation, with experimental comparisons, will be presented. In addition to the typical heating associated with windward-facing surfaces, several other sources of significant differential heating were observed near the dome-plate interface and due to a trailing horseshoe vortex of small size. Data were collected over a long time record (50 seconds) and comments will be given about ignoring transient thermal effects in hypersonic boundary layer calculations. An assessment of gas thermal model assumptions will also be discussed. Supported by the U.S. Air Force Research Laboratory Air Vehicles Directorate under contract number FA8650-06-2-3620.
Ishak, Nazila; Hashim, Hasmawani; Khairul Anuar Mohamed, Muhammad; Sarif, Norhafizah Md; Rosli, Norhayati; Zuki Salleh, Mohd
2017-09-01
In this study, the numerical solution of the thermal radiation effects on a stagnation point flow past a stretching/shrinking sheet in a Maxwell fluid with slip condition is considered. The transformed boundary layer equations are solved numerically using the Runge-Kutta-Fehlberg (RKF) method. Numerical solutions are obtained for the skin friction coefficient and the wall temperature as well as the temperature and the velocity profiles. The features of the flow and the heat transfer characteristics for various values of Prandtl number, stretching/shrinking parameter, thermal radiation parameter, Maxwell parameter, dimensionless velocity slip parameter and thermal slip parameter are analyzed and discussed.
Porous materials for thermal management under extreme conditions.
Clyne, T W; Golosnoy, I O; Tan, J C; Markaki, A E
2006-01-15
A brief analysis is presented of how heat transfer takes place in porous materials of various types. The emphasis is on materials able to withstand extremes of temperature, gas pressure, irradiation, etc. i.e. metals and ceramics, rather than polymers. A primary aim is commonly to maximize either the thermal resistance (i.e. provide insulation) or the rate of thermal equilibration between the material and a fluid passing through it (i.e. to facilitate heat exchange). The main structural characteristics concern porosity (void content), anisotropy, pore connectivity and scale. The effect of scale is complex, since the permeability decreases as the structure is refined, but the interfacial area for fluid-solid heat exchange is, thereby, raised. The durability of the pore structure may also be an issue, with a possible disadvantage of finer scale structures being poor microstructural stability under service conditions. Finally, good mechanical properties may be required, since the development of thermal gradients, high fluid fluxes, etc. can generate substantial levels of stress. There are, thus, some complex interplays between service conditions, pore architecture/scale, fluid permeation characteristics, convective heat flow, thermal conduction and radiative heat transfer. Such interplays are illustrated with reference to three examples: (i) a thermal barrier coating in a gas turbine engine; (ii) a Space Shuttle tile; and (iii) a Stirling engine heat exchanger. Highly porous, permeable materials are often made by bonding fibres together into a network structure and much of the analysis presented here is oriented towards such materials.
Boundary condition-selective length dependence of the flexural rigidity of microtubules
Zhang, Jin; Wang, Chengyuan
2017-07-01
Length-dependent flexural rigidity (FR) is observed experimentally for microtubules (MTs) subjected to certain boundary conditions. To shed some light on this unique feature, we have studied the FR of MTs with different boundary conditions. A molecular structural mechanics method is employed to accurately describe the real boundary conditions imposed on MTs in experiments. Some of component protofilaments of MTs are blocked at the ends while others are free. In addition, linked kinesin is treated as an elastic body rather than a rigid body. Our simulations show that for relatively long MTs having a length comparable to those measured in experiments the length-dependent rigidity is detected only for those with fixed-free and fixed-fixed ends, which is consistent with the experimental observation. To capture the physics leading to the above phenomenon, Timoshenko beam model is adopted accounting for both transverse shear effect (TSE) and imperfect boundary effect (IBE). Comparison between TSE and IBE indicates that the boundary condition-selective length-dependence achieved for the FR of relatively long MTs is primarily a result of the influence of IBE rather than TSE.
Energy Technology Data Exchange (ETDEWEB)
Mirzabeigy, Alborz; Madoliat, Reza [Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Dabbagh, Vahid [University of Malaya, Kuala Lumpur (Malaysia)
2017-02-15
In this paper, free transverse vibration of two parallel beams connected through Winkler type elastic layer is investigated. Euler- Bernoulli beam hypothesis has been applied and it is assumed that boundary conditions of upper and lower beams are similar while arbitrary without any limitation even for non-ideal boundary conditions. Material properties and cross-section geometry of beams could be different from each other. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. Explicit expressions are derived for the natural frequencies. In order to verify accuracy of results, the problem once again solved using modified Adomian decomposition method. Comparison between results indicates excellent accuracy of proposed formulation for any arbitrary boundary conditions. Derived explicit formulation is simplest method to determine natural frequencies of double-beam systems with high level of accuracy in comparison with other methods in literature.
Non-diagonal boundary conditions for gl(1|1) super spin chains
Energy Technology Data Exchange (ETDEWEB)
Grabinski, Andre M; Frahm, Holger, E-mail: frahm@itp.uni-hannover.d [Institut fuer Theoretische Physik, Leibniz Universitaet Hannover, Appelstrasse 2, 30167 Hannover (Germany)
2010-01-29
We study a one-dimensional model of free fermions with gl(1|1) supersymmetry and demonstrate how non-diagonal boundary conditions can be incorporated into the framework of the graded quantum inverse scattering method (gQISM) by means of super matrices with entries from a superalgebra. For super Hermitian twists and open boundary conditions subject to a certain constraint, we solve the eigenvalue problem for the super transfermatrix by means of the graded algebraic Bethe ansatz technique (gABA) starting from a fermionic coherent state. For generic boundary conditions the algebraic Bethe ansatz cannot be applied. In this case the spectrum of the super transfermatrix is obtained from a functional relation.
Fang, Angbo
2008-12-08
Parallel to the highly successful Ericksen-Leslie hydrodynamic theory for the bulk behavior of nematic liquid crystals (NLCs), we derive a set of coupled hydrodynamic boundary conditions to describe the NLC dynamics near NLC-solid interfaces. In our boundary conditions, translational flux (flow slippage) and rotational flux (surface director relaxation) are coupled according to the Onsager variational principle of least energy dissipation. The application of our boundary conditions to the truly bistable π -twist NLC cell reveals a complete picture of the dynamic switching processes. It is found that the thus far overlooked translation-rotation dissipative coupling at solid surfaces can accelerate surface director relaxation and enhance the flow rate. This can be utilized to improve the performance of electro-optical nematic devices by lowering the required switching voltages and reducing the switching times. © 2008 The American Physical Society.
Heat Transfer Boundary Conditions in the RELAP5-3D Code
Energy Technology Data Exchange (ETDEWEB)
Richard A. Riemke; Cliff B. Davis; Richard R. Schultz
2008-05-01
The heat transfer boundary conditions used in the RELAP5-3D computer program have evolved over the years. Currently, RELAP5-3D has the following options for the heat transfer boundary conditions: (a) heat transfer correlation package option, (b) non-convective option (from radiation/conduction enclosure model or symmetry/insulated conditions), and (c) other options (setting the surface temperature to a volume fraction averaged fluid temperature of the boundary volume, obtaining the surface temperature from a control variable, obtaining the surface temperature from a time-dependent general table, obtaining the heat flux from a time-dependent general table, or obtaining heat transfer coefficients from either a time- or temperature-dependent general table). These options will be discussed, including the more recent ones.
Sensitivity of an idealized subtropical gyre to the eastern boundary conditions
Directory of Open Access Journals (Sweden)
I. Láiz
2001-07-01
Full Text Available The flow pattern of the North Atlantic Subtropical Gyre (NASG is simulated using a highly idealised one-layer quasi-geostrophic wind-driven model. The novel feature of the model is the specification of the eastern boundary conditions. This is an upwelling favourable region with a quasi-permanent southward flowing coastal jet, which is fed by the eastern branch of the Canary Current. The corresponding boundary conditions are non-zero normal flux and constant potential vorticity, the latter being consistent with the generation of anticyclonic vorticity by the coastal jet. We examine the sensitivity of the model to the eastern boundary conditions and compare the results with recent observations for the region.
Reconsidering the boundary conditions for a dynamic, transient mode I crack problem
Leise, Tanya
2008-11-01
A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.
Fraga Filho, Carlos Alberto Dutra
2017-11-01
The aim of this paper is to present a computational algorithmic implementation of physical reflective boundary conditions and applications, for use in particle methods. It is motivated by the lack of a straightforward study in the literature dedicated to the presentation of this reflective boundary condition, based on Newton's restitution law and the foundations of analytic geometry. Particular attention is given here to the procedures of collision detection and response. The importance of the consistency of input data and an appropriate temporal integration technique for use in the particle method is also discussed. Validation tests are performed, with the results of the algorithm verified using analytical results. Numerical simulations of static and dynamic problems are carried out. The analysis of the numerical results shows that the physical reflective boundary conditions are consistent and that the algorithm has been properly implemented.
Attractor of Beam Equation with Structural Damping under Nonlinear Boundary Conditions
Directory of Open Access Journals (Sweden)
Danxia Wang
2015-01-01
Full Text Available Simultaneously, considering the viscous effect of material, damping of medium, and rotational inertia, we study a kind of more general Kirchhoff-type extensible beam equation utt-uxxtt+uxxxx-σ(∫0l(ux2dxuxx-ϕ(∫0l(ux2dxuxxt=q(x, in [0,L]×R+ with the structural damping and the rotational inertia term. Little attention is paid to the longtime behavior of the beam equation under nonlinear boundary conditions. In this paper, under nonlinear boundary conditions, we prove not only the existence and uniqueness of global solutions by prior estimates combined with some inequality skills, but also the existence of a global attractor by the existence of an absorbing set and asymptotic compactness of corresponding solution semigroup. In addition, the same results also can be proved under the other nonlinear boundary conditions.
Constraint-preserving boundary conditions in the 3+1 first-order approach
Bona, C
2010-01-01
A set of stable energy-momentum constraint-preserving boundary conditions are proposed for the first-order Z4 case. No linear modes appear in the robust stability test. Also, a modified finite-differences stencil for boundary points is presented, which avoids the corner and vertex points even in cartesian-like grids. Moreover, the proposed boundary conditions are tested in a strong field scenario, the Gowdy waves metric, showing that the accumulated amount of energy-momentum constraint violations is of the same order of magnitude than the one generated by either periodic or reflection conditions, which are exact in the Gowdy waves case. As a side result, a new symmetrizer is explicitly given, which extends the parametric domain of symmetric hyperbolicity for the Z4 formalism. The aplication of these results to first-order BSSN-like formalisms is also considered.
(2,2) and (0,4) supersymmetric boundary conditions in 3d N =4 theories and type IIB branes
Chung, Hee-Joong; Okazaki, Tadashi
2017-10-01
The half-BPS boundary conditions preserving N =(2 ,2 ) and N =(0 ,4 ) supersymmetry in 3d N =4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Nahm-like equations arise in the vector multiplet BPS boundary condition preserving N =(0 ,4 ) supersymmetry, and Robin-type boundary conditions appear for the hypermultiplet coupled to the vector multiplet when N =(2 ,2 ) supersymmetry is preserved. The half-BPS boundary conditions are realized in the brane configurations of type IIB string theory.
Douillet-Grellier, Thomas; Pramanik, Ranjan; Pan, Kai; Albaiz, Abdulaziz; Jones, Bruce D.; Williams, John R.
2017-10-01
This paper develops a method for imposing stress boundary conditions in smoothed particle hydrodynamics (SPH) with and without the need for dummy particles. SPH has been used for simulating phenomena in a number of fields, such as astrophysics and fluid mechanics. More recently, the method has gained traction as a technique for simulation of deformation and fracture in solids, where the meshless property of SPH can be leveraged to represent arbitrary crack paths. Despite this interest, application of boundary conditions within the SPH framework is typically limited to imposed velocity or displacement using fictitious dummy particles to compensate for the lack of particles beyond the boundary interface. While this is enough for a large variety of problems, especially in the case of fluid flow, for problems in solid mechanics there is a clear need to impose stresses upon boundaries. In addition to this, the use of dummy particles to impose a boundary condition is not always suitable or even feasibly, especially for those problems which include internal boundaries. In order to overcome these difficulties, this paper first presents an improved method for applying stress boundary conditions in SPH with dummy particles. This is then followed by a proposal of a formulation which does not require dummy particles. These techniques are then validated against analytical solutions to two common problems in rock mechanics, the Brazilian test and the penny-shaped crack problem both in 2D and 3D. This study highlights the fact that SPH offers a good level of accuracy to solve these problems and that results are reliable. This validation work serves as a foundation for addressing more complex problems involving plasticity and fracture propagation.
Directory of Open Access Journals (Sweden)
G Boroni
2017-03-01
Full Text Available Lattice Boltzmann Method (LBM has shown great potential in fluid simulations, but performance issues and difficulties to manage complex boundary conditions have hindered a wider application. The upcoming of Graphic Processing Units (GPU Computing offered a possible solution for the performance issue, and methods like the Immersed Boundary (IB algorithm proved to be a flexible solution to boundaries. Unfortunately, the implicit IB algorithm makes the LBM implementation in GPU a non-trivial task. This work presents a fully parallel GPU implementation of LBM in combination with IB. The fluid-boundary interaction is implemented via GPU kernels, using execution configurations and data structures specifically designed to accelerate each code execution. Simulations were validated against experimental and analytical data showing good agreement and improving the computational time. Substantial reductions of calculation rates were achieved, lowering down the required time to execute the same model in a CPU to about two magnitude orders.
Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
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Markus Holzleitner
2016-01-01
Full Text Available We investigate the dependence of the \\(L^1\\to L^{\\infty}\\ dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at \\(0\\. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, \\(l\\in (0,1/2\\. However, for nonpositive angular momenta, \\(l\\in (-1/2,0]\\, the standard \\(O(|t|^{-1/2}\\ decay remains true for all self-adjoint realizations.
Mathematical analysis of the Navier-Stokes equations with non standard boundary conditions
Tidriri, M. D.
1995-01-01
One of the major applications of the domain decomposition time marching algorithm is the coupling of the Navier-Stokes systems with Boltzmann equations in order to compute transitional flows. Another important application is the coupling of a global Navier-Stokes problem with a local one in order to use different modelizations and/or discretizations. Both of these applications involve a global Navier-Stokes system with nonstandard boundary conditions. The purpose of this work is to prove, using the classical Leray-Schauder theory, that these boundary conditions are admissible and lead to a well posed problem.
DEFF Research Database (Denmark)
Richards, H.L.; Kolesik, M.; Lindgård, P.-A.
1997-01-01
Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider the effe......Magnetization switching in highly anisotropic single-domain ferromagnets has been previously shown to be qualitatively described by the droplet theory of metastable decay and simulations of two-dimensional kinetic Ising systems with periodic boundary conditions. In this paper we consider...
Free vibration of functionally graded parabolic and circular panels with general boundary conditions
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Zhang Hong
2017-01-01
Full Text Available The purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.
Constraints on core-mantle boundary topography from models of thermal and thermochemical convection
Deschamps, Frédéric; Rogister, Yves; Tackley, Paul J.
2018-01-01
Mantle flow induces dynamic topography at the core-mantle boundary (CMB), with distribution and amplitude that depend on details of the flow. To assess whether observations of CMB topography can give constraints on deep mantle structure, we determine CMB dynamic topography associated with different models of mantle convection, including thermochemical and purely thermal models. We investigate the influence of key controlling parameters, specifically the thermal viscosity ratio (ΔηT) and, for thermochemical models, the density contrast (ΔρC) and viscosity ratio (ΔηC) between primordial and regular materials. In purely thermal models, plume clusters induce positive topography with an amplitude that decreases with increasing ΔηT. In thermochemical models with moderate density contrasts, around 100-200 kg m-3, reservoirs of dense material induce depressions in CMB topography, surrounded by a ridge of positive topography. The average depression depth and ridge height increase with increasing ΔρC and ΔηC, but decrease with increasing ΔηT. We find that for purely thermal models or thermochemical models with ΔρC ˜ 90 kg m-3 and less, the long-wavelength (spherical harmonic degrees up to l = 4) dynamic topography and shear wave velocity anomalies predicted by thermochemical distributions anticorrelate. By contrast, for models with ΔρC ≥ 100 kg m-3 and ΔηC > 1, long-wavelength dynamic topography and shear wave velocity anomalies correlate well. This potentially provides a test to infer the nature, that is, either purely or mostly thermal (ΔρC ≤ 100 kg m-3 m-3) or strongly thermochemical (ΔρC ≥ 100 kg m-3), of the low shear wave velocity provinces observed by global tomographic images. The presence of post-perovskite, provided that its viscosity is similar to that of bridgmanite, does not alter these conclusions.
Numerical Study of Outlet Boundary Conditions for Unsteady Turbulent Internal Flows Using the NCC
Liu, Nan-Suey; Shih, Tsan-Hsing
2009-01-01
This paper presents the results of studies on the outlet boundary conditions for turbulent internal flow simulations. Several outlet boundary conditions have been investigated by applying the National Combustion Code (NCC) to the configuration of a LM6000 single injector flame tube. First of all, very large eddy simulations (VLES) have been performed using the partially resolved numerical simulation (PRNS) approach, in which both the nonlinear and linear dynamic subscale models were employed. Secondly, unsteady Reynolds averaged Navier- Stokes (URANS) simulations have also been performed for the same configuration to investigate the effects of different outlet boundary conditions in the context of URANS. Thirdly, the possible role of the initial condition is inspected by using three different initial flow fields for both the PRNS/VLES simulation and the URANS simulation. The same grid is used for all the simulations and the number of mesh element is about 0.5 million. The main purpose of this study is to examine the long-time behavior of the solution as determined by the imposed outlet boundary conditions. For a particular simulation to be considered as successful under the given initial and boundary conditions, the solution must be sustainable in a physically meaningful manner over a sufficiently long period of time. The commonly used outlet boundary condition for steady Reynolds averaged Navier-Stokes (RANS) simulation is a fixed pressure at the outlet with all the other dependent variables being extrapolated from the interior. The results of the present study suggest that this is also workable for the URANS simulation of the LM6000 injector flame tube. However, it does not work for the PRNS/VLES simulation due to the unphysical reflections of the pressure disturbances at the outlet boundary. This undesirable situation can be practically alleviated by applying a simple unsteady convection equation for the pressure disturbances at the outlet boundary. The
Javidi Shirvan, Alireza; Choquet, Isabelle; Nilsson, Håkan; Jasak, Hrvoje
2018-01-01
The boundary coupling high-intensity electric arc and refractory cathode is characterized by three sub-layers: the cathode sheath, the Knudsen layer and the pre-sheath. A self-consistent coupling boundary condition accounting for these three sub-layers is presented; its novel property is to take into account a non-uniform distribution of electron emitters on the surface of the refractory cathode. This non-uniformity is due to cathode non-homogeneity induced by arcing. The computational model is applied to a one-dimensional test case to evaluate the validity of different modeling assumptions. It is also applied coupling a thoriated tungsten cathode with an argon plasma (assumed to be in local thermal equilibrium) to compare the calculation results with uniform and non-uniform distribution of the electron emitters to experimental measurements. The results show that the non-uniformity of the electron emitters' distribution has a significant effect on the calculated properties. It leads to good agreement with the cathode surface temperature, and with the plasma temperature in the hottest region. Some differences are observed in colder plasma regions, where deviation from local thermal equilibrium is known to occur.
