Surface free energy for systems with integrable boundary conditions
International Nuclear Information System (INIS)
Goehmann, Frank; Bortz, Michael; Frahm, Holger
2005-01-01
The surface free energy is the difference between the free energies for a system with open boundary conditions and the same system with periodic boundary conditions. We use the quantum transfer matrix formalism to express the surface free energy in the thermodynamic limit of systems with integrable boundary conditions as a matrix element of certain projection operators. Specializing to the XXZ spin-1/2 chain we introduce a novel 'finite temperature boundary operator' which characterizes the thermodynamical properties of surfaces related to integrable boundary conditions
Boundary conditions for soft glassy flows: slippage and surface fluidization.
Mansard, Vincent; Bocquet, Lydéric; Colin, Annie
2014-09-28
We explore the question of surface boundary conditions for the flow of a dense emulsion. We make use of microlithographic tools to create surfaces with well controlled roughness patterns and measure using dynamic confocal microscopy both the slip velocity and the shear rate close to the wall, which we relate to the notion of surface fluidization. Both slippage and wall fluidization depend non-monotonously on the roughness. We interpret this behavior within a simple model in terms of the building of a stratified layer and the activation of plastic events by the surface roughness.
Effective velocity boundary condition at a mixed slip surface
Sbragaglia, M.; Prosperetti, Andrea
2007-01-01
This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for
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.
Directory of Open Access Journals (Sweden)
R. H. H. Janssen
2012-08-01
Full Text Available We study the combined effects of land surface conditions, atmospheric boundary layer dynamics and chemistry on the diurnal evolution of biogenic secondary organic aerosol in the atmospheric boundary layer, using a model that contains the essentials of all these components. First, we evaluate the model for a case study in Hyytiälä, Finland, and find that it is able to satisfactorily reproduce the observed dynamics and gas-phase chemistry. We show that the exchange of organic aerosol between the free troposphere and the boundary layer (entrainment must be taken into account in order to explain the observed diurnal cycle in organic aerosol (OA concentration. An examination of the budgets of organic aerosol and terpene concentrations show that the former is dominated by entrainment, while the latter is mainly driven by emission and chemical transformation. We systematically investigate the role of the land surface, which governs both the surface energy balance partitioning and terpene emissions, and the large-scale atmospheric process of vertical subsidence. Entrainment is especially important for the dilution of organic aerosol concentrations under conditions of dry soils and low terpene emissions. Subsidence suppresses boundary layer growth while enhancing entrainment. Therefore, it influences the relationship between organic aerosol and terpene concentrations. Our findings indicate that the diurnal evolution of secondary organic aerosols (SOA in the boundary layer is the result of coupled effects of the land surface, dynamics of the atmospheric boundary layer, chemistry, and free troposphere conditions. This has potentially some consequences for the design of both field campaigns and large-scale modeling studies.
Effect of reactor finiteness on the boundary condition at the surface of a booster section
International Nuclear Information System (INIS)
Wassef, W.A.
1982-01-01
Effect of reactor finiteness on the boundary condition at the surface of an absorbing booster embedded in the reactor core is studied and formulated. The model used in these calculations depends on the Pl-Transport coupling technique. This method takes into consideration the rigorous neutron transport behavior inside the booster medium, while the Pl-approximation in the bulk of the scattering medium surrounding the booster which can be considered infinite in most practical applications. The neutron flux gradient parallel to the surface of the booster is considered. The geometrical configuration of the reactor core cross section is circular or rectangular. Finiteness of the reactor is introduced in the general formulation through its dimensions or buckling. Extensive numerical results are given to demonstrate the dependence of the boundary condition at the surface of the booster section on the reactor finiteness and the different physical parameters
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.
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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
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.
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.
The boundary condition for vertical velocity and its interdependence with surface gas exchange
Directory of Open Access Journals (Sweden)
A. S. Kowalski
2017-07-01
Full Text Available The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface. This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux–gradient relationships (eddy diffusivities requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube – with vapour transport into an overlying, horizontal airstream – was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.
The boundary condition for vertical velocity and its interdependence with surface gas exchange
Kowalski, Andrew S.
2017-07-01
The law of conservation of linear momentum is applied to surface gas exchanges, employing scale analysis to diagnose the vertical velocity (w) in the boundary layer. Net upward momentum in the surface layer is forced by evaporation (E) and defines non-zero vertical motion, with a magnitude defined by the ratio of E to the air density, as w = E/ρ. This is true even right down at the surface where the boundary condition is w|0 = E/ρ|0 (where w|0 and ρ|0 represent the vertical velocity and density of air at the surface). This Stefan flow velocity implies upward transport of a non-diffusive nature that is a general feature of the troposphere but is of particular importance at the surface, where it assists molecular diffusion with upward gas migration (of H2O, for example) but opposes that of downward-diffusing species like CO2 during daytime. The definition of flux-gradient relationships (eddy diffusivities) requires rectification to exclude non-diffusive transport, which does not depend on scalar gradients. At the microscopic scale, the role of non-diffusive transport in the process of evaporation from inside a narrow tube - with vapour transport into an overlying, horizontal airstream - was described long ago in classical mechanics and is routinely accounted for by chemical engineers, but has been neglected by scientists studying stomatal conductance. Correctly accounting for non-diffusive transport through stomata, which can appreciably reduce net CO2 transport and marginally boost that of water vapour, should improve characterisations of ecosystem and plant functioning.
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.
Long-term climate change: the evolution of shield surface boundary conditions
International Nuclear Information System (INIS)
Peltier, W