Zhang, Jialin; Chen, Qian; Li, Jiaji; Zuo, Chao
2017-02-01
The transport of intensity equation (TIE) is a powerful tool for direct quantitative phase retrieval in microscopy imaging. However, there may be some problems when dealing with the boundary condition of the TIE. The previous work introduces a hard-edged aperture to the camera port of the traditional bright field microscope to generate the boundary signal for the TIE solver. Under this Neumann boundary condition, we can obtain the quantitative phase without any assumption or prior knowledge about the test object and the setup. In this paper, we will demonstrate the effectiveness of this method based on some experiments in practice. The micro lens array will be used for the comparison of two TIE solvers results based on introducing the aperture or not and this accurate quantitative phase imaging technique allows measuring cell dry mass which is used in biology to follow cell cycle, to investigate cell metabolism, or to address effects of drugs.
Energy Technology Data Exchange (ETDEWEB)
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Rahimi, Mohammad; Karimi-Varzaneh, Hossein Ali; Böhm, Michael C; Müller-Plathe, Florian; Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul
2011-04-21
A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.
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Huimin Liu
2017-01-01
Full Text Available This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.
Lee, Man
2012-02-22
A microchannel heat sink, integrated with pressure and temperature microsensors, is utilized to study single-phase liquid flow forced convection under a uniform heat flux boundary condition. Utilizing a waferbond-and-etch- back technology, the heat source, temperature and pressure sensors are encapsulated in a thin composite membrane capping the microchannels, thus allowing experimentally good control of the thermal boundary conditions. A three-dimensional physical model has been constructed to facilitate numerical simulations of the heat flux distribution. The results indicate that upstream the cold working fluid absorbs heat, while, within the current operating conditions, downstream the warmer working fluid releases heat. The Nusselt number is computed numerically and compared with experimental and analytical results. The wall Nusselt number in a microchannel can be estimated using classical analytical solutions only over a limited range of the Reynolds number, Re: both the top and bottom Nusselt numbers approach 4 for Re < 1, while the top and bottom Nusselt numbers approach 0 and 5.3, respectively, for Re > 100. The experimentally estimated Nusselt number for forced convection is highly sensitive to the location of the temperature measurements used in calculating the Nusselt number. © 2012 IOP Publishing Ltd.
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Yanmei Sun
2012-01-01
Full Text Available By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.
Thermal advantage of tracking solar collectors under Danish weather conditions
DEFF Research Database (Denmark)
Andersen, Elsa; Dragsted, Janne; Furbo, Simon
2010-01-01
Theoretical investigations have been carried out with the aim to elucidate the thermal advantage of tracking solar collectors for different weather conditions in Kgs. Lyngby, Denmark (55.8°N), and for the weather conditions in Sisimiut, Greenland (66.9°N), just north of the arctic circle....... The investigations are based on calculations with a newly developed program. Measured weather data from a solar radiation measurement station at Technical University of Denmark in Kgs. Lyngby Denmark in the period 1990 to 2002 and the Danish Design Reference Year, DRY data file are used in the investigations....... The weather data used for Sisimiut are based on a Test Reference Year, TRY weather data file. The thermal advantages of different tracking strategies is investigated for two flat plate solar collectors with different efficiencies, operated at different temperature levels. The investigations show...
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Thomas von Larcher
2015-01-01
Full Text Available We present results of numerical simulations of baroclinic driven flows in the thermally driven rotating annulus using the immersed boundary method for modeling of the boundary conditions. The Navier-Stokes equations in the Boussinesq approximation are solved in the Eulerian flux-form advection scheme with the geophysical flow solver EULAG as numerical framework. We test our approach against results of an appropriate laboratory experiment with water as working fluid and directly aim at the wavy flow regime where complex flows and regular wave patterns are generally observed but where centrifugal effects and turbulence is of minor importance. Multivariate statistical methods are used for analyzing time series of computed temperature data. We, here, present the outcome of the time series data analysis at particular parameter points, and specifically analyze a complex wave-wave interaction, and, secondly, a wave mode switch where the azimuthal wave number changes to the next higher one. The numerical results are highly consistent with the experimental observations. That encourage us to focus on our actual goal as the next step, that is the irregular flow regime found at large rotation rates where the centrifugal force has an increasing effect on flow states and where multiple scale flows are generally observed.
On the strongly damped wave equation and the heat equation with mixed boundary conditions
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Aloisio F. Neves
2000-01-01
Full Text Available We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
DEFF Research Database (Denmark)
Andersen, Michael; Abel, Sarah Maria Niebe; Erleben, Kenny
2017-01-01
We address the task of computing solutions for a separating fluid-solid wall boundary condition model. We present an embarrassingly parallel, easy to implement, fluid LCP solver.We are able to use greater domain sizes than previous works have shown, due to our new solver. The solver exploits matrix...
On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population
Boulanouar, Mohamed
2013-04-01
In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.
Notes on wave theory in heat conduction: a new boundary condition.
Kronberg, Alexandre E.; Benneker, A.H.; Benneker, A.H.; Westerterp, K.R.
1997-01-01
The physical basis behind the simple hyperbolic heat transport model is discussed. The model equations are interpreted as energy equations for a system in a state of local nonequilibrium. On this basis a new boundary condition for the hyperbolic model is proposed when the temperature of a surface is
DEFF Research Database (Denmark)
Janssen, Hans; Blocken, Bert; Roels, Staf
2007-01-01
While the numerical simulation of moisture transfer inside building components is currently undergoing standardisation, the modelling of the atmospheric boundary conditions has received far less attention. This article analyses the modelling of the wind-driven-rain load on building facades by par...
Boundary lubrication by brushed salivary conditioning films and their degree of glycosylation
Veeregowda, Deepak H; van der Mei, Henderina; de Vries, Jacob; Rutland, Mark W; Valle-Delgado, Juan J; Sharma, Prashant K; Busscher, Hendrik
2012-01-01
Toothbrushing, though aimed at biofilm removal, also affects the lubricative function of adsorbed salivary conditioning films (SCFs). Different modes of brushing (manual, powered, rotary-oscillatory or sonically driven) influence the SCF in different ways. Our objectives were to compare boundary
OpenCL-Based FPGA Accelerator for 3D FDTD with Periodic and Absorbing Boundary Conditions
Directory of Open Access Journals (Sweden)
Hasitha Muthumala Waidyasooriya
2017-01-01
Full Text Available Finite difference time domain (FDTD method is a very poplar way of numerically solving partial differential equations. FDTD has a low operational intensity so that the performances in CPUs and GPUs are often restricted by the memory bandwidth. Recently, deeply pipelined FPGA accelerators have shown a lot of success by exploiting streaming data flows in FDTD computation. In spite of this success, many FPGA accelerators are not suitable for real-world applications that contain complex boundary conditions. Boundary conditions break the regularity of the data flow, so that the performances are significantly reduced. This paper proposes an FPGA accelerator that computes commonly used absorbing and periodic boundary conditions in many 3D FDTD applications. Accelerator is designed using a “C-like” programming language called OpenCL (open computing language. As a result, the proposed accelerator can be customized easily by changing the software code. According to the experimental results, we achieved over 3.3 times and 1.5 times higher processing speed compared to the CPUs and GPUs, respectively. Moreover, the proposed accelerator is more than 14 times faster compared to the recently proposed FPGA accelerators that are capable of handling complex boundary conditions.
Application of impedance boundary conditions to numerical solution of corrugated circular horns
DEFF Research Database (Denmark)
Iskander, K; Shafai, L; Frandsen, Aksel
1982-01-01
An integral equation method is used to formulate the problem of scattering by rotationally symmetric horn antennas. The excitation is assumed to be due to an infinitesimal dipole antenna, while the secondary field is obtained by assuming anisotropic impedance boundary conditions on the horn surface...
Directory of Open Access Journals (Sweden)
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
DEFF Research Database (Denmark)
Madsen, Søren; Pinna, Rodney; Randolph, M. F.
2015-01-01
of large-diameter bucket foundations. Since shell structures are generally sensitive to initially imperfect geometries, eigenmode-affine imperfections are introduced in a nonlinear finite-element analysis. The influence of modelling the real lid structure compared to classic boundary conditions...
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Shayma Adil Murad
2011-01-01
Full Text Available We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
An inherently stable boundary-condition-transfer algorithm for muffler analysis
Kar, T.; Munjal, M. L.
2005-07-01
Wave coupling exists in the wave propagation in multiple interacting ducts within a waveguide. One may use the segmentation approach, decoupling approach, eigenvalue approach, or the matrizant approach to derive the overall transfer matrix for the muffler section with interacting ducts, and then apply the terminal boundary conditions to obtain a two-by-two transfer matrix. In such instances, a boundary condition applied to a vector is given as a linear combination of its components. Spatial dimensions along with parameters like impedance of the perforated interface may yield numerical instability during computation leading to inaccurate prediction of the acoustic performance of mufflers. Here, an inherently stable boundary-condition-transfer approach is discussed to analyze the plane wave propagation in suchlike mufflers and applied to waveguides of variable cross-sectional area. The concept of pseudo boundary conditions applied to the state vector at an intermediate point is outlined. The method is checked for self-consistency and shown to be stable even for extreme geometries.
Directory of Open Access Journals (Sweden)
Charyyar Ashyralyyev
2015-07-01
Full Text Available This article studies the numerical solution of inverse problems for the multidimensional elliptic equation with Dirichlet-Neumann boundary conditions and Neumann type overdetermination. We present first and second order accuracy difference schemes. The stability and almost coercive stability inequalities for the solution are obtained. Numerical examples with explanation on the implementation illustrate the theoretical results.
Nonlinear parabolic problems with Neumann-type boundary conditions and L^1-data
Directory of Open Access Journals (Sweden)
Abderrahmane El Hachimi
2007-11-01
$$ \\frac{\\partial u}{\\partial t}-\\triangle_{p}u+\\alpha(u=f \\quad \\text{in } ]0,\\ T[\\times\\Omega, $$ with Neumann-type boundary conditions and initial data in $L^1$. Our approach is based essentially on the time discretization technique by Euler forward scheme.
Nonlinear Fredholm alternative for the p-Laplacian under nonhomogeneous Neumann boundary condition
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Gustavo Ferron Madeira
2016-08-01
Full Text Available The nonlinear Fredholm alternative for the p-Laplacian in higher dimensions is established when nonhomogeneous terms appear in the equation and in the Neumann boundary condition. Further, the geometry of the associated energy functional is described and compared with the Dirichlet counterpart. The proofs require only variational methods.
Menges, J.; Walter, F.; Vogel, B.; Bruch, H.
2011-01-01
Transformational leadership (TFL) climate describes the degree to which leaders throughout an organization engage in TFL behaviors. In this study, we investigate performance linkages, mechanisms, and boundary conditions of TFL climate at the organizational level of analysis. In a sample of 158
Directory of Open Access Journals (Sweden)
Valery Romanovski
2008-12-01
Full Text Available We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Boundary conditions for the use of personal ventilation over mixing ventilation in open plan offices
DEFF Research Database (Denmark)
Petersen, Steffen; Hviid, Christian Anker
2013-01-01
This paper investigates the boundary conditions for choosing a combined Personal Ventilation (PV) and Mixing Ventilation (MV) over conventional mixing ventilation in an office with multiple workers. A simplified procedure for annual performance assessment of PV/MV systems in terms of air quality,...
On The Stabilization of the Linear Kawahara Equation with Periodic Boundary Conditions
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Patricia N. da Silva
2015-03-01
Full Text Available We study the stabilization of global solutions of the linear Kawahara equation (K with periodic boundary conditions under the effect of a localized damping mechanism. The Kawahara equation is a model for small amplitude long waves. Using separation of variables, the Ingham inequality, multiplier techniques and compactness arguments we prove the exponential decay of the solutions of the (K model.
Optimal trajectory generation for generalization of discrete movements with boundary condition
DEFF Research Database (Denmark)
Herzog, Sebastian; Wörgötter, Florentin; Kulvicius, Tomas
2016-01-01
Trajectory generation methods play an important role in robotics since they are essential for the execution of actions. In this paper we present a novel trajectory generation method for generalization of accurate movements with boundary conditions. Our approach originates from optimal control the...
Semilinear Evolution Problems with Ventcel-Type Conditions on Fractal Boundaries
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Maria Rosaria Lancia
2014-01-01
Full Text Available A semilinear parabolic transmission problem with Ventcel's boundary conditions on a fractal interface S or the corresponding prefractal interface Sh is studied. Regularity results for the solution in both cases are proved. The asymptotic behaviour of the solutions of the approximating problems to the solution of limit fractal problem is analyzed.
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Romanovski Valery
2008-01-01
Full Text Available We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions
DEFF Research Database (Denmark)
Hesthaven, Jan; Gottlieb, D.
1996-01-01
The purpose of this paper is to present asymptotically stable open boundary conditions for the numerical approximation of the compressible Navier-Stokes equations in three spatial dimensions. The treatment uses the conservation form of the Navier-Stokes equations and utilizes linearization...
Grunau, H.-Ch.; Sweers, G.
1995-01-01
Higher order elliptic partial dierential equations with Dirichlet boundary conditions in general do not satisfy a maximum principle. Polyharmonic operators on balls are an exception. Here it is shown that in IR2 small perturbations of polyharmonic operators and of the domain preserve the maximum
Null exact controllability of the parabolic equations with equivalued surface boundary condition
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available This paper is devoted to showing the null exact controllability for a class of parabolic equations with equivalued surface boundary condition. Our method is based on the duality argument and global Carleman-type estimate for a parabolic operator.
In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions
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Xianjie Shi
2014-01-01
Full Text Available In comparison with the out-of-plane vibrations of annular plates, far less attention has been paid to the in-plane vibrations which may also play a vital important role in affecting the sound radiation from and power flows in a built-up structure. In this investigation, a generalized Fourier series method is proposed for the in-plane vibration analysis of annular plates with arbitrary boundary conditions along each of its edges. Regardless of the boundary conditions, the in-plane displacement fields are invariantly expressed as a new form of trigonometric series expansions with a drastically improved convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates and determined using the Rayleigh-Ritz technique. Unlike most of the existing studies, the presented method can be readily and universally applied to a wide spectrum of in-plane vibration problems involving different boundary conditions, varying material, and geometric properties with no need of modifying the basic functions or adapting solution procedures. Several numerical examples are presented to demonstrate the effectiveness and reliability of the current solution for predicting the in-plane vibration characteristics of annular plates subjected to different boundary conditions.
Wijnant, Ysbrand H.; Spiering, R.M.E.J.; Blijderveen, M.; de Boer, Andries
2006-01-01
Previous research has shown that viscothermal wave propagation in narrow gaps can efficiently be described by means of the low reduced frequency model. For simple geometries and boundary conditions, analytical solutions are available. For example, Beltman [4] gives the acoustic pressure in the gap
Evidence for Cretaceous-Paleogene boundary bolide “impact winter” conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
Evidence for Cretaceous-Paleogene boundary bolide "impact winter" conditions from New Jersey, USA
Vellekoop, J.; Esmeray-Senlet, S.; Miller, K.G.; Browning, J.V.; Sluijs, A.; van de Schootbrugge, B.; Sinninghe Damsté, J.S.; Brinkhuis, H.
2016-01-01
Abrupt and short-lived “impact winter” conditions have commonly been implicated as the main mechanism leading to the mass extinction at the Cretaceous-Paleogene (K-Pg) boundary (ca. 66 Ma), marking the end of the reign of the non-avian dinosaurs. However, so far only limited evidence has been
DEFF Research Database (Denmark)
Duggen, Lars; Lopes, Natasha; Willatzen, Morten
2011-01-01
The finite-element method (FEM) is used to simulate the photoacoustic signal in a cylindrical resonant photoacoustic cell. Simulations include loss effects near the cell walls that appear in the boundary conditions for the inhomogeneous Helmholtz equation governing the acoustic pressure. Reasonab...
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Saowaluk Chasreechai
2015-01-01
Full Text Available We study existence and uniqueness results for Caputo fractional sum-difference equations with fractional sum boundary value conditions, by using the Banach contraction principle and Schaefer’s fixed point theorem. Our problem contains different numbers of order in fractional difference and fractional sums. Finally, we present some examples to show the importance of these results.
Damage detection of fatigue cracks under nonlinear boundary condition using subharmonic resonance.
Zhang, Mengyang; Xiao, Li; Qu, Wenzhong; Lu, Ye
2017-05-01
In recent years, the nonlinear ultrasonic technique has been widely utilized for detecting fatigue crack, one of the most common forms of damage. However, one of limitations associated with this technique is that nonlinearities can be produced not only by damage but also by various intrinsic effects such as boundary conditions. The objective of this paper is to demonstrate the application of a nonlinear ultrasonic subharmonic method for detecting fatigue cracks with nonlinear boundary conditions. The fatigue crack was qualitatively modeled as two elastic, frictionless half spaces that enter into contact during vibration and where the contact obeys the basic Hertz contact law. The nonlinear ordinary differential equation drawn from the developed model was solved with the method of multiple scales. The threshold of subharmonic generation was studied. Different threshold behaviors between the nonlinear boundary condition and the fatigue crack were found that can be used to distinguish the source of nonlinear subharmonic features. To evaluate the proposed method, experiments using an aluminum plate with a fatigue crack were conducted to quantitatively verify the subharmonic resonance range. Two surface-bonded piezoelectric transducers were used to generate and receive ultrasonic wave signals. The experimental results demonstrated that the subharmonic component of the sensing signal could be used to detect the fatigue crack and further to distinguish it from inherent nonlinear boundary conditions. Copyright © 2017 Elsevier B.V. All rights reserved.
6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
Fujimoto, Yukihiro; Hasegawa, Kouhei; Nishiwaki, Kenji; Sakamoto, Makoto; Tatsumi, Kentaro
2017-09-01
We classify possible boundary conditions of a 6d Dirac fermion Ψ on a rectangle under the requirement that the 4d Lorentz structure is maintained, and derive the profiles and spectrum of the zero modes and nonzero KK modes under the two specific boundary conditions, (i) 4d-chirality positive components being zero at the boundaries and (ii) internal chirality positive components being zero at the boundaries. In the case of (i), twofold degenerated chiral zero modes appear which are localized towards specific directions of the rectangle pointed by an angle parameter θ. This leads to an implication for a new direction of pursuing the origin of three generations in the matter fields of the standard model, even though triple-degenerated zero modes are not realized in the six dimensions. When such 6d fermions couple with a 6d scalar with a vacuum expectation value, θ contributes to a mass matrix of zero-mode fermions consisting of Yukawa interactions. The emergence of the angle parameter θ originates from a rotational symmetry in the degenerated chiral zero modes on the rectangle extra dimensions since they do not feel the boundaries. In the case of (ii), this rotational symmetry is promoted to the two-dimensional conformal symmetry though no chiral massless zero mode appears. We also discuss the correspondence between our model on a rectangle and orbifold models in some details.
Shishkina, Olga; Wagner, Sebastian; Horn, Susanne
2014-03-01
We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers Pr as functions of the angle β between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we apply the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a nonhorizontal free-stream flow above the viscous boundary layer. Based on our direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection for Pr=0.1, 1, and 10 and moderate Rayleigh numbers up to 108 we evaluate the value of β that is found to be around 0.7π for all investigated cases. Our theoretical predictions for the boundary layer thicknesses for this β and the considered Pr are in good agreement with the DNS results.
DEFF Research Database (Denmark)
Villafruela, J.M.; Olmedo, Inés; Ruiz de Adana, M.
2013-01-01
This paper analyses the dispersion of the exhaled contaminants by humans in indoor environments, with special attention to the exhalation jet and its interaction with the indoor airflow pattern in both mixing and displacement ventilation conditions. The way in which three different numerical...... different environmental conditions and to validate whether a steady boundary condition of the exhalation flow may simulate human breathing in an effective and accurate way. The results show a very good agreement of the numerical results obtained for Test a and the experimental data. This fact confirms...... the use of numerical simulation as a powerful tool to predict the contaminant distribution exhaled by a human. The numerical tests with steady boundary conditions for the exhalation flow require a transitory resolution procedure and the predictions provided by these models display some discrepancies...
On a third order parabolic equation with a nonlocal boundary condition
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Abdelfatah Bouziani
2000-01-01
Full Text Available In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.
Tao, Lei; Theruvakkattil Sreenivasan, Sreeprasad; Shahsavari, Rouzbeh
2017-01-11
Improving heat transfer in hybrid nano/microelectronic systems is a challenge, mainly due to the high thermal boundary resistance (TBR) across the interface. Herein, we focus on gallium nitride (GaN)/diamond interface-as a model system with various high power, high temperature, and optoelectronic applications-and perform extensive reverse nonequilibrium molecular dynamics simulations, decoding the interplay between the pillar length, size, shape, hierarchy, density, arrangement, system size, and the interfacial heat transfer mechanisms to substantially reduce TBR in GaN-on-diamond devices. We found that changing the conventional planar interface to nanoengineered, interlaced architecture with optimal geometry results in >80% reduction in TBR. Moreover, introduction of conformal graphene buffer layer further reduces the TBR by ∼33%. Our findings demonstrate that the enhanced generation of intermediate frequency phonons activates the dominant group velocities, resulting in reduced TBR. This work has important implications on experimental studies, opening up a new space for engineering hybrid nano/microelectronics.
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Mohd Hafizi Mat Yasin
2013-01-01
Full Text Available We present the numerical investigation of the steady mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium saturated by a nanofluid. The governing partial differential equations are reduced to the ordinary differential equations, using the similarity transformations. The similarity equations are solved numerically for three types of metallic or nonmetallic nanoparticles, namely, copper (Cu, alumina (Al2O3, and titania (TiO2, in a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter φ of the nanofluid on the flow and heat transfer characteristics. The skin friction coefficient and the velocity and temperature profiles are presented and discussed.
Adesanya, S. O.; Oluwadare, E. O.; Falade, J. A.; Makinde, O. D.
2015-12-01
In this paper, the free convective flow of magnetohydrodynamic fluid through a channel with time periodic boundary condition is investigated by taking the effects of Joule dissipation into consideration. Based on simplifying assumptions, the coupled governing equations are reduced to a set of nonlinear boundary valued problem. Approximate solutions are obtained by using semi-analytical Adomian decomposition method. The effect of pertinent parameters on the fluid velocity, temperature distribution, Nusselt number and skin friction are presented graphically and discussed. The result of the computation shows that an increase in the magnetic field intensity has significant influence on the fluid flow.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
POSITIVE SOLUTIONS OF A NONLINEAR THREE-POINT EIGENVALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS
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FAOUZI HADDOUCHI
2015-11-01
Full Text Available In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP for the following second-order differential equation u''(t + \\lambda a(tf(u(t = 0; 0 0 is a parameter, 0 <\\eta < 1, 0 <\\alpha < 1/{\\eta}. . By using the properties of the Green's function and Krasnoselskii's fixed point theorem on cones, the eigenvalue intervals of the nonlinear boundary value problem are considered, some sufficient conditions for the existence of at least one positive solutions are established.
Latyshev, A. V.; Yushkanov, A. A.
2013-03-01
The second Stokes problem concerning the behavior of a rarefied gas in the half-space bounded over a plate undergoing harmonic in-plane oscillations is solved analytically using the Bhat-nagar-Gross-Krook equation with Cercignani boundary conditions for gas molecules reflecting from the wall. The distribution function of the gas molecules is constructed. The gas velocity in the half-space and near the wall, the drag force exerted by the gas on the boundary, and the energy dissipation rate per unit area of the oscillating plate are found.
Energy Technology Data Exchange (ETDEWEB)
Sarkadi, Peter; Schaffrath, Andreas [TUeV NORD SysTec GmbH und Co. KG, Hamburg (Germany)
2009-07-01
In the frame of a PWR reactor safety analysis the TUEV Nord Sys Tec GmbH has analyzed the plant behavior in case of a steam generator tube leakage using the thermal hydraulic code ATHLET and realistic initial and boundary conditions. The aim of the analysis was to show that the response of the emergency cooling criteria including the activation of safety injection pumps can be avoided. The Activation of the safety injection pumps could jeopardize the activity retention.
Green's Function for Discrete Second-Order Problems with Nonlocal Boundary Conditions
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Roman Svetlana
2011-01-01
Full Text Available We investigate a second-order discrete problem with two additional conditions which are described by a pair of linearly independent linear functionals. We have found the solution to this problem and presented a formula and the existence condition of Green's function if the general solution of a homogeneous equation is known. We have obtained the relation between two Green's functions of two nonhomogeneous problems. It allows us to find Green's function for the same equation but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.
Kosaka, Atsushi
2012-01-01
We consider a positive solution of the Emden equation with the critical Sobolev exponent on a geodesic ball in S3. In the case of the Dirichlet boundary condition, Bandle and Peletier [2] proved the precise result on the existence of a positive radial solution. We investigate the same equation with the third kind boundary condition and obtain a more general result. Namely we prove that the existence and the nonexistence of solutions depend on the geodesic radius and the boundary condition. Mo...
Zhu, Dongming; Miller, Robert A.
1999-01-01
Laser high heat flux test approaches have been established to obtain critical properties of ceramic thermal barrier coatings (TBCs) under near-realistic temperature and thermal gradients that may he encountered in advanced engine systems. Thermal conductivity change kinetics of a thin ceramic coating were continuously monitored in real time at various test temperatures. A significant thermal conductivity increase was observed during the laser simulated engine heat flux tests. For a 0.25 mm thick ZrO2-8%Y2O3 coating system, the overall thermal conductivity increased from the initial value of 1.0 W/m-K to 1. 15 W/m-K, 1. 19 W/m-K and 1.5 W/m-K after 30 hour testing at surface temperatures of 990C, 1100C, and 1320C. respectively. Hardness and modulus gradients across a 1.5 mm thick TBC system were also determined as a function of laser testing time using the laser sintering/creep and micro-indentation techniques. The coating Knoop hardness values increased from the initial hardness value of 4 GPa to 5 GPa near the ceramic/bond coat interface, and to 7.5 GPa at the ceramic coating surface after 120 hour testing. The ceramic surface modulus increased from an initial value of about 70 GPa to a final value of 125 GPa. The increase in thermal conductivity and the evolution of significant hardness and modulus gradients in the TBC systems are attributed to sintering-induced micro-porosity gradients under the laser-imposed high thermal gradient conditions. The test techniques provide a viable means for obtaining coating data for use in design, development, stress modeling, and life prediction for various thermal barrier coating applications.
Effect of boundary conditions on magnetocapacitance effect in a ring-type magnetoelectric structure
Zhang, Juanjuan
2017-12-01
By considering the nonlinear magneto-elastic coupling relationships of magnetostrictive materials, an analytical model is proposed. The resonance frequencies can be accurately predicted by this theoretical model, and they are in good agreement with experimental data. Subsequently, the magnetocapacitance effect in a ring-type magnetoelectric (ME) structure with different boundary conditions is investigated, and it is found that various mechanical boundaries, the frequency, the magnetic field, the geometric size, and the interface bonding significantly affect the capacitance of the ME structure. Further, additional resonance frequencies can be predicted by considering appropriate imperfect interface bonding. Finally, the influence of an external force on the capacitance is studied. The result shows that an external force on the boundary changes the capacitance, but has only a weak influence on the resonance frequency.
Moment-based boundary conditions for lattice Boltzmann simulations of natural convection in cavities
Allen, Rebecca
2016-06-29
We study a multiple relaxation time lattice Boltzmann model for natural convection with moment-based boundary conditions. The unknown primary variables of the algorithm at a boundary are found by imposing conditions directly upon hydrodynamic moments, which are then translated into conditions for the discrete velocity distribution functions. The method is formulated so that it is consistent with the second order implementation of the discrete velocity Boltzmann equations for fluid flow and temperature. Natural convection in square cavities is studied for Rayleigh numbers ranging from 103 to 108. An excellent agreement with benchmark data is observed and the flow fields are shown to converge with second order accuracy. Copyright © 2016 Inderscience Enterprises Ltd.
Pfeiffer, M.; Munz, C.-D.; Fasoulas, S.
2015-08-01
In a numerical solution of the Maxwell-Vlasov system, the consistency with the charge conservation and divergence conditions has to be kept solving the hyperbolic evolution equations of the Maxwell system, since the vector identity ∇ ṡ (∇ × u →) = 0 and/or the charge conservation of moving particles may be not satisfied completely due to discretization errors. One possible method to force the consistency is the hyperbolic divergence cleaning. This hyperbolic constraint formulation of Maxwell's equations has been proposed previously, coupling the divergence conditions to the hyperbolic evolution equations, which can then be treated with the same numerical method. We pick up this method again and show that electrostatic limit may be obtained by accentuating the divergence cleaning sub-system and converging to steady state. Hence, the electrostatic case can be treated by the electrodynamic code with reduced computational effort. In addition, potential boundary conditions as often given in practical applications can be coupled in a similar way to get appropriate boundary conditions for the field equations. Numerical results are shown for an electric dipole, a parallel-plate capacitor, and a Langmuir wave. The use of potential boundary conditions is demonstrated in an Einzel lens simulation.
Characterisation of net type thermal insulators at 1.8 K low boundary temperature
Peón-Hernández, G; Szeless, Balázs
1997-01-01
The Large Hadron Collider's superconducting magnets are cooled by superfluid helium at 1.8 K and housed in cryostats that minimise the heat inleak to this temperature level by extracting heat at 70 and 5 K. In the first generation of prototype cryostats, the radiative heat to the 1.8 K temperature level accounted for 70 % of the total heat inleak. An alternative to enhance the cryostat thermal performance incorporates a thermalised radiation screen at 5 K. In order to avoid contact between the 5 K radiation screen and the cold mass, insulators are placed between both surfaces. Sets of commercial fibre glass nets are insulator candidates to minimise the heat inleak caused by a accidental contact between the two temperature levels. A model to estimate their performance is presented. A set-up to thermally characterise them has been designed and is also described in the paper. Finally, results as a function of the number of the spacer nets, the boundary temperatures and the compressive force in the spacer are pre...
Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid
2014-01-01
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.
Ramesh, K.
2017-07-01
In the current article, we have discussed the Poiseuille flow of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium using slip boundary conditions under the effect of heat transfer. The equations governing the fluid flow are modeled in Cartesian coordinate system. The energy equation is considered under the effects viscous dissipation and heat generation. Analytical solutions for the velocity and temperature profiles are obtained. The effects of the various involved parameters on the velocity and temperature profiles are studied and the results are presented through the graphs. It is observed from our analysis that, with increase of slip parameter and pressure gradient increase the velocity. The temperature is an increasing function of heat generation parameter, Brinkman number, thermal slip parameter and non-Newtonian fluid parameter.
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A. Kamran
Full Text Available A numerical study of Casson nanofluid past horizontal stretching surface with magnetic effect and Joule heating are presented. Slip and thermal convective boundary conditions are considered in the study. A numerical technique of Keller box is applied to the nonlinear ODEs which are obtained by applying the similarity transformation to the nonlinear partial differential equations. The magnetic field and Joule heating effects are observed graphically. Also the strength of convective heat exchange (Nusselt number and the strength of mass exchange (Sherwood number are analyzed. It is noted that Nusselt number declines whereas Sherwood number rises by increasing Eckert number. The impact of increasing Hartman number resulted in the decrease of both Sherwood and Nusselt number. Keywords: Casson nanofluid, Magnetohydrodynamic, Joule heating, Keller box method
Thermal shock behaviour of different tungsten grades under varying conditions
Energy Technology Data Exchange (ETDEWEB)
Wirtz, Oliver Marius
2012-07-19
Thermonuclear fusion power plants are a promising option to ensure the energy supply for future generations, but in many fields of research enormous challenges have to be faced. A major step on the way to the prototype fusion reactor DEMO will be ITER which is build in Cadarache, southern France. One of the most critical issues is the field of in-vessel materials and components, in particular the plasma facing materials (PFM). PFMs that will be used in a device like ITER have to withstand severe environmental conditions in terms of steady state and transient thermal loads as well as high particle fluxes such as hydrogen, helium and neutrons. Candidate wall materials are beryllium, tungsten and carbon based materials like CFC (carbon fibre composite). Tungsten is the most promising material for an application in the divertor region with very severe loading conditions and it will most probably also be used as PFM for DEMO. Hence, this work focuses on the investigation of the thermal shock response of different tungsten grades in order to understand the damage mechanisms and to identify material parameters which influence this behaviour under ITER and DEMO relevant operation conditions. Therefore the microstructure and the mechanical and thermal properties of five industrially manufactured tungsten grades were characterised. All five tungsten grades were exposed to transient thermal events with very high power densities of up to 1.27 GWm{sup -2} at varying base temperatures between RT and 600 C in the electron beam device JUDITH 1. The pulse numbers were limited to a maximum of 1000 in order to avoid immoderate workload on the test facility and to have enough time to cover a wide range of loading conditions. The results of this damage mapping enable to define different damage and cracking thresholds for the investigated tungsten grades and to identify certain material parameters which influence the location of these thresholds and the distinction of the induced
Gatsonis, Nikolaos A.; Chamberlin, Ryan E.; Averkin, Sergey N.
2013-01-01
The mathematical and computational aspects of the direct simulation Monte Carlo on unstructured tetrahedral grids (U3DSMC) with a Kinetic-Moment (KM) boundary conditions method are presented. The algorithms for particle injection, particle loading, particle motion, and particle tracking are presented. The KM method applicable to a subsonic or supersonic inflow/outflow boundary, couples kinetic (particle) U3DSMC properties with fluid (moment) properties. The KM method obtains the number density, temperature and mean velocity needed to define the equilibrium, drifting Maxwellian distribution at a boundary. The moment component of KM is based on the local one dimensional inviscid (LODI) boundary conditions method consistent with the 5-moment compressible Euler equations. The kinetic component of KM is based on U3DSMC for interior properties and the equilibrium drifting Maxwellian at the boundary. The KM method is supplemented with a time-averaging procedure, allows for choices in sampling-cell procedures, minimizes fluctuations and accelerates the convergence in subsonic flows. Collision sampling in U3DSMC implements the no-time-counter method and includes elastic and inelastic collisions. The U3DSMC with KM boundary conditions is validated and verified extensively with simulations of subsonic nitrogen flows in a cylindrical tube with imposed inlet pressure and density and imposed outlet pressure. The simulations cover the regime from slip to free-molecular with inlet Knudsen numbers between 0.183 and 18.27 and resulting inlet Mach numbers between 0.037 and 0.027. The pressure and velocity profiles from U3DSMC-KM simulations are compared with analytical solutions obtained from first-order and second-order slip boundary conditions. Mass flow rates from U3DSMC-KM are compared with validated analytical solutions for the entire Knudsen number regime considered. Error and sensitivity analysis is performed and numerical fractional errors are in agreement with theoretical
Conditions for the appearance of boundary modes in topological phases of Heisenberg spin ladders
Robinson, Neil; Atland, Alexander; Egger, Reinhold; Gergs, Nkilas; Konik, Robert; Li, Wei; Schuricht, Dirk; Tsvelik, Alexei; Weichselbaum, Andreas
We consider the problem of delineating the necessary conditions for the appearance of boundary modes in extended SU (2) Heisenberg spin ladders. Specifically, we study Heisenberg ladders with rung exchange, J⊥, and ring exchange, JX, that admit a field theoretic description in terms of Majorana fermions in the continuum limit. In this description there are four Majorana fermions, arranged in a triplet and a singlet. This suggests there are four distinct phases, corresponding to the configurations of the signs of the triplet mt and singlet ms masses. We label these phases as: Haldane (mt > 0 ,ms 0), VBS+ (mt ,ms > 0) and VBS- (mt ,ms VBS+ phase, where all the Majorana fermions have gapless boundary modes. The absence of a gapless boundary mode in the rung singlet phase is surprising; we find that the singlet mode can become gapless if open boundary conditions are replaced with a continuous change in lattice parameters. We suggest a symmetry-allowed modification to the low-energy effective theory which may be responsible for this behavior.
Air Quality and Meteorological Boundary Conditions during the MCMA-2003 Field Campaign
Sosa, G.; Arriaga, J.; Vega, E.; Magaña, V.; Caetano, E.; de Foy, B.; Molina, L. T.; Molina, M. J.; Ramos, R.; Retama, A.; Zaragoza, J.; Martínez, A. P.; Márquez, C.; Cárdenas, B.; Lamb, B.; Velasco, E.; Allwine, E.; Pressley, S.; Westberg, H.; Reyes, R.
2004-12-01
A comprehensive field campaign to characterize photochemical smog in the Mexico City Metropolitan Area (MCMA) was conducted during April 2003. An important number of equipment was deployed all around the urban core and its surroundings to measure gas and particles composition from the various sources and receptor sites. In addition to air quality measurements, meteorology variables were also taken by regular weather meteorological stations, tethered balloons, radiosondes, sodars and lidars. One important issue with regard to the field campaign was the characterization of the boundary conditions in order to feed meteorological and air quality models. Four boundary sites were selected to measure continuously criteria pollutants, VOC and meteorological variables at surface level. Vertical meteorological profiles were measured at three other sites : radiosondes in Tacubaya site were launched every six hours daily; tethered balloons were launched at CENICA and FES-Cuautitlan sites according to the weather conditions, and one sodar was deployed at UNAM site in the south of the city. Additionally to these measurements, two fixed meteorological monitoring networks deployed along the city were available to complement these measurements. In general, we observed that transport of pollutants from the city to the boundary sites changes every day, according to the coupling between synoptic and local winds. This effect were less important at elevated sites such as Cerro de la Catedral and ININ, where synoptic wind were more dominant during the field campaign. Also, local sources nearby boundary sites hide the influence of pollution coming from the city some days, particularly at the La Reforma site.
Kyncl, Martin; Pelant, Jaroslav
We work with the system of partial differential equations describing the non-stationary compressible turbulent fluid flow. It is a characteristic feature of the hyperbolic equations, that there is a possible raise of discontinuities in solutions, even in the case when the initial conditions are smooth. The fundamental problem in this area is the solution of the so-called Riemann problem for the split Euler equations. It is the elementary problem of the one-dimensional conservation laws with the given initial conditions (LIC - left-hand side, and RIC - right-hand side). The solution of this problem is required in many numerical methods dealing with the 2D/3D fluid flow. The exact (entropy weak) solution of this hyperbolical problem cannot be expressed in a closed form, and has to be computed by an iterative process (to given accuracy), therefore various approximations of this solution are being used. The complicated Riemann problem has to be further modified at the close vicinity of boundary, where the LIC is given, while the RIC is not known. Usually, this boundary problem is being linearized, or roughly approximated. The inaccuracies implied by these simplifications may be small, but these have a huge impact on the solution in the whole studied area, especially for the non-stationary flow. Using the thorough analysis of the Riemann problem we show, that the RIC for the local problem can be partially replaced by the suitable complementary conditions. We suggest such complementary conditions accordingly to the desired preference. This way it is possible to construct the boundary conditions by the preference of total values, by preference of pressure, velocity, mass flow, temperature. Further, using the suitable complementary conditions, it is possible to simulate the flow in the vicinity of the diffusible barrier. On the contrary to the initial-value Riemann problem, the solution of such modified problems can be written in the closed form for some cases. Moreover
DEFF Research Database (Denmark)
Steskens, Paul Wilhelmus Maria Hermanus; Rode, Carsten; Janssen, Hans
2008-01-01
Current models to predict heat, air and moisture (HAM) conditions in building components assume uniform boundary conditions, both for the temperature and relative humidity of the air in an indoor space as well as for the surface transfer coefficients. Such models cannot accurately predict the HAM...... conditions in the component and on the surface of the component with non-uniform air temperature or relative humidity distributions in an indoor space. Moreover, the heat and moisture surface transfer coefficients strongly depend on the local air velocity, local temperature, water-material interactions...... and water content at the material surface and surface texture of the material. The objective of the present paper is to analyze the influence of the non-uniform local air velocity near the surface of a building component on the HAM conditions in the component. A case study and sensitivity study have been...
DEFF Research Database (Denmark)
Escolano-Carrasco, José; Jacobsen, Finn; López, J.J.
2008-01-01
The finite-difference time-domain (FDTD) method provides a simple and accurate way of solving initial boundary value problems. However, most acoustic problems involve frequency dependent boundary conditions, and it is not easy to include such boundary conditions in an FDTD model. Although solutions...... to this problem exist, most of them have high computational costs, and stability cannot always be ensured. In this work, a solution is proposed based on "mixing modelling strategies"; this involves separating the FDTD mesh and the boundary conditions (a digital filter representation of the impedance...
Transition of MHD kink-stability properties between line-tied and non-line-tied boundary conditions.
Sun, X; Intrator, T P; Dorf, L; Furno, I; Lapenta, G
2008-05-23
Magnetic flux tubes or flux ropes in plasmas are important in nature and the laboratory. Axial boundary conditions strongly affect flux rope behavior, but this has never been systematically investigated. We experimentally demonstrate for the first time axial boundary conditions that are continuously varied between ideal magnetohydrodynamic (MHD) line-tied (fixed) and non-line-tied (free). In contrast with the usual interpretation that mechanical plasma motion is MHD line-tied to a conducting boundary, we constrain boundary plasma motion to cause the line-tied condition.
Directory of Open Access Journals (Sweden)
Tristan A Bekinschtein
2011-12-01
Full Text Available Classical (trace conditioning is a specific variant of associative learning in which a neutral stimulus leads to the subsequent prediction of an emotionally charged or noxious stimulus after a temporal gap. When conditioning is concurrent with a distraction task, only participants who can report the relationship (the contingency between stimuli explicitly show associative learning. This suggests that consciousness is a prerequisite for trace conditioning. We review and question three main controversies concerning this view. Firstly, virtually all animals, even invertebrate sea slugs, show this type of learning; secondly, unconsciously perceived stimuli may elicit trace conditioning; and thirdly, some vegetative state patients show trace learning. We discuss and analyze these seemingly contradictory arguments to find the theoretical boundaries of consciousness in classical conditioning. We conclude that trace conditioning remains one of the best measures to test conscious processing in the absence of explicit reports.
INDOOR THERMAL CONDITION OF FACTORY BUILDING IN BANGLADESH
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Muhammed Abdullah Al Sayem Khan
2011-12-01
Full Text Available Bangladesh is a developing country and has a lot of factories for different products for local use and also export to abroad. Garments industries are one of the top most items of exported items. A huge number of populations are working in garments industries. But these factories are not well designed in sense of the thermal environment. Workers experiences sickness related to indoor environment. The productions of these factories are affected due to employees’ health condition. The research is done in two different methods. One is empirical data collection using thermal data loggers and the other is questionnaire survey on the spots for three factory buildings. The field study was conducted in four different months of the same year during winter and summer period. Expected findings of this research are that the indoor environment is not comfortable for works at day time during summer season. This research will help the factory workers in providing a comfortable thermal environment and also help the employers or factory owners to increase their production margin.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses...
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses are app...
Lattice QCD with open boundary conditions and twisted-mass reweighting
Lüscher, Martin
2013-01-01
Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into instabilities triggered by accidental near-zero modes of the lattice Dirac operator. As already noted in ref. [1], the first problem is bypassed if open boundary conditions are imposed in the time direction, while the second can potentially be overcome through twisted-mass determinant reweighting [2]. In this paper, we show that twisted-mass reweighting works out as expected in QCD with open boundary conditions and 2+1 flavours of O(a) improved Wilson quarks. Further algorithmic improvements are tested as well and a few physical quantities are computed for illustration.
Performance advantages of CPML over UPML absorbing boundary conditions in FDTD algorithm
Gvozdic, Branko D.; Djurdjevic, Dusan Z.
2017-01-01
Implementation of absorbing boundary condition (ABC) has a very important role in simulation performance and accuracy in finite difference time domain (FDTD) method. The perfectly matched layer (PML) is the most efficient type of ABC. The aim of this paper is to give detailed insight in and discussion of boundary conditions and hence to simplify the choice of PML used for termination of computational domain in FDTD method. In particular, we demonstrate that using the convolutional PML (CPML) has significant advantages in terms of implementation in FDTD method and reducing computer resources than using uniaxial PML (UPML). An extensive number of numerical experiments has been performed and results have shown that CPML is more efficient in electromagnetic waves absorption. Numerical code is prepared, several problems are analyzed and relative error is calculated and presented.
Reflected forward-backward SDEs and obstacle problems with boundary conditions
Directory of Open Access Journals (Sweden)
Jin Ma
2001-01-01
Full Text Available In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short. More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved.......Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
A Monte Carlo method for solving the one-dimensional telegraph equations with boundary conditions
Acebrón, Juan A.; Ribeiro, Marco A.
2016-01-01
A Monte Carlo algorithm is derived to solve the one-dimensional telegraph equations in a bounded domain subject to resistive and non-resistive boundary conditions. The proposed numerical scheme is more efficient than the classical Kac's theory because it does not require the discretization of time. The algorithm has been validated by comparing the results obtained with theory and the Finite-difference time domain (FDTD) method for a typical two-wire transmission line terminated at both ends with general boundary conditions. We have also tested transmission line heterogeneities to account for wave propagation in multiple media. The algorithm is inherently parallel, since it is based on Monte Carlo simulations, and does not suffer from the numerical dispersion and dissipation issues that arise in finite difference-based numerical schemes on a lossy medium. This allowed us to develop an efficient numerical method, capable of outperforming the classical FDTD method for large scale problems and high frequency signals.
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Zhang Sheng
2016-01-01
Full Text Available In this paper, variable separation method combined with the properties of Mittag-Leffler function is used to solve a variable-coefficient time fractional advection-dispersion equation with initial and boundary conditions. As a result, a explicit exact solution is obtained. It is shown that the variable separation method can provide a useful mathematical tool for solving the time fractional heat transfer equations.
Czech Academy of Sciences Publication Activity Database
Haslinger, Jaroslav; Kučera, R.; Šátek, V.
2017-01-01
Roč. 22, October 2017 (2017), s. 1-14 ISSN 1081-2865 R&D Projects: GA MŠk LQ1602; GA ČR(CZ) GA17-01747S Institutional support: RVO:68145535 Keywords : Stokes system * threshold slip boundary conditions * solution dependent slip function Subject RIV: BA - General Mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
Initial-boundary value problem with a nonlocal condition for a viscosity equation
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Abdelfatah Bouziani
2002-01-01
Full Text Available This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial-boundary value problem which combine Neumann and integral conditions for a viscosity equation. The proof is based on an energy inequality and on the density of the range of the linear operator corresponding to the abstract formulation of the studied problem.
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Feng Hanying
2011-01-01
Full Text Available The expression and properties of Green's function for a class of nonlinear fractional differential equations with integral boundary conditions are studied and employed to obtain some results on the existence of positive solutions by using fixed point theorem in cones. The proofs are based on the reduction of the problem considered to the equivalent Fredholm integral equation of the second kind. The results significantly extend and improve many known results even for integer-order cases.
Kanguzhin, Baltabek; Tokmagambetov, Niyaz
2013-01-01
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator $L.$ The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convol...
Yang, Yongqin; Chen, Shaochun
2010-03-01
A new nonconforming triangular element for the equations of planar linear elasticity with pure traction boundary conditions is considered. By virtue of construction of the element, the discrete version of Korn's second inequality is directly proved to be valid. Convergence rate of the finite element methods is uniformly optimal with respect to [lambda]. Error estimates in the energy norm and L2-norm are O(h2) and O(h3), respectively.
The Kramers problem with accommodative boundary conditions for quantum Fermi gases
Kostikov, A. A.; Latyshev, A. V.; Yushkanov, A. A.
2008-09-01
The Kramers problem of isothermal slip of a quantum Fermi gas with Cercignani boundary conditions is solved analytically. The velocity of isothermal slip is obtained as a function of the accommodation coefficient and the reduced chemical potential—the ratio of the chemical potential to the product of Boltzmann's constant and the absolute temperature. The distribution function of the molecules is presented in explicit form.
Additional Boundary Condition for a Wire Medium Connected to a Metallic Surface
Silveirinha, Mário G.; Fernandes, Carlos A.; Costa, Jorge R.
2007-01-01
WOS:000255793900001 (Nº de Acesso Web of Science) In this work, we demonstrate that the interaction of electromagnetic waves with a microstructured material formed by metallic wires connected to a metallic surface can be described using homogenization methods provided an additional boundary condition (ABC) is considered. The ABC is derived by taking into account the specific microstructure of the wire medium. To illustrate the application of the result, we characterize a substrate formed b...
A Boundary Value Problem with Multivariables Integral Type Condition for Parabolic Equations
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A. L. Marhoune
2009-01-01
Full Text Available We study a boundary value problem with multivariables integral type condition for a class of parabolic equations. We prove the existence, uniqueness, and continuous dependence of the solution upon the data in the functional wieghted Sobolev spaces. Results are obtained by using a functional analysis method based on two-sided a priori estimates and on the density of the range of the linear operator generated by the considered problem.
Masses, decay constants and electromagnetic form-factors with twisted boundary conditions
Bijnens, Johan
2015-01-01
We discuss some of the effects of twisted boundary conditions in finite volume using continuum SU(3) Chiral Perturbation Theory. We point out how broken cubic symmetry affects the definitions of quantities such as form-factors. Using the $\\pi^+$ as an example, we give one loop results for the mass, decay constants and electromagnetic form-factor and illustrate how the relevant Ward identities are satisfied.
Sescu, A.; Meneveau, C. V.
2012-12-01
Recent LES studies of the interaction between neutral atmospheric boundary layer (ABL) and infinitely large arrays of wind turbines have led to derivations of new similarity relations within the surface layer. A similar analysis in non-neutral conditions is not trivial, since achieving statistically stationary conditions in LES is challenging. For example, the heat flux at the ground forces vertical profiles of mean temperature to vary significantly over time. The focus of this work is on using an artificial heat source or sink, in a region located above ABL, that maintains the overall temperature field inside the ABL stationary. This goal is achieved by using a PI control algorithm, designed to keep constant the initial horizontally averaged temperature at a specified height and above. Another controller is used to drive the flow within the ABL, causing the mean velocity to achieve a prescribed direction at a specified height. This is done by controlling a source term in the momentum equations. This term is deactivated once the flow becomes statistically stationary and the geostrophic wind aligns with the desired direction at a given height. A suite of simulations at various resolutions, with and without wind turbines, and with different levels of thermal stratification are presented to test the effectiveness of the control algorithm. Streamwise velocity contours in unstable ABL interacting with 24 wind turbines. Streamwise velocity contours in stable ABL interacting with 24 wind turbines.
Energy Technology Data Exchange (ETDEWEB)
Petracca, S. [Salerno Univ. (Italy)
1996-08-01
Debye potentials, the Lorentz reciprocity theorem, and (extended) Leontovich boundary conditions can be used to obtain simple and accurate analytic estimates of the longitudinal and transverse coupling impedances of (piecewise longitudinally uniform) multi-layered pipes with non simple transverse geometry and/or (spatially inhomogeneous) boundary conditions. (author)
Reyes, Jonathan; Shadwick, B. A.
2016-10-01
Modeling the evolution of a short, intense laser pulse propagating through an underdense plasma is of particular interest in the physics of laser-plasma interactions. Numerical models are typically created by first discretizing the equations of motion and then imposing boundary conditions. Using the variational principle of Chen and Sudan, we spatially discretize the Lagrangian density to obtain discrete equations of motion and a discrete energy conservation law which is exactly satisfied regardless of the spatial grid resolution. Modifying the derived equations of motion (e.g., enforcing boundary conditions) generally ruins energy conservation. However, time-dependent terms can be added to the Lagrangian which force the equations of motion to have the desired boundary conditions. Although some foresight is needed to choose these time-dependent terms, this approach provides a mechanism for energy to exit the closed system while allowing the conservation law to account for the loss. An appropriate time discretization scheme is selected based on stability analysis and resolution requirements. We present results using this variational approach in a co-moving coordinate system and compare such results to those using traditional second-order methods. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY- 1104683.
Vibration analysis of multi-span beam system under arbitrary boundary and coupling conditions
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ZHENG Chaofan
2017-08-01
Full Text Available In order to overcome the difficulties of studying the vibration analysis model of a multi-span beam system under various boundary and coupling conditions, this paper constructs a free vibration analysis model of a multi-span beam system on the basis of the Bernoulli-Euler beam theory. The vibration characteristics of a multi-span beam system under arbitrary boundary supports and elastic coupling conditions are investigated using the current analysis model. Unlike most existing techniques, the beam displacement function is generally sought as an improved Fourier cosine series, and four sine terms are introduced to overcome all the relevant discontinuities or jumps of elastic boundary conditions. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh-Ritz method, and the vibration problem of multi-span bean systems is converted into a standard eigenvalue problem concerning the unknown displacement expansion coefficient. By comparing the free vibration characteristics of the proposed method with those of the FEA method, the efficiency and accuracy of the present method are validated, providing a reliable and theoretical basis for multi-span beam system structure in engineering applications.
Energy Technology Data Exchange (ETDEWEB)
Rosnitskiy, P., E-mail: pavrosni@yandex.ru; Yuldashev, P., E-mail: petr@acs366.phys.msu.ru; Khokhlova, V., E-mail: vera@acs366.phys.msu.ru [Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow (Russian Federation)
2015-10-28
An equivalent source model was proposed as a boundary condition to the nonlinear parabolic Khokhlov-Zabolotskaya (KZ) equation to simulate high intensity focused ultrasound (HIFU) fields generated by medical ultrasound transducers with the shape of a spherical shell. The boundary condition was set in the initial plane; the aperture, the focal distance, and the initial pressure of the source were chosen based on the best match of the axial pressure amplitude and phase distributions in the Rayleigh integral analytic solution for a spherical transducer and the linear parabolic approximation solution for the equivalent source. Analytic expressions for the equivalent source parameters were derived. It was shown that the proposed approach allowed us to transfer the boundary condition from the spherical surface to the plane and to achieve a very good match between the linear field solutions of the parabolic and full diffraction models even for highly focused sources with F-number less than unity. The proposed method can be further used to expand the capabilities of the KZ nonlinear parabolic equation for efficient modeling of HIFU fields generated by strongly focused sources.
Musharbash, Eleonora; Nobile, Fabio
2018-02-01
In this paper we propose a method for the strong imposition of random Dirichlet boundary conditions in the Dynamical Low Rank (DLR) approximation of parabolic PDEs and, in particular, incompressible Navier Stokes equations. We show that the DLR variational principle can be set in the constrained manifold of all S rank random fields with a prescribed value on the boundary, expressed in low rank format, with rank smaller then S. We characterize the tangent space to the constrained manifold by means of a Dual Dynamically Orthogonal (Dual DO) formulation, in which the stochastic modes are kept orthonormal and the deterministic modes satisfy suitable boundary conditions, consistent with the original problem. The Dual DO formulation is also convenient to include the incompressibility constraint, when dealing with incompressible Navier Stokes equations. We show the performance of the proposed Dual DO approximation on two numerical test cases: the classical benchmark of a laminar flow around a cylinder with random inflow velocity, and a biomedical application for simulating blood flow in realistic carotid artery reconstructed from MRI data with random inflow conditions coming from Doppler measurements.
Boundary conditions and the generalized metric formulation of the double sigma model
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Chen-Te Ma
2015-09-01
Full Text Available Double sigma model with strong constraints is equivalent to the ordinary sigma model by imposing a self-duality relation. The gauge symmetries are the diffeomorphism and one-form gauge transformation with the strong constraints. We consider boundary conditions in the double sigma model from three ways. The first way is to modify the Dirichlet and Neumann boundary conditions with a fully O(D,D description from double gauge fields. We perform the one-loop β function for the constant background fields to find low-energy effective theory without using the strong constraints. The low-energy theory can also have O(D,D invariance as the double sigma model. The second way is to construct different boundary conditions from the projectors. The third way is to combine the antisymmetric background field with field strength to redefine an O(D,D generalized metric. We use this generalized metric to reconstruct a consistent double sigma model with the classical and quantum equivalence.
Bendine, Kouider; Wankhade, Rajan L.
2017-12-01
Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped-clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.
Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil
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Yunsuo Duan
2008-01-01
Full Text Available Computational methods such as the finite difference time domain (FDTD play an important role in simulating radiofrequency (RF coils used in magnetic resonance imaging (MRI. The choice of absorbing boundary conditions affects the final outcome of such studies. We have used FDTD to assess the Berenger's perfectly matched layer (PML as an absorbing boundary condition for computation of the resonance patterns and electromagnetic fields of RF coils. We first experimentally constructed a high-pass birdcage head coil, measured its resonance pattern, and used it to acquire proton (1H phantom MRI images. We then computed the resonance pattern and B1 field of the coil using FDTD with a PML as an absorbing boundary condition. We assessed the accuracy and efficiency of PML by adjusting the parameters of the PML and comparing the calculated results with measured ones. The optimal PML parameters that produce accurate (comparable to the experimental findings FDTD calculations are then provided for the birdcage head coil operating at 127.72 MHz, the Larmor frequency of 1H at 3 Tesla (T.
Bendine, Kouider; Wankhade, Rajan L.
2017-10-01
Piezoelectric actuators are effectively used to control the response of light weight structures in shape, vibration and buckling. Optimization for the shape control of piezoelectric beam is the recent challenge which requires proper numerical technique to perform. The shape control of a composite beam using surface-bounded piezoelectric actuators has been investigated in the present work. The mathematical model is developed using two-node Timoshenko beam element coupling with the theory of linear piezoelectricity. First-order shear deformation theory is employed in the formulation to consider the effect of shear. In the analysis, the effect of the actuators position for different set of boundary conditions is investigated. For different boundary conditions which include clamped-free-, clamped-clamped- and simply supported beam, optimisation of piezoelectric patch location is investigated. Moreover, a genetic algorithm is adopted and implemented to optimize the required voltage to maintain the desired shape of the beam. This optimization technique is applied to different cases of composite beams with varying the boundary condition.
Deep geothermal sources for electricity production in Slovakia: thermal conditions
Majcin, Dušan; Král, Miroslav; Bilčík, Dušan; Šujan, Martin; Vranovská, Andrea
2017-03-01
The contribution presents the results of geothermic interpretation approaches applied to measured geothermal data and is focused to determination of the thermal conditions both for application of classic hydrothermal sources exploitation and specialized EGS technologies for electricity production in the region of Slovakia and adjacent areas. Primarily, the heat flow density data and the temperature distribution measurements in boreholes were interpreted by classic 1D interpolation and extrapolation methods. New terrestrial heat flow density map for the studied area was constructed using the values determined in boreholes, their interpretations, the newest outcomes of geothermal modelling methods based both on steady-state and transient heat transfer approaches, and on other recently gained geoscientific knowledge. Thereafter, we constructed the maps of temperature field distribution for selected depth levels up to 6000 m below the surface and the final map of the isothermal surface depths for the reservoir temperature of 160° C. This final map serves for the appraisal of the effective application of the binary cycle power plant technology in Slovakia in terms of thermal conditions.
Liu, Hualin; Zhao, Wenwen; Chen, Weifang
2016-11-01
Gas or liquid flow through small channels has become more and more popular due to the micro-electro-mechanical systems (MEMS) fabrication technologies such as micro-motors, electrostatic comb-drive, micro-chromatographs, micro-actuators, micro-turbines and micro-pumps, etc. The flow conditions in and around these systems are always recognized as typical transitional regimes. Under these conditions, the mean free path of gas molecules approaches the characteristic scale of the micro-devices itself, and due to the little collisions the heat and momentum cannot equilibrate between the wall and fluids quickly. Couette flow is a simple and critical model in fluid dynamics which focuses on the mechanism of the heat transfer in shear-driven micro-cavities or micro-channels. Despite numerous work on the numerical solutions of the Couette flow, how to propose stable and accurate slip boundary conditions in rarefied flow conditions still remains to be elucidated. In this paper, converged solutions for steady-state micro Couette flows are obtained by using conventional Burnett equations with a set of modified slip boundary conditions. Instead of using the physical variables at the wall, the modified slip conditions use the variables at the edge of the Knudsen layer based on a physically plausible assumption in literature that Knudsen layer has a thickness only in the order of a mean free path and molecules are likely to travel without collision in this layer. Numerical results for non-dimensional wall shear stress and heat flux are compared with those of the DSMC solutions. Although there are not much improvement in the accuracy by using this modified slip conditions, the modified conditions perform much better than the unmodified slip conditions for numerical stabilization. All results show that the set of conventional Burnett equations with second order modified conditions are proved to be an appropriate model for the micro-Couette flows.
Sheng, Yin; Zhang, Hao; Zeng, Zhigang
2017-10-01
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
Nonlinear convection in reaction-diffusion equations under dynamical boundary conditions
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Gaelle Pincet Mailly
2013-01-01
Full Text Available We study the blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term $partial_t u = Delta u - g(u cdot abla u + f(u$ in a bounded domain of $mathbb{R}^N$ under the dissipative dynamical boundary conditions $sigma partial_t u + partial_u u =0$. Some conditions on g and f are discussed to state if the positive solutions blow up in finite time or not. Moreover, for certain classes of nonlinearities, an upper-bound for the blow-up time can be derived and the blow-up rate can be determined.
Nonexistence of Global Solutions to an Elliptic Equation with a Dynamical Boundary Condition
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Stanislav I. POHOZAEV
2004-01-01
Full Text Available We consider the equation Delta u = 0 posed in Q := (0;+inftyimes Omega, Omega:= { x=(x',x_N/ x'in R^{N-1}, x_N >0}, with the dynamical boundary conditionB(t,x',0u_{tt} + A(t,x',0u_t - u_{x_N} geq D(t, x',0|u|^q on Sigma := (0,+infty imes R^{N-1} imes {0} and give conditions on the coeﬃcient functions A(t,x',0; B(t,x',0 and D(t;x',0 for the nonexistence of global solutions.
Real-time gauge/gravity duality and ingoing boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Rees, Balt C. van [ITFA, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)
2009-07-15
In Lorentzian gauge/gravity duality, a proper understanding of initial conditions is essential. I discuss the precise relation between purely ingoing conditions at the horizon for bulk fields and retarded boundary correlation functions, as well as the generalization to higher-point functions. Some open questions can be answered only within the recently developed framework of [K. Skenderis and B. C. van Rees Phys. Rev. Lett. 101 (2008) 081601, (arXiv:0805.0150 [hep-th]), K. Skenderis and B. C. van Rees (arXiv:0812.2909 [hep-th])].
Heat exchange studies on coconut oil cells as thermal energy storage for room thermal conditioning
Sutjahja, I. M.; Putri, Widya A.; Fahmi, Z.; Wonorahardjo, S.; Kurnia, D.
2017-07-01
As reported by many thermal environment experts, room air conditioning might be controlled by thermal mass system. In this paper we discuss the performance of coconut oil cells as room thermal energy storage. The heat exchange mechanism of coconut oil (CO) which is one of potential organic Phase Change Material (PCM) is studied based on the results of temperature measurements in the perimeter and core parts of cells. We found that the heat exchange performance, i.e. heat absorption and heat release processes of CO cells are dominated by heat conduction in the sensible solid from the higher temperature perimeter part to the lower temperature core part and heat convection during the solid-liquid phase transition and sensible liquid phase. The capability of heat absorption as measured by the reduction of air temperature is not influenced by CO cell size. Besides that, the application of CO as the thermal mass has to be accompanied by air circulation to get the cool sensation of the room’s occupants.
Heat and mass transfer boundary conditions at the surface of a heated sessile droplet
Ljung, Anna-Lena; Lundström, T. Staffan
2017-12-01
This work numerically investigates how the boundary conditions of a heated sessile water droplet should be defined in order to include effects of both ambient and internal flow. Significance of water vapor, Marangoni convection, separate simulations of the external and internal flow, and influence of contact angle throughout drying is studied. The quasi-steady simulations are carried out with Computational Fluid Dynamics and conduction, natural convection and Marangoni convection are accounted for inside the droplet. For the studied conditions, a noticeable effect of buoyancy due to evaporation is observed. Hence, the inclusion of moisture increases the maximum velocities in the external flow. Marangoni convection will, in its turn, increase the velocity within the droplet with up to three orders of magnitude. Results furthermore show that the internal and ambient flow can be simulated separately for the conditions studied, and the accuracy is improved if the internal temperature gradient is low, e.g. if Marangoni convection is present. Simultaneous simulations of the domains are however preferred at high plate temperatures if both internal and external flows are dominated by buoyancy and natural convection. The importance of a spatially resolved heat and mass transfer boundary condition is, in its turn, increased if the internal velocity is small or if there is a large variation of the transfer coefficients at the surface. Finally, the results indicate that when the internal convective heat transport is small, a rather constant evaporation rate may be obtained throughout the drying at certain conditions.
Heat and mass transfer boundary conditions at the surface of a heated sessile droplet
Ljung, Anna-Lena; Lundström, T. Staffan
2017-07-01
This work numerically investigates how the boundary conditions of a heated sessile water droplet should be defined in order to include effects of both ambient and internal flow. Significance of water vapor, Marangoni convection, separate simulations of the external and internal flow, and influence of contact angle throughout drying is studied. The quasi-steady simulations are carried out with Computational Fluid Dynamics and conduction, natural convection and Marangoni convection are accounted for inside the droplet. For the studied conditions, a noticeable effect of buoyancy due to evaporation is observed. Hence, the inclusion of moisture increases the maximum velocities in the external flow. Marangoni convection will, in its turn, increase the velocity within the droplet with up to three orders of magnitude. Results furthermore show that the internal and ambient flow can be simulated separately for the conditions studied, and the accuracy is improved if the internal temperature gradient is low, e.g. if Marangoni convection is present. Simultaneous simulations of the domains are however preferred at high plate temperatures if both internal and external flows are dominated by buoyancy and natural convection. The importance of a spatially resolved heat and mass transfer boundary condition is, in its turn, increased if the internal velocity is small or if there is a large variation of the transfer coefficients at the surface. Finally, the results indicate that when the internal convective heat transport is small, a rather constant evaporation rate may be obtained throughout the drying at certain conditions.
Homogenization of the stochastic Navier–Stokes equation with a stochastic slip boundary condition
Bessaih, Hakima
2015-11-02
The two-dimensional Navier–Stokes equation in a perforated domain with a dynamical slip boundary condition is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the holes. We consider a scaling (ᵋ for the viscosity and 1 for the density) that will lead to a time-dependent limit problem. However, the noncritical scaling (ᵋ, β > 1) is considered in front of the nonlinear term. The homogenized system in the limit is obtained as a Darcy’s law with memory with two permeabilities and an extra term that is due to the stochastic perturbation on the boundary of the holes. The nonhomogeneity on the boundary contains a stochastic part that yields in the limit an additional term in the Darcy’s law. We use the two-scale convergence method after extending the solution with 0 inside the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. Due to the stochastic integral, the pressure that appears in the variational formulation does not have enough regularity in time. This fact made us rely only on the variational formulation for the passage to the limit on the solution. We obtain a variational formulation for the limit that is solution of a Stokes system with two pressures. This two-scale limit gives rise to three cell problems, two of them give the permeabilities while the third one gives an extra term in the Darcy’s law due to the stochastic perturbation on the boundary of the holes.
A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions
Winter, M.; Schott, B.; Massing, A.; Wall, W. A.
2018-03-01
In this work a Nitsche-based imposition of generalized Navier conditions on cut meshes for the Oseen problem is presented. Other methods from literature dealing with the generalized Navier condition impose this condition by means of substituting the tangential Robin condition in a classical Galerkin way. These methods work fine for a large slip length coefficient but lead to conditioning and stability issues when it approaches zero. We introduce a novel method for the weak imposition of the generalized Navier condition which remains well-posed and stable for arbitrary choice of slip length, including zero. The method proposed here builds on the formulation done by [1]. They impose a Robin condition for the Poisson problem by means of Nitsche's method for an arbitrary combination of the Dirichlet and Neumann parts of the condition. The analysis conducted for the proposed method is done in a similar fashion as in [2], but is done here for a more general type of boundary condition. The analysis proves stability for all flow regimes and all choices of slip lengths. Also an L2-optimal estimate for the velocity error is shown, which was not conducted in the previously mentioned work. A numerical example is carried out for varying slip lengths to verify the robustness and stability of the method with respect to the choice of slip length. Even though proofs and formulations are presented for the more general case of an unfitted grid method, they can easily be reduced to the simpler case of a boundary-fitted grid with the removal of the ghost-penalty stabilization terms.
Energy dissipation in the Nagel-Schreckenberg model with open boundary condition
Zhang, Wei; Zhang, Wei
2014-01-01
In this paper, we numerically investigate energy dissipation caused by traffic in the Nagel-Schreckenberg (NaSch) model with open boundary conditions (OBC). Boundary results in excess energy dissipation. The effects of the stochastic boundary conditions on energy dissipation are discussed. The behaviors of energy dissipation in different traffic phase are distinct. As an order parameter, energy dissipation rate E d characterizes the phase transition behaviors well. It is shown that there is no true free-flow state in nondeterministic NaSch model with OBC. We refer to this non-true free-flow state as quasi-free-flow (QFF) phase in which there are interactions between vehicles caused by stochastic braking but no backward moving jam exists. In the maximum current phase, E d is minimal thus the social payoff is maximal. Energy dissipation profiles in QFF, jammed and maximum current phase are presented. Theoretical analyses are in good agreement with numerical results for the case v max = 1.
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Rais Ahmad
2012-01-01
Full Text Available Guided wave technique is an efficient method for monitoring structural integrity by detecting and forecasting possible damages in distributed pipe networks. Efficient detection depends on appropriate selection of guided wave modes as well as signal processing techniques. Fourier analysis and wavelet analysis are two popular signal processing techniques that provide a flexible set of tools for solving various fundamental problems in science and engineering. In this paper, effective ways of using Fourier and Wavelet analyses on guided wave signals for detecting defects in steel pipes are discussed for different boundary conditions. This research investigates the effectiveness of Fourier transforms and Wavelet analysis in detecting defects in steel pipes. Cylindrical Guided waves are generated by piezo-electric transducers and propagated through the pipe wall boundaries in a pitch-catch system. Fourier transforms of received signals give information regarding the propagating guided wave modes which helps in detecting defects by selecting appropriate modes that are affected by the presence of defects. Continuous wavelet coefficients are found to be sensitive to defects. Several types of mother wavelet functions such as Daubechies, Symlet, and Meyer have been used for the continuous wavelet transform to investigate the most suitable wavelet function for defect detection. This research also investigates the effect of different boundary conditions on wavelet transforms for different mother wavelet functions.
Impacts of boundary condition changes on regional climate projections over West Africa
Kim, Jee Hee; Kim, Yeonjoo; Wang, Guiling
2017-06-01
Future projections using regional climate models (RCMs) are driven with boundary conditions (BCs) typically derived from global climate models. Understanding the impact of the various BCs on regional climate projections is critical for characterizing their robustness and uncertainties. In this study, the International Center for Theoretical Physics Regional Climate Model Version 4 (RegCM4) is used to investigate the impact of different aspects of boundary conditions, including lateral BCs and sea surface temperature (SST), on projected future changes of regional climate in West Africa, and BCs from the coupled European Community-Hamburg Atmospheric Model 5/Max Planck Institute Ocean Model are used as an example. Historical, future, and several sensitivity experiments are conducted with various combinations of BCs and CO2 concentration, and differences among the experiments are compared to identify the most important drivers for RCMs. When driven by changes in all factors, the RegCM4-produced future climate changes include significantly drier conditions in Sahel and wetter conditions along the Guinean coast. Changes in CO2 concentration within the RCM domain alone or changes in wind vectors at the domain boundaries alone have minor impact on projected future climate changes. Changes in the atmospheric humidity alone at the domain boundaries lead to a wetter Sahel due to the northward migration of rain belts during summer. This impact, although significant, is offset and dominated by changes of other BC factors (primarily temperature) that cause a drying signal. Future changes of atmospheric temperature at the domain boundaries combined with SST changes over oceans are sufficient to cause a future climate that closely resembles the projection that accounts for all factors combined. Therefore, climate variability and changes simulated by RCMs depend primarily on the variability and change of temperature aspects of the RCM BCs. Moreover, it is found that the response
Thermal separation in near-axis boundary layers with intense swirl
Herrada, M. A.; Pérez-Saborid, M.; Barrero, A.
1999-12-01
Swirling flows have a wide range of applications and exhibit a variety of interesting features. Gas cooling near the axis in these flows, the so-called Ranque-Hilsch effect, is one of them. To gain insight into this phenomenon, we have analyzed the thermal, near-axis boundary layer of a gas jet driven by a class of conical inviscid quasi-incompressible flows whose axial and azimuthal velocity components, w and v, and stagnation temperature, Tt, behave near the axis as w=W0rm-2,v=LW0rm-2, and Tt-Tr=T0r2(m-2), where z and r are the axial and radial coordinates, L is the Squire number directly related to the swirl strength, m is any real number such as 1⩽mRanque-Hilsch effect) when the effect of both heat conduction and the work done by viscous forces are taken into account. It is also found that there exists an optimum value Lop for which the cooling effect reaches a sharp maximum and that small deviations of L from Lop reduce drastically the cooling effect. The appropriate tuning of Lop can be dramatically important for the efficient operation of Ranque-Hilsch tubes. The influence of the Prandtl number and the rest of the parameters of the problem has been also considered.
Tang, Liang; Cong, Shengyi; Ling, Xianzhang; Ju, Nengpan
2017-01-01
Boundary conditions can significantly affect a slope's behavior under strong earthquakes. To evaluate the importance of boundary conditions for finite element (FE) simulations of a shake-table experiment on the slope response, a validated three-dimensional (3D) nonlinear FE model is presented, and the numerical and experimental results are compared. For that purpose, the robust graphical user-interface "SlopeSAR", based on the open-source computational platform OpenSees, is employed, which simplifies the effort-intensive pre- and post-processing phases. The mesh resolution effect is also addressed. A parametric study is performed to evaluate the influence of boundary conditions on the FE model involving the boundary extent and three types of boundary conditions at the end faces. Generally, variations in the boundary extent produce inconsistent slope deformations. For the two end faces, fixing the y-direction displacement is not appropriate to simulate the shake-table experiment, in which the end walls are rigid and rough. In addition, the influence of the length of the 3D slope's top face and the width of the slope play an important role in the difference between two types of boundary conditions at the end faces (fixing the y-direction displacement and fixing the ( y, z) direction displacement). Overall, this study highlights that the assessment of a comparison between a simulation and an experimental result should be performed with due consideration to the effect of the boundary conditions.
Problem of the boundary condition in quantum cosmology: a simple example
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Zhuk, Alexander
1988-10-01
The quantum cosmological minisuperspace model with a massless scalar field with a potential lambdahi/sup 4/ is investigated. The Hartle-Hawking proposal gives the possibility of picking a particular solution of the Wheeler-DeWitt equation in the space of the imaginary conformal factor a and scalar field phi. An analytic expression for this solution is obtained and an analytic continuation to the space of real ..cap alpha.. and phi is performed. The boundary conditions on the surface a = O, phi=+-infinityare psi(a=O, phi=+-infinity=1. It is shown that near this boundary the psi have exponential behaviour. In the region where the interaction between gravity and the scalar field plays the main role the psi have an oscillation behaviour and this leads to the inflation of the universe. (author).
Sithole, Hloniphile M.; Mondal, Sabyasachi; Sibanda, Precious; Motsa, Sandile S.
2017-11-01
The main focus of this study is on unsteady Maxwell nanofluid flow over a shrinking surface with convective and slip boundary conditions. The objective is to give an evaluation of the impact and significance of Brownian motion and thermophoresis when the nanofluid particle volume fraction flux at the boundary is zero. The transformed equations are solved numerically using the spectral local linearization method. We present an analysis of the residual errors to show the accuracy and convergence of the spectral local linearization method. We explore the effect of magnetic field and thermophoresis parameters on the heat transfer rate. We show, among other results, that an increase in particle Brownian motion leads to a decrease in the concentration profiles but concentration profiles increase with the increasing value of thermophoresis parameter
On Coupled p-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions
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Aziz Khan
2017-01-01
Full Text Available This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs with nonlinear p-Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. The functions involved in the proposed coupled system are continuous and satisfy certain growth conditions. By using topological degree theory some conditions are established which ensure the existence and uniqueness of solution to the proposed problem. Further, certain conditions are developed corresponding to Hyers-Ulam type stability for the positive solution of the considered coupled system of FDEs. Also, from applications point of view, we give an example.
Energy Technology Data Exchange (ETDEWEB)
Huang, Haoxiang; Kumar, Satish, E-mail: satish.kumar@me.gatech.edu [G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States); Chen, Liang [School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi (China); Varshney, Vikas [Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433 (United States); Universal Technology Corporation, Dayton, Ohio 45432 (United States); Roy, Ajit K. [Materials and Manufacturing Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433 (United States)
2016-09-07
Carbon nanostructures such as carbon nanotube (CNT), graphene, and carbon fibers can be used as fillers in amorphous polymers to improve their thermal properties. In this study, the effect of covalent bonding of CNT with poly(ether ketone) (PEK) on interfacial thermal interactions is investigated using non-equilibrium molecular dynamics simulations. The number of covalent bonds between (20, 20) CNT and PEK is varied in the range of 0–80 (0%–6.25%), and the thermal boundary conductance is computed. The analysis reveals that covalent functionalization of CNT atoms can enhance the thermal boundary conductance by an order of magnitude compared to the non-functionalized CNT-PEK interface at a high degree of CNT functionalization. Besides strengthening the thermal coupling, covalent functionalization is also shown to modify the phonon spectra of CNT. The transient spectral energy analysis shows that the crosslinks cause faster energy exchange from CNT to PEK in different frequency bands. The oxygen atom of hydroxyl group of PEK contributes energy transfer in the low frequency band, while aromatic and carbonyl carbon atoms play a more significant role in high frequency bands. In addition, by analyzing the relaxation time of the spectral temperature of different frequency bands of CNT, it is revealed that with increasing number of bonds, both lower frequency vibrational modes and higher frequency modes efficiently couple across the CNT-PEK interface and contribute in thermal energy transfer from CNT to the matrix.
Reis, Tim
2012-01-01
We present lattice Boltzmann simulations of rarefied flows driven by pressure drops along two-dimensional microchannels. Rarefied effects lead to non-zero cross-channel velocities, nonlinear variations in the pressure along the channel. Both effects are absent in flows driven by uniform body forces. We obtain second-order accuracy for the two components of velocity the pressure relative to asymptotic solutions of the compressible Navier-Stokes equations with slip boundary conditions. Since the common lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier-Maxwell slip boundary conditions that relate the tangential velocity to the strain rate at the boundary. We use these conditions to solve for the unknown distribution functions that propagate into the domain across the boundary. We achieve second-order accuracy by reformulating these conditions for the second set of distribution functions that arise in the derivation of the lattice Boltzmann method by an integration along characteristics. Our moment formalism is also valuable for analysing the existing boundary conditions. It reveals the origin of numerical slip in the bounce-back other common boundary conditions that impose conditions on the higher moments, not on the local tangential velocity itself. © 2012 American Institute of Physics.
Park, Hyunwook; Pan, Xiaomin; Lee, Changhoon; Choi, Jung-Il
2016-06-01
A novel immersed boundary (IB) method based on an implicit direct forcing (IDF) scheme is developed for incompressible viscous flows. The key idea for the present IDF method is to use a block LU decomposition technique in momentum equations with Taylor series expansion to construct the implicit IB forcing in a recurrence form, which imposes more accurate no-slip boundary conditions on the IB surface. To accelerate the IB forcing convergence during the iterative procedure, a pre-conditioner matrix is introduced in the recurrence formulation of the IB forcing. A Jacobi-type parameter is determined in the pre-conditioner matrix by minimizing the Frobenius norm of the matrix function representing the difference between the IB forcing solution matrix and the pre-conditioner matrix. In addition, the pre-conditioning parameter is restricted due to the numerical stability in the recurrence formulation. Consequently, the present pre-conditioned IDF (PIDF) enables accurate calculation of the IB forcing within a few iterations. We perform numerical simulations of two-dimensional flows around a circular cylinder and three-dimensional flows around a sphere for low and moderate Reynolds numbers. The result shows that PIDF yields a better imposition of no-slip boundary conditions on the IB surfaces for low Reynolds number with a fairly larger time step than IB methods with different direct forcing schemes due to the implicit treatment of the diffusion term for determining the IB forcing. Finally, we demonstrate the robustness of the present PIDF scheme by numerical simulations of flow around a circular array of cylinders, flows around a falling sphere, and two sedimenting spheres in gravity.
Hink, R.
2015-09-01
The choice of materials for rocket chamber walls is limited by its thermal resistance. The thermal loads can be reduced substantially by the blowing out of gases through a porous surface. The k- ω-based turbulence models for computational fluid dynamic simulations are designed for smooth, non-permeable walls and have to be adjusted to account for the influence of injected fluids. Wilcox proposed therefore an extension for the k- ω turbulence model for the correct prediction of turbulent boundary layer velocity profiles. In this study, this extension is validated against experimental thermal boundary layer data from the Thermosciences Division of the Department of Mechanical Engineering from the Stanford University. All simulations are performed with a finite volume-based in-house code of the German Aerospace Center. Several simulations with different blowing settings were conducted and discussed in comparison to the results of the original model and in comparison to an additional roughness implementation. This study has permitted to understand that velocity profile corrections are necessary in contrast to additional roughness corrections to predict the correct thermal boundary layer profile of effusive cooled walls. Finally, this approach is applied to a two-dimensional simulation of an effusive cooled rocket chamber wall.
Energy Technology Data Exchange (ETDEWEB)
Zhi-Gang Feng
2012-05-31
The simulation of particulate flows for industrial applications often requires the use of two-fluid models, where the solid particles are considered as a separate continuous phase. One of the underlining uncertainties in the use of the two-fluid models in multiphase computations comes from the boundary condition of the solid phase. Typically, the gas or liquid fluid boundary condition at a solid wall is the so called no-slip condition, which has been widely accepted to be valid for single-phase fluid dynamics provided that the Knudsen number is low. However, the boundary condition for the solid phase is not well understood. The no-slip condition at a solid boundary is not a valid assumption for the solid phase. Instead, several researchers advocate a slip condition as a more appropriate boundary condition. However, the question on the selection of an exact slip length or a slip velocity coefficient is still unanswered. Experimental or numerical simulation data are needed in order to determinate the slip boundary condition that is applicable to a two-fluid model. The goal of this project is to improve the performance and accuracy of the boundary conditions used in two-fluid models such as the MFIX code, which is frequently used in multiphase flow simulations. The specific objectives of the project are to use first principles embedded in a validated Direct Numerical Simulation particulate flow numerical program, which uses the Immersed Boundary method (DNS-IB) and the Direct Forcing scheme in order to establish, modify and validate needed energy and momentum boundary conditions for the MFIX code. To achieve these objectives, we have developed a highly efficient DNS code and conducted numerical simulations to investigate the particle-wall and particle-particle interactions in particulate flows. Most of our research findings have been reported in major conferences and archived journals, which are listed in Section 7 of this report. In this report, we will present a
Thermal analysis on NAC-STC spent fuel transport cask under different transport conditions
Energy Technology Data Exchange (ETDEWEB)
Xu, Yumei [Institute of Process Equipment, Zhejiang University, Hangzhou (China); Yang, Jian, E-mail: zdhjkz@zju.edu.cn [Institute of Process Equipment, Zhejiang University, Hangzhou (China); Xu, Chao; Wang, Weiping [Institute of Process Equipment, Zhejiang University, Hangzhou (China); Ma, Zhijun [Department of Material Engineering, South China University of Technology, Guangzhou (China)
2013-12-15
Highlights: • Spent fuel cask was investigated as a whole instead of fuel assembly alone. • The cask was successfully modeled and meshed after several simplifications. • Equivalence method was used to calculate the properties of parts. • Both the integral thermal field and peak values are captured to verify safety. • The temperature variations of key parts were also plotted. - Abstract: Transport casks used for conveying spent nuclear fuel are inseparably related to the safety of the whole reprocessing system for spent nuclear fuel. Thus they must be designed according to rigorous safety standards including thermal analysis. In this paper, for NAC-STC cask, a finite element model is established based on some proper simplifications on configurations and the heat transfer mechanisms. Considering the complex components and gaps, the equivalence method is presented to define their material properties. Then an equivalent convection coefficient is introduced to define boundary conditions. Finally, the temperature field is captured and analyzed under both normal and accident transport conditions by using ANSYS software. The validity of numerical calculation is given by comparing its results with theoretical calculation. Obtaining the integral distribution laws of temperature and peak temperature values of all vital components, the security of the cask can be evaluated and verified.
Effects of boundary conditions on bistable behaviour in axisymmetrical shallow shells.
Sobota, P M; Seffen, K A
2017-07-01
Multistable shells are thin-walled structures that have more than one stable state of self-stress. We consider isotropic axisymmetrical shallow shells of arbitrary polynomial shapes using a Föppl-von Kármán analytical model. By employing a Rayleigh-Ritz approach, we identify stable shapes from local minima in the strain energy formulation, and we formally characterize the level of influence of the boundary conditions on the critical geometry for achieving bistable inversion-an effect not directly answered in the literature. Systematic insight is afforded by connecting the boundary to ground through sets of extensional and rotational linear springs. For typical cap-like shells, it is shown that bistability is generally enhanced when the extensional spring stiffness increases and when the rotational spring stiffness decreases, i.e. when boundary movements in-plane are resisted but when their rotations are not; however, for certain other shapes and large in-plane stiffness values, bistability can be enhanced by resisting but not entirely preventing edge rotations. Our predictions are furnished as detailed regime maps of the critical geometry, which are accurately correlated against finite-element analysis. Furthermore, the suitabilities of single degree-of-freedom models, for which solutions are achieved in closed form, are evaluated and compared to our more accurate predictions.
On the numerical solution of the diffusion equation with a nonlocal boundary condition
Directory of Open Access Journals (Sweden)
Dehghan Mehdi
2003-01-01
Full Text Available Parabolic partial differential equations with nonlocal boundary specifications feature in the mathematical modeling of many phenomena. In this paper, numerical schemes are developed for obtaining approximate solutions to the initial boundary value problem for one-dimensional diffusion equation with a nonlocal constraint in place of one of the standard boundary conditions. The method of lines (MOL semidiscretization approach is used to transform the model partial differential equation into a system of first-order linear ordinary differential equations (ODEs. The partial derivative with respect to the space variable is approximated by a second-order finite-difference approximation. The solution of the resulting system of first-order ODEs satisfies a recurrence relation which involves a matrix exponential function. Numerical techniques are developed by approximating the exponential matrix function in this recurrence relation. We use a partial fraction expansion to compute the matrix exponential function via Pade approximations, which is particularly useful in parallel processing. The algorithm is tested on a model problem from the literature.
Casimir Effect Under Quasi-Periodic Boundary Condition Inspired by Nanotubes
Feng, Chao-Jun; Li, Xin-Zhou; Zhai, Xiang-Hua
2014-01-01
When one studies the Casimir effect, the periodic (anti-periodic) boundary condition is usually taken to mimic a periodic (anti-periodic) structure for a scalar field living in a flat space with a non-Euclidean topology. However, there could be an arbitrary phase difference between the value of the scalar field on one endpoint of the unit structure and that on the other endpoint, such as the structure of nanotubes. Then, in this paper, a periodic condition on the ends of the system with an additional phase factor, which is called the "quasi-periodic" condition, is imposed to investigate the corresponding Casimir effect. And an attractive or repulsive Casimir force is found, whose properties depend on the phase angle value. Especially, the Casimir effect disappears when the phase angle takes a particular value. High dimensional spacetime case is also investigated.
Revisiting the boundary conditions for second-harmonic generation at metal-dielectric interfaces
Nireekshan Reddy, K.; Chen, Parry Y.; Fernández-Domínguez, Antonio I.; Sivan, Yonatan
2017-09-01
We study second-harmonic generation (SHG) arising from surface nonlinearity at a metal-dielectric interface using a spectral decomposition method. Since our method avoids the need to consider the generalized boundary condition across the metal-dielectric interface in the presence of a perpendicular surface source, we retrieve the known discontinuity of the tangential component of the electric field ($E_{\\parallel}^ {2\\omega}$) for a general geometry, based on a purely mathematical argument. Further, we reaffirm the standard convention of the implementation of this condition, namely, that the surface dipole source radiates as if placed outside the metal surface for arbitrary geometries. We also study and explain the spectral dependence of the discontinuity of the tangential component of the electric field at second harmonic. Finally, we note that the default settings of the commercial numerical package COMSOL Multiphysics fail to account for the $E_{\\parallel}^ {2\\omega}$-discontinuity. We provide a simple recipe that corrects the boundary condition within these existing settings.
A Resistive Boundary Condition Enhanced DGTD Scheme for the Transient Analysis of Graphene
Li, Ping
2015-04-24
In this paper, the electromagnetic (EM) features of graphene are characterized by a discontinuous Galerkin timedomain (DGTD) algorithm with a resistive boundary condition (RBC). The atomically thick graphene is equivalently modeled using a RBC by regarding the graphene as an infinitesimally thin conductive sheet. To incorporate RBC into the DGTD analysis, the surface conductivity of the graphene composed of contributions from both intraband and interband terms is firstly approximated by rational basis functions using the fastrelaxation vector-fitting (FRVF) method in the Laplace-domain. Next, through the inverse Laplace transform, the corresponding time-domain matrix equations in integral can be obtained. Finally, these matrix equations are solved by time-domain finite integral technique (FIT). For elements not touching the graphene sheet, however, the well-known Runge-Kutta (RK) method is employed to solve the two first-order time-derivative Maxwell’s equations. The application of the surface boundary condition significantly alleviates the memory consuming and the limitation of time step size required by Courant-Friedrichs-Lewy (CFL) condition. To validate the proposed algorithm, various numerical examples are presented and compared with available references.
Detecting Unsteady Blade Row Interaction in a Francis Turbine using a Phase-Lag Boundary Condition
Wouden, Alex; Cimbala, John; Lewis, Bryan
2013-11-01
For CFD simulations in turbomachinery, methods are typically used to reduce the computational cost. For example, the standard periodic assumption reduces the underlying mesh to a single blade passage in axisymmetric applications. If the simulation includes only a single array of blades with an uniform inlet condition, this assumption is adequate. However, to compute the interaction between successive blade rows of differing periodicity in an unsteady simulation, the periodic assumption breaks down and may produce inaccurate results. As a viable alternative the phase-lag boundary condition assumes that the periodicity includes a temporal component which, if considered, allows for a single passage to be modeled per blade row irrespective of differing periodicity. Prominently used in compressible CFD codes for the analysis of gas turbines/compressors, the phase-lag boundary condition is adapted to analyze the interaction between the guide vanes and rotor blades in an incompressible simulation of the 1989 GAMM Workshop Francis turbine using OpenFOAM. The implementation is based on the ``direct-storage'' method proposed in 1977 by Erdos and Alzner. The phase-lag simulation is compared with available data from the GAMM workshop as well as a full-wheel simulation. Funding provided by DOE Award number: DE-EE0002667.
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Gözde Sarı
2013-01-01
Full Text Available An investigation into the dynamic behavior of a slightly curved resonant microbeam having nonideal boundary conditions is presented. The model accounts for midplane stretching, an applied axial load, and a small AC harmonic force. The ends of the curved microbeam are on immovable simple supports and the microbeam is resting on a nonlinear elastic foundation. The forced vibration response of curved microbeam due to the small AC load is obtained analytically by means of direct application of the method of multiple scales (a perturbation method. The effects of the nonlinear elastic foundation as well as the effect of curvature on the vibrations of the microbeam are examined. It is found that the effect of curvature is of softening type. For sufficiently high values of the coefficients, the elastic foundation and the axial load may suppress the softening behavior resulting in hardening behavior of the nonlinearity. The frequencies and mode shapes obtained are compared with the ideal boundary conditions case and the differences between them are contrasted on frequency-response curves. The frequency response and nonlinear frequency curves obtained may provide a reference for the choice of reasonable resonant conditions, design, and industrial applications of such systems. Results may be beneficial for future experimental and theoretical works on MEMS.
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
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Verschaeve, Joris C. G.
2011-07-01
The present thesis focuses on two distinct topics of computational fluid dynamics. The first one, treated in part I, focuses on the no-slip boundary conditions for the lattice Boltzmann method, whereas the second one, presented in part II, proposes a high order accurate description of the interface in two-phase flow computations for volume tracking in two dimensions.Part I of the present thesis presents an important issue in the framework of the lattice Boltzmann method, namely no-slip boundary conditions. Since the central object of the lattice Boltzmann method is the particle distribution function, the implementation of the no-slip boundary condition, although straightforward for continuum Navier Stokes solvers, is more involved. Additional physical arguments for the no-slip boundary condition at straight walls are presented. This leads to an alternative formulation of the no-slip boundary condition for the lattice Boltzmann method. This boundary condition is second order accurate with respect to the grid spacing and conserves mass. The origin of numerical instabilities observed for a variety of other boundary conditions is investigated, and it is shown how these can be removed leading to stable boundary conditions. Some arguments unifying different formulations of the no-slip boundary condition are presented. In addition to straight boundary conditions, the question of curved boundary conditions is treated. These represent an elevated level of complexity, since the lattice Boltzmann method is only defined for equidistant Cartesian grids. The curved boundary condition in the present thesis conserves the second order accuracy of the lattice Boltzmann method.Due to the complexity of two-phase flow problems, the majority of numerical methods in this field displays a rather low order of accuracy. In part II of the present thesis, a subproblem of the two-phase flow problem, namely the tracking of the interface is treated. Two different interface descriptions allowing
Analytic theory of curvature effects for wave problems with general boundary conditions
DEFF Research Database (Denmark)
Willatzen, Morten; Gravesen, Jens; Voon, L. C. Lew Yan
2010-01-01
A formalism based on a combination of differential geometry and perturbation theory is used to obtain analytic expressions for confined eigenmode changes due to general curvature effects. In cases of circular-shaped and helix-shaped structures, where alternative analytic solutions can be found......, the perturbative solution is shown to yield the same result. The present technique allows the generalization of earlier results to arbitrary boundary conditions. The power of the method is illustrated using examples based on Maxwell’s and Schrödinger’s equations for applications in photonics and nanoelectronics....
Effects from magnetic boundary conditions in superconducting-magnetic proximity systems
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Thomas E. Baker
2016-05-01
Full Text Available A superconductor-magnetic proximity system displays singlet-triplet pair correlations in the magnetization as a function of inhomogeneities of the magnetic profile. We discuss how the magnetic boundary conditions affects differently the curvature and winding number of rotating magnetizations in the three commonly used structures to generate long range triplet components: an exchange spring, a helical structure and a misaligned magnetic multilayer. We conclude that the choice of the system is dictated by the goal one wishes to achieve in designing a spintronic device but note that only the exchange spring presently offers an experimentally realizable magnetic profile that is tunable.
The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons
Kweon, Jae Ryong
2017-03-01
In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.
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R. C. Mittal
2014-01-01
Full Text Available We present a technique based on collocation of cubic B-spline basis functions to solve second order one-dimensional hyperbolic telegraph equation with Neumann boundary conditions. The use of cubic B-spline basis functions for spatial variable and its derivatives reduces the problem into system of first order ordinary differential equations. The resulting system subsequently has been solved by SSP-RK54 scheme. The accuracy of the proposed approach has been confirmed with numerical experiments, which shows that the results obtained are acceptable and in good agreement with the exact solution.
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M. Stewart
2015-02-01
Full Text Available The determination of the piezoelectric coefficient of thin films using interferometry is hindered by bending contributions. Using finite element analysis (FEA simulations, we show that the Lefki and Dormans approximations using either single or double-beam measurements cannot be used with finite top electrode sizes. We introduce a novel method for characterising piezoelectric thin films which uses a differential measurement over the discontinuity at the electrode edge as an internal reference, thereby eliminating bending contributions. This step height is shown to be electrode size and boundary condition independent. An analytical expression is derived which gives good agreement with FEA predictions of the step height.
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E. Tohidi
2014-01-01
Full Text Available The problem of solving several types of one-dimensional parabolic partial differential equations (PDEs subject to the given initial and nonlocal boundary conditions is considered. The main idea is based on direct collocation and transforming the considered PDEs into their associated algebraic equations. After approximating the solution in the Legendre matrix form, we use Legendre operational matrix of differentiation for representing the mentioned algebraic equations clearly. Three numerical illustrations are provided to show the accuracy of the presented scheme. High accurate results with respect to the Bernstein Tau technique and Sinc collocation method confirm this accuracy.
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Silva, Davi J.M.; Nunes, Carlos E.A.; Alves Filho, Hermes; Barros, Ricardo C., E-mail: davijmsilva@yahoo.com.br, E-mail: ceanunes@yahoo.com.br, E-mail: rcbarros@pq.cnpq.br [Secretaria Municipal de Educacao de Itaborai, RJ (Brazil); Universidade Estacio de Sa (UNESA), Rio de Janeiro, RJ (Brazil); Universidade do Estado do Rio de Janeiro (UERJ), Novra Friburgo, RJ (Brazil). Instituto Politecnico. Departamento de Modelagem Computacional
2017-11-01
Discussed here is the accuracy of approximate albedo boundary conditions for energy multigroup discrete ordinates (S{sub N}) eigenvalue problems in two-dimensional rectangular geometry for criticality calculations in neutron fission reacting systems, such as nuclear reactors. The multigroup (S{sub N}) albedo matrix substitutes approximately the non-multiplying media around the core, e.g., baffle and reflector, as we neglect the transverse leakage terms within these non-multiplying regions. Numerical results to a typical model problem are given to illustrate the accuracy versus the computer running time. (author)
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Inayat Ullah
2013-01-01
Full Text Available A steady two-dimensional axisymmetric flow of an incompressible viscous fluid under the influence of a uniform transverse magnetic field with slip boundary condition is studied. An ordinary nonlinear differential equation is formed by transforming the Navier-Stokes equations using the transformation . Differential transform and optimal homotopy analysis methods have been used to obtain the solutions by varying pertinent flow parameters. By using residuals in each case, the validity of solutions is established. Excellent results are obtained by using the proposed schemes. The influence of different parameters on the flow is shown through graphs.
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Aqlan Mohammed H.
2016-01-01
Full Text Available We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
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Nicolae Tarfulea
2009-10-01
Full Text Available We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.
Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields
Rasband, S. N.; Turner, L.
1981-01-01
It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.
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Nee Alexander
2015-01-01
Full Text Available Mathematical modeling of radiant heating of a closed rectangular area under conditions of convective heat transfer at the external boundaries is passed. The fields of temperature and stream function, illustrating the unsteady nature of the heat transfer were obtained. The extent influence of convective heat transfer at the external boundaries on the circulating flows formation in the gas cavity are shown.
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Ahmed Alsaedi
2016-08-01
Full Text Available In this article, we study a boundary value problem of coupled systems of nonlinear Riemann-Liouvillle fractional integro-differential equations supplemented with nonlocal Riemann-Liouvillle fractional integro-differential boundary conditions. Our results rely on some standard tools of the fixed point theory. An illustrative example is also discussed.
Boundary conditions for General Relativity on AdS{sub 3} and the KdV hierarchy
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Pérez, Alfredo; Tempo, David; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-06-20
It is shown that General Relativity with negative cosmological constant in three spacetime dimensions admits a new family of boundary conditions being labeled by a nonnegative integer k. Gravitational excitations are then described by “boundary gravitons” that fulfill the equations of the k-th element of the KdV hierarchy. In particular, k=0 corresponds to the Brown-Henneaux boundary conditions so that excitations are described by chiral movers. In the case of k=1, the boundary gravitons fulfill the KdV equation and the asymptotic symmetry algebra turns out to be infinite-dimensional, abelian and devoid of central extensions. The latter feature also holds for the remaining cases that describe the hierarchy (k>1). Our boundary conditions then provide a gravitational dual of two noninteracting left and right KdV movers, and hence, boundary gravitons possess anisotropic Lifshitz scaling with dynamical exponent z=2k+1. Remarkably, despite spacetimes solving the field equations are locally AdS, they possess anisotropic scaling being induced by the choice of boundary conditions. As an application, the entropy of a rotating BTZ black hole is precisely recovered from a suitable generalization of the Cardy formula that is compatible with the anisotropic scaling of the chiral KdV movers at the boundary, in which the energy of AdS spacetime with our boundary conditions depends on z and plays the role of the central charge. The extension of our boundary conditions to the case of higher spin gravity and its link with different classes of integrable systems is also briefly addressed.
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Emilio Sassine
2017-12-01
Full Text Available The reliable estimation of buildings energy needs for cooling and heating is essential for any eventual thermal improvement of the envelope or the HVAC equipment. This paper presents an interesting method to evaluate the thermal performance of a massive wall by using the frequency-domain regression (FDR method to calculate CTF coefficients by means of the Fourier transform. The method is based on the EN ISO 13786 (2007 procedure by using the Taylor expansion for the elements of the heat matrix. Numerical results were validated through an experimental heating box with stochastic boundary conditions on one side of the wall representing real weather conditions and constant temperature profile on the other side representing the inside ambiance in real cases. Finally, a frequency analysis was performed in order to assess the validity and accuracy of the method used. The results show that development to the second order is sufficient to predict the thermal behavior of the studied massive wall in the range of frequencies encountered in the building applications (one hour time step. This method is useful for thermal transfer analysis in real weather conditions where the outside temperature is stochastic; it also allows the evaluation of the thermal performance of a wall through a frequency analysis.
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Adamopoulou, Theodora [Department of Environmental and Natural Resources Management, University of Western Greece (formerly of University of Ioannina), Seferi 2, Agrinio GR30100 (Greece); Papadaki, Maria I., E-mail: mpapadak@cc.uoi.gr [Department of Environmental and Natural Resources Management, University of Western Greece (formerly of University of Ioannina), Seferi 2, Agrinio GR30100 (Greece); Kounalakis, Manolis [Department of Environmental and Natural Resources Management, University of Western Greece (formerly of University of Ioannina), Seferi 2, Agrinio GR30100 (Greece); Vazquez-Carreto, Victor; Pineda-Solano, Alba [Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A and M University, College Station, TX 77843 (United States); Wang, Qingsheng [Department of Fire Protection and Safety and Department of Chemical Engineering, Oklahoma State University, 494 Cordell South, Stillwater, OK 74078 (United States); Mannan, M.Sam [Mary Kay O’Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A and M University, College Station, TX 77843 (United States)
2013-06-15
Highlights: • Hydroxylamine thermal decomposition enthalpy was measured using larger quantities. • The rate at which heat is evolved depends on hydroxylamine concentration. • Decomposition heat is strongly affected by the conditions and the selected baseline. • The need for enthalpy measurements using a larger reactant mass is pinpointed. • Hydroxylamine decomposition in the presence of argon is much faster than in air. -- Abstract: Thermal decomposition of hydroxylamine, NH{sub 2}OH, was responsible for two serious accidents. However, its reactive behavior and the synergy of factors affecting its decomposition are not being understood. In this work, the global enthalpy of hydroxylamine decomposition has been measured in the temperature range of 130–150 °C employing isoperibolic calorimetry. Measurements were performed in a metal reactor, employing 30–80 ml solutions containing 1.4–20 g of pure hydroxylamine (2.8–40 g of the supplied reagent). The measurements showed that increased concentration or temperature, results in higher global enthalpies of reaction per unit mass of reactant. At 150 °C, specific enthalpies as high as 8 kJ per gram of hydroxylamine were measured, although in general they were in the range of 3−5 kJ g{sup −1}. The accurate measurement of the generated heat was proven to be a cumbersome task as (a) it is difficult to identify the end of decomposition, which after a fast initial stage, proceeds very slowly, especially at lower temperatures and (b) the environment of gases affects the reaction rate.
Hu, Pan; Wu, Tao; Wang, Hui-Zhi; Qi, Xin-Zheng; Yao, Jie; Cheng, Xiao-Dong; Chen, Wei; Zhang, Ying-Ze
2017-02-01
To observe the effects of boundary conditions and connect conditions on biomechanics predictions in finite element (FE) pelvic models. Three FE pelvic models were constructed to analyze the effect of boundary conditions and connect conditions in the hip joint: an intact pelvic model assumed contact of the hip joint on both sides (Model I); and a pelvic model assumed the hip joint connecting surfaces fused together with (Model II) or without proximal femurs (Model III). The model was validated by bone surface strains obtained from strain gauges in an in vitro pelvic experiment. Vertical load was applied to the pelvic specimen, and the same load was simulated in the FE model. There was a strong correlation between the FE analysis results of Model I and the experimental results (R 2 = 0.979); meanwhile, the correlation coefficient and the linear regression function increased slightly with increasing load force. Comparing the three models, the stress values in the point near the pubic symphysis in Model III were 48.52 and 39.1% lower, respectively, in comparison with Models I and II. Furthermore, the stress values on the dome region of the acetabulum in Models II and III were 103.61 and 390.53% less than those of Model I. Besides, the posterior acetabular wall stress values of Model II were 197.15 and 305.17% higher than those of Models I and III, respectively. These findings suggest that the effect of the connect condition in the hip joint should not be neglected, especially in studies related to clinical applications. © 2017 Chinese Orthopaedic Association and John Wiley & Sons Australia, Ltd.
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Salomatov Vladimir
2016-01-01
Full Text Available This work is dedicated to the search for the exact analytical dependences of microwave heating due to absorption of a plane electromagnetic wave by coal layer with asymmetric and non-uniform heat dissipation conditions I and III kind. Some of simplifications have been made, such as one-dimensional problem, uniformity and isotropic coal material, and the constancy of the electrical properties of thermal coal during heating of microwave radiation. This has led to the fact that the Maxwell’s task is solved separately from the Fourier’s task, and a heat source generated in the carbon layer is subject to Bouguer law. For the system of equations of heat transfer has been found a new dependent variable, which is to simplify the search for a final solution. All this has given the possibility of finding rigorous analytical solution of the problem of microwave heating of the coal layer in the presence of asymmetric and inhomogeneous boundary conditions I and III kind.
Buckling of Nonprismatic Column on Varying Elastic Foundation with Arbitrary Boundary Conditions
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Ahmad A. Ghadban
2017-01-01
Full Text Available Buckling of nonprismatic single columns with arbitrary boundary conditions resting on a nonuniform elastic foundation may be considered as the most generalized treatment of the subject. The buckling differential equation for such columns is extremely difficult to solve analytically. Thus, the authors propose a numerical approach by discretizing the column into a finite number of segments. Each segment has constants E (modulus of elasticity, I (moment of inertia, and β (subgrade stiffness. Next, an exact analytical solution is derived for each prismatic segment resting on uniform elastic foundation. These segments are then assembled in a matrix from which the critical buckling load is obtained. The derived formulation accounts for different end boundary conditions. Validation is performed by benchmarking the present results against analytical solutions found in the literature, showing excellent agreement. After validation, more examples are solved to illustrate the power and flexibility of the proposed method. Overall, the proposed method provides reasonable results, and the examples solved demonstrate the versatility of the developed approach and some of its many possible applications.
Spectroscopy of {sup 12}C within the boundary condition for three-body resonant states
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Kurokawa, Chie [Meme Media Laboratory, Hokkaido University, Sapporo 060-8628 (Japan)]. E-mail: chie@nucl.sci.hokudai.ac.jp; Kato, Kiyoshi [Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810 (Japan)
2007-08-01
The 3{alpha}-cluster structure of excited states in {sup 12}C is investigated by taking into account the correct boundary condition for three-body resonant states. In this study, we adopt the Complex Scaling Method (CSM), which enables us to obtain the resonant states that can be described as square integrable states with the same boundary conditions as those of the bound states, and calculate not only resonance energies but also the total decay widths of the 3{alpha} system. We compare the calculated resonance parameters to the experimental data and also to the previous 3{alpha} model results obtained with a bound state approximation. Our results well explain the many observed levels and give an assurance for the presence of the second 2{sup +} state, which is expected by the 3{alpha} model calculations with the approximations of bound state or two-body scattering. As for the negative-parity states, it is considered that the calculated 4{sup -} state is assigned to the observed E{sub x}=13.4MeV state. Through the calculation of channel amplitudes, the obtained third 0{sup +} state is found to have a s-wave dominant and a more dilute structure compared to the second 0{sup +} state.
Itu, Lucian; Sharma, Puneet; Suciu, Constantin; Moldoveanu, Florin; Comaniciu, Dorin
2017-03-01
We propose a hierarchical parameter estimation framework for performing patient-specific hemodynamic computations in arterial models, which use structured tree boundary conditions. A calibration problem is formulated at each stage of the hierarchical framework, which seeks the fixed point solution of a nonlinear system of equations. Common hemodynamic properties, like resistance and compliance, are estimated at the first stage in order to match the objectives given by clinical measurements of pressure and/or flow rate. The second stage estimates the parameters of the structured trees so as to match the values of the hemodynamic properties determined at the first stage. A key feature of the proposed method is that to ensure a large range of variation, two different structured tree parameters are personalized for each hemodynamic property. First, the second stage of the parameter estimation framework is evaluated based on the properties of the outlet boundary conditions in a full body arterial model: the calibration method converges for all structured trees in less than 10 iterations. Next, the proposed framework is successfully evaluated on a patient-specific aortic model with coarctation: only six iterations are required for the computational model to be in close agreement with the clinical measurements used as objectives, and overall, there is a good agreement between the measured and computed quantities. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Effect of 3D boundary conditions on rift propagation or failure to break.
Le Pourhiet, Laetitia; Watremez, Louise; Delescluse, Matthias
2017-04-01
Oblique rift segments are generally modelled using two type of set-ups. The first one consist of off-set weak notches which are pulled in a cylindrical manner, the second one consist at pulling obliquely on wide weak zone inside which a system of en-echellon grabben can develop. These two set up produce diverging segments of constant age and younger oblique segments which localise after some delays which depends on the offset of the diverging segments and the rheology of the lithosphere. In this study, we propose a different set-up which consist at seeding only one diverging weak segments and at letting the continental rupture propagate through the model in order to assess 1/ how 3D boundary conditions affect the speed on propagation of the continental break-up and 2/ how the structure that form at the front of the propagating break-up affect the propagation it-self. We find that a cylindrical boundary condition or extension in the direction of propagation favour very rapid continental break-up propagation, narrow rift zones and extremely linear diverging segments. On the contrary, when a slight compression is applied in the direction of rift propagation. The propagation is slow and might even stop completely. This slow down in propagation results in an increase of pre-breakup structuration of the margins and can even cause segmentation of final spreading. The numerical models are finally compared to natural examples from the Atlantic and the South China Sea.
Rudyak, V. Yu.; Krakhalev, M. N.; Sutormin, V. S.; Prishchepa, O. O.; Zyryanov, V. Ya.; Liu, J.-H.; Emelyanenko, A. V.; Khokhlov, A. R.
2017-11-01
Polymer-dispersed liquid crystal composites have been a focus of study for a long time for their unique electro-optical properties and manufacturing by "bottom-up" techniques at large scales. In this paper, nematic liquid crystal oblate droplets with conical boundary conditions (CBCs) under the action of electric field were studied by computer simulations and polarized optical microscopy. Droplets with CBCs were shown to prefer an axial-bipolar structure, which combines a pair of boojums and circular disclinations on a surface. In contrast to droplets with degenerate planar boundary conditions (PBCs), hybridization of the two structure types in droplets with CBCs leads to a two-minima energy profile, resulting in an abrupt structure transition and bistable behavior of the system. The nature of the low-energy barrier in droplets with CBCs makes it highly sensitive to external stimuli, such as electric or magnetic fields, temperature, and light. In particular, the value of the electric field of the structure reorientation in droplets with CBCs was found to be a few times smaller than the one for droplets with PBCs, and the droplet state remained stable after switching off the voltage.
Charged hadrons in local finite-volume QED+QCD with C* boundary conditions
Lucini, Biagio; Ramos, Alberto; Tantalo, Nazario
2016-01-01
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charg...
Sensitivity of Pliocene climate simulations in MRI-CGCM2.3 to respective boundary conditions
Kamae, Youichi; Yoshida, Kohei; Ueda, Hiroaki
2016-08-01
Accumulations of global proxy data are essential steps for improving reliability of climate model simulations for the Pliocene warming climate. In the Pliocene Model Intercomparison Project phase 2 (PlioMIP2), a part project of the Paleoclimate Modelling Intercomparison Project phase 4, boundary forcing data have been updated from the PlioMIP phase 1 due to recent advances in understanding of oceanic, terrestrial and cryospheric aspects of the Pliocene palaeoenvironment. In this study, sensitivities of Pliocene climate simulations to the newly archived boundary conditions are evaluated by a set of simulations using an atmosphere-ocean coupled general circulation model, MRI-CGCM2.3. The simulated Pliocene climate is warmer than pre-industrial conditions for 2.4 °C in global mean, corresponding to 0.6 °C warmer than the PlioMIP1 simulation by the identical climate model. Revised orography, lakes, and shrunk ice sheets compared with the PlioMIP1 lead to local and remote influences including snow and sea ice albedo feedback, and poleward heat transport due to the atmosphere and ocean that result in additional warming over middle and high latitudes. The amplified higher-latitude warming is supported qualitatively by the proxy evidences, but is still underestimated quantitatively. Physical processes responsible for the global and regional climate changes should be further addressed in future studies under systematic intermodel and data-model comparison frameworks.
Investigating the non-classical boundary conditions relevant to strain gradient theories
Jafari, Akbar; Ezzati, Meysam
2017-02-01
In the present study, two classes of non-classical constitutive equations consisting of the first and the second order strain gradients theories (FSG and SSG) were applied in order to develop the governing equations of static and free vibrational behavior of beam structures. The governing equations in orders of six and eight were constructed for FSG and SSG theories, respectively. Therefore, higher order or in other words non-classical boundary conditions (HOBCs or NCBCs) came into play in addition to the classical ones (CBCs). Some explanations were presented about the concept of the non-classical boundary conditions. Analytical and finite element (FE) approaches were employed to solve the governing equations. The analytical solutions were utilized in validation and convergence study of FE results. Comparisons were made with the relevant data reported in the open literature; however, to the best of the authors' knowledge, few references have been published on SSG theory and HOBCs. In the numerical studies, the effects of applying different combinations of CBCs and HOBCs to the static and free vibration behaviors of the beam were investigated. Moreover, the impacts of non-classical elastic constants and the beam size on its behavior were also studied.
Mackowski, Daniel W.; Knight, Roy W.
1993-01-01
One of the most promising applications of microgravity (micro-g) environments is the manufacture of exotic and high-quality crystals in closed cylindrical ampoules using physical vapor transport (PVT) processes. The quality enhancements are believed to be due to the absence of buoyant convection in the weightless environment - resulting in diffusion-limited transport of the vapor. In a typical experiment, solid-phase sample material is initially contained at one end of the ampoule. The sample is made to sublime into the vapor phase and deposit onto the opposite end by maintaining the source at an elevated temperature with respect to the deposit. Identification of the physical factors governing both the rates and uniformity of crystal growth, and the optimization of the micro-g technology, will require an accurate modeling of the vapor transport within the ampoule. Previous micro-g modeling efforts have approached the problem from a 'classical' convective/diffusion formulation, in which convection is driven by the action of buoyancy on thermal and solutal density differences. The general conclusion of these works have been that in low gravity environments the effect of buoyancy on vapor transport is negligible, and vapor transport occurs in a diffusion-limited mode. However, it has been recently recognized than in the non-isothermal (and often low total pressure) conditions encountered in ampoules, the commonly-assumed no-slip boundary condition to the differential equations governing fluid motion can be grossly unrepresentative of the actual situation. Specifically, the temperature gradients can give rise to thermal creep flows at the ampoule side walls. In addition, temperature gradients in the vapor itself can, through the action of thermal stress, lead to bulk fluid convection.
CSIR Research Space (South Africa)
Shatalov, MY
2007-04-01
Full Text Available . The dispersion curves are plotted for propagating waves for non-axisymmetric vibrations of the cylinder. It is shown that the dispersion curves are sensitive to the form of electric boundary conditions...
Directory of Open Access Journals (Sweden)
Muhammad Tahir
2012-11-01
Full Text Available This article shows the uniqueness of a solution to a Bitsadze system of equations, with a boundary-value problem that has four additional single point conditions. It also shows how to construct the solution.
Directory of Open Access Journals (Sweden)
Vali Parvaneh
2011-01-01
Full Text Available The effects of boundary conditions and defects on the buckling behavior of SWCNTs are investigated using a structural mechanics model. Due to the application of carbon nanotubes in different fields such as NEMS, where they are subjected to different loading and boundary conditions, an investigation of buckling behavior of nanotubes with different boundary conditions is necessary. Critical buckling loads and the effects of vacancy and Stone-Wales defects were studied for zigzag and armchair nanotubes with various boundary conditions and aspect ratios (length/diameter. The comparison of our results with those of the buckling of shells with cutouts indicates that vacancy defects in carbon nanotubes can most likely be modeled as cutouts of the shells. Finally, a hybrid vacancy defect and Stone-Wales defect are also developed, and their effect on the critical buckling loads is studied.
Vignon-Clementel, Irene; Jansen, K E; Taylor, C A; 10.1080/10255840903413565
2010-01-01
The simulation of blood flow and pressure in arteries requires outflow boundary conditions that incorporate models of downstream domains. We previously described a coupled multidomain method to couple analytical models of the downstream domains with 3D numerical models of the upstream vasculature. This prior work either included pure resistance boundary conditions or impedance boundary conditions based on assumed periodicity of the solution. However, flow and pressure in arteries are not necessarily periodic in time due to heart rate variability, respiration, complex transitional flow or acute physiological changes. We present herein an approach for prescribing lumped parameter outflow boundary conditions that accommodate transient phenomena. We have applied this method to compute haemodynamic quantities in different physiologically relevant cardiovascular models, including patient-specific examples, to study non-periodic flow phenomena often observed in normal subjects and in patients with acquired or congen...
Planck scale boundary conditions in the standard model with singlet scalar dark matter
Energy Technology Data Exchange (ETDEWEB)
Haba, Naoyuki [Graduate School of Science and Engineering, Shimane University, Matsue, Shimane 690-8504 (Japan); Kaneta, Kunio [Kavli IPMU (WPI), The University of Tokyo, Kashiwa, Chiba 277-8568 (Japan); Takahashi, Ryo [Graduate School of Science and Engineering, Shimane University, Matsue, Shimane 690-8504 (Japan)
2014-04-04
We investigate Planck scale boundary conditions on the Higgs sector of the standard model with a gauge singlet scalar dark matter. We will find that vanishing self-coupling and Veltman condition at the Planck scale are realized with the 126 GeV Higgs mass and top pole mass, 172 GeV≲M{sub t}≲173.5 GeV, where a correct abundance of scalar dark matter is obtained with mass of 300 GeV≲m{sub S}≲1 TeV. It means that the Higgs potential is flat at the Planck scale, and this situation can not be realized in the standard model with the top pole mass.
Baroclinic Planetary Boundary-Layer Model for Neutral and Stable Stratification Conditions
Djolov, G. D.; Yordanov, D. L.; Syrakov, D. E.
The temperature and wind profiles in abaroclinic atmospheric boundary layer (ABL) are investigated.Assuming stationary conditions, the turbulent state in the ABL forstable and neutral conditions is uniquely determined by the Rossbynumber, the external stratification parameter and two externalbaroclinic parameters. A simple two-layer baroclinic model isdeveloped. It consists of a surface layer (SL) and overlyingEkman-type layer. The system of dynamic and heat transfer equations isclosed using K-theory. In the SL the turbulent exchangecoefficient is consistent with the results of similarity theorywhile in the Ekman layer it is assumed constant. The universalfunctions in the resistance, heat and humidity transfer laws arededuced from the analytical solutions for the wind and temperatureprofiles. The solutions of the ABL resistance laws for theinternal ABL parameters, necessary for the calculations of the ABLprofiles, are approximated in terms of the external ABLparameters. Favourable agreement of model results with theavailable experimental data is demonstrated.
On the Boundary Condition for Water at a Hydrophobic, Dense Surface
Walther, J. H.; Jaffe, R. L.; Werder, T.; Halicioglu, T.; Koumoutsakos, P.
2002-01-01
We study the no-slip boundary conditions for water at a hydrophobic (graphite) surface using non-equilibrium molecular-dynamics simulations. For the planar Couette flow, we find a slip length of 64 nm at 1 bar and 300 K, decreasing with increasing system pressure to a value of 31 nm at 1000 bar. Changing the properties of the interface to from hydrophobic to strongly hydrophilic reduces the slip to 14 nm. Finally, we study the flow of water past an array of carbon nanotubes mounted in an inline configuration with a spacing of 16.4 x 16.4 nm. For tube diameters of 1.25 and 2.50 nm we find drag coefficients in good agreement with the macroscopic, Navier-Stokes values. For carbon nanotubes, the no-slip condition is valid to within the definition of the position of the interface.
Directory of Open Access Journals (Sweden)
Handlovičová Angela
2016-01-01
Full Text Available In this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.
Directory of Open Access Journals (Sweden)
Hua-Cheng Zhou
2016-02-01
Full Text Available This article is devoted to investigating the existence of solutions to fractional multi-point boundary-value problems at resonance in a Hilbert space. More precisely, the dimension of the kernel of the fractional differential operator with the boundary conditions be any positive integer. We point out that the problem is new even when the system under consideration is reduced to a second-order ordinary differential system with resonant boundary conditions. We show that the considered system admits at least a solution by applying coincidence degree theory first introduced by Mawhin. An example is presented to illustrate our results.
Pendlebury, Diane; Gravel, Sylvie; Moran, Michael D.; Lupu, Alexandru
2018-02-01
A regional air quality forecast model, GEM-MACH, is used to examine the conditions under which a limited-area air quality model can accurately forecast near-surface ozone concentrations during stratospheric intrusions. Periods in 2010 and 2014 with known stratospheric intrusions over North America were modelled using four different ozone lateral boundary conditions obtained from a seasonal climatology, a dynamically-interpolated monthly climatology, global air quality forecasts, and global air quality reanalyses. It is shown that the mean bias and correlation in surface ozone over the course of a season can be improved by using time-varying ozone lateral boundary conditions, particularly through the correct assignment of stratospheric vs. tropospheric ozone along the western lateral boundary (for North America). Part of the improvement in surface ozone forecasts results from improvements in the characterization of near-surface ozone along the lateral boundaries that then directly impact surface locations near the boundaries. However, there is an additional benefit from the correct characterization of the location of the tropopause along the western lateral boundary such that the model can correctly simulate stratospheric intrusions and their associated exchange of ozone from stratosphere to troposphere. Over a three-month period in spring 2010, the mean bias was seen to improve by as much as 5 ppbv and the correlation by 0.1 depending on location, and on the form of the chemical lateral boundary condition.
Characterizing summertime chemical boundary conditions for airmasses entering the US West Coast
Directory of Open Access Journals (Sweden)
G. G. Pfister
2011-02-01
Full Text Available The objective of this study is to analyze the pollution inflow into California during summertime and how it impacts surface air quality through combined analysis of a suite of observations and global and regional models. The focus is on the transpacific pollution transport investigated by the NASA Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS mission in June 2008. Additional observations include satellite retrievals of carbon monoxide and ozone by the EOS Aura Tropospheric Emissions Spectrometer (TES, aircraft measurements from the MOZAIC program and ozonesondes. We compare chemical boundary conditions (BC from the MOZART-4 global model, which are commonly used in regional simulations, with measured concentrations to quantify both the accuracy of the model results and the variability in pollution inflow. Both observations and model reflect a large variability in pollution inflow on temporal and spatial scales, but the global model captures only about half of the observed free tropospheric variability. Model tracer contributions show a large contribution from Asian emissions in the inflow. Recirculation of local US pollution can impact chemical BC, emphasizing the importance of consistency between the global model simulations used for BC and the regional model in terms of emissions, chemistry and transport. Aircraft measurements in the free troposphere over California show similar concentration ranges, variability and source contributions as free tropospheric air masses over ocean, but caution has to be taken that local pollution aloft is not misinterpreted as inflow. A flight route specifically designed to sample boundary conditions during ARCTAS-CARB showed a prevalence of plumes transported from Asia and thus may not be fully representative for average inflow conditions. Sensitivity simulations with a regional model with altered BCs show that the temporal variability in the pollution inflow does
Investigating effects of boundary conditions on the evaluation of R-factor of un-braced steel frames
Directory of Open Access Journals (Sweden)
Masood M.M. Irheem
2017-08-01
Full Text Available Design of Structures to resist seismic load depends on the theory of dissipation in elastic of energy that already exists in response modification factor “R-factor”. The main problem in codes gives a constant value for R-factor, since change in boundary conditions of building change in behavior of steel frame structures and that effect on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of un-braced steel frames under change in boundary conditions as change in the direction of strong axis of column and support type beside to variation in story and bay number to be 9 frame and each frame has 8 different boundary conditions as sum of 72 case for analysis. These frames were analyzed by using nonlinear static “pushover” analysis using SAP2000 program. As a result of this study R-factor does not has a constant value, when change in boundary conditions R-factor directly changes, minimum value of 8 boundary conditions is close to the code value that is mean the code is more conservative and give a large factor of safety. Ductility reduction factor increases with increasing number of story for all boundary conditions, but overstrength has different rule. Response modification factor, overstrength factor and ductility reduction factor decrease when fundamentals period increasing for the studied frames.
Thermal denaturation of sunflower globulins in low moisture conditions
Energy Technology Data Exchange (ETDEWEB)
Rouilly, A.; Orliac, O.; Silvestre, F.; Rigal, L
2003-03-05
DSC analysis in pressure resisting pans of sunflower oil cake makes appear the endothermic peak of sunflower globulins denaturation. Its temperature decreases from 189.5 to 119.9 deg. C while the corresponding enthalpy increases from 2.6 to 3.3 J/g of sample, or from 6.7 to 12.2 J/g of dry protein, when the samples moisture content varies from 0 to 30.0% of the total weight. The plot of the denaturation temperature versus the moisture content is not linear but has a rounded global shape and seems to follow the hydration behavior of the proteins, modeled with the sorption isotherm. As it can be seen on scanning electron microscopy (SEM) micrographs, protein corpuscles 'melt' after such a thermal treatment and large aggregates form by coagulation. Moisture dependence of the 'fusion' temperature of native proteic organization, in low moisture conditions, offers so a new characterization method for the use of vegetable proteins in agro-materials.
Finite-Rate Ablation Boundary Conditions for Carbon-Phenolic Heat-Shield
Chen, Y.-K.; Milos, Frank S.
2003-01-01
A formulation of finite-rate ablation surface boundary conditions, including oxidation, nitridation, and sublimation of carbonaceous material with pyrolysis gas injection, has been developed based on surface species mass conservation. These surface boundary conditions are discretized and integrated with a Navier-Stokes solver. This numerical procedure can predict aerothermal heating, chemical species concentration, and carbonaceous material ablation rate over the heatshield surface of re-entry space vehicles. In this study, the gas-gas and gas-surface interactions are established for air flow over a carbon-phenolic heatshield. Two finite-rate gas-surface interaction models are considered in the present study. The first model is based on the work of Park, and the second model includes the kinetics suggested by Zhluktov and Abe. Nineteen gas phase chemical reactions and four gas-surface interactions are considered in the present model. There is a total of fourteen gas phase chemical species, including five species for air and nine species for ablation products. Three test cases are studied in this paper. The first case is a graphite test model in the arc-jet stream; the second is a light weight Phenolic Impregnated Carbon Ablator at the Stardust re-entry peak heating conditions, and the third is a fully dense carbon-phenolic heatshield at the peak heating point of a proposed Mars Sample Return Earth Entry Vehicle. Predictions based on both finite-rate gas- surface interaction models are compared with those obtained using B' tables, which were created based on the chemical equilibrium assumption. Stagnation point convective heat fluxes predicted using Park's finite-rate model are far below those obtained from chemical equilibrium B' tables and Zhluktov's model. Recession predictions from Zhluktov's model are generally lower than those obtained from Park's model and chemical equilibrium B' tables. The effect of species mass diffusion on predicted ablation rate is also
He, Zhuohui J.; Chang, Clarence T.
2017-01-01
Combustion dynamics data were collected at the NASA Glenn Research Center's CE-5 flame tube test facility under combustor outlet choked conditions. Two 9-point Swirl-Venturi Lean Direct Injection (SV-LDI) configurations were tested in a rectangular cuboid combustor geometry. Combustion dynamic data were measured at different engine operational conditions up to inlet air pressure and temperature of 24.13 bar and 828 K, respectively. In this study, the effects of acoustic cavity resonance, precessing vortex core (PVC), and non-uniform thermal expansion on the dynamic noise spectrum are identified by comparing the dynamic data that collected at various combustor inlet conditions along with combustor geometric calculations. The results show that the acoustic cavity resonance noises were seen in the counter-rotating pilot configuration but not in the co-rotating pilot configuration. Dynamic pressure noise band at around 0.9 kHz was only detected at the P'41 location (9.8 cm after fuel injector face) but not at the P'42 location (29 cm after the fuel injector face); the amplitude of this noise band depended on the thermal expansion ratio (T4/T3). The noise band at around 1.8 kHz was found to depend on the inlet air pressure or the air density inside the combustor. The PVC frequency was not observed in these two configurations.
Towards Dynamic Realism for Solar Wind Boundary Conditions Used in Global Heliospheric Models
Thatcher, L. J.; Mueller, H.; Heiderer, A.
2009-12-01
The two Voyager missions have demonstrated the highly time-dependent nature of the outer heliosphere, and the measurements from IBEX will require, for proper interpretation of the data, theoretical models that incorporate this time-dependence. Our research group uses multifluid HD models of the global heliosphere with idealized, simplified solar wind conditions for the inner boundary of the simulations. For this contribution, solar wind data of the past four solar cycles, taken from NASA's OMNI data set, is used to build a realistic inner boundary data set for our simulations. This data set is time-dependent so as to realistically represent changes in solar wind characteristics through the solar cycle and capture the corresponding transient effects in the heliosphere. We have had preliminary success with our data set, extrapolating OMNI data, which is entirely Sun-Earth directed, to fill the entire ecliptic disc. The success of the results confirmed to us that, with some improvements, our central technique would create a solar win data set sufficiently realistic for heliospheric simulations. To refine the data set, independent analyses and categorization of data will be performed. Four solar wind regimes are envisioned, undisturbed fast and slow wind, ICME wind, and 'other' wind, the catchall category. After we have categorized the entire OMNI data set, our extrapolations will represent the behavior of each regime in a more realistic fashion. Preliminary results for global heliospheric simulations will be presented.
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Auken, Esben; Han, Muran; Li, Jianhui
2017-10-01
We implemented an edge-based finite element time domain (FETD) modeling algorithm for simulating controlled-source electromagnetic (CSEM) data. The modeling domain is discretized using unstructured tetrahedral mesh and we consider a finite difference discretization of time using the backward Euler method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies.
Velocity and magnetic field measurements of Taylor plumes in SSX under different boundary conditions
Kaur, Manjit; Brown, M. R.; Han, J.; Shrock, J. E.; Schaffner, D. A.
2016-10-01
The SSX device has been modified by the addition of a 1 m long glass extension for accommodating pulsed theta pinch coils. The Taylor plumes are launched from a magnetized plasma gun and flow to an expansion volume downstream. The time of flight (TOF) measurements of these plumes are carried out using a linear array of Ḃ probes (separated by 10cm). TOF of the plasma plumes from one probe location to the next is determined by direct comparison of the magnetic field structures as well as by carrying out a cross-correlation analysis. With the glass boundary, the typical velocity of the Taylor plumes is found to be 25km /s , accompanied by a fast plasma (>= 50km /s) at the leading edge. Magnetic field embedded in the Taylor plumes is measured in the expansion chamber using a three-dimensional array of Ḃ probes and is found to be 700G . Some flux conservation of the Taylor plumes is provided by using a resistive (soak time 3 μs) and a mesh (soak time 170 μs > discharge time) liner around the glass tube for improving the downstream Taylor state velocity as well as the magnetic field. The results from these different boundary conditions will be presented. Work supported by DOE OFES and ARPA-E ALPHA programs.
On the Energetics of a Damped Beam-Like Equation for Different Boundary Conditions
Directory of Open Access Journals (Sweden)
SAJAD HUSSAIN SANDILO
2017-04-01
Full Text Available In this paper, the energy estimates for a damped linear homogeneous beam-like equation will be considered. The energy estimates will be studied for different BCs (Boundary Conditions for the axially moving continuum. The problem has physical and engineering application. The applications are mostly occurring in models of conveyor belts and band-saw blades. The research study is focused on the Dirichlet, the Neumann and the Robin type of BCs. From physical point of view, the considered mathematical model expounds the transversal vibrations of a moving belt system or moving band-saw blade. It is assumed that a viscous damping parameter and the horizontal velocity are positive and constant. It will be shown in this paper that change in geometry or the physics of the boundaries can affect the stability properties of the system in general and stability depends on the axial direction of the motion. In all cases of the BCs, it will be shown that there is energy decay due to viscous damping parameter and it will also be shown that in some cases there is no conclusion whether the beam energy decreases or increases. The detailed physical interpretation of all terms and expressions is provided and studied in detail.
Thermal performance of marketed SDHW systems under laboratory conditions
DEFF Research Database (Denmark)
Furbo, Simon; Andersen, Elsa; Fan, Jianhua
A test facility for solar domestic hot water systems, SDHW systems was established at the Technical University of Denmark in 1992. During the period 1992-2012 21 marketed SDHW systems, 16 systems from Danish manufacturers and 5 systems from manufacturers from abroad, have been tested in the test ...... comfort, avoiding simple errors, using the low flow principle and heat stores with a high degree of thermal stratification and by using components with good thermal characteristics....... to the models were fitted in such a way, that the calculated thermal performance is in good agreement with the measured thermal performance, both for a typical winter period and for a typical summer period. In this way it is possible to use the simulation models to calculate the yearly thermal performance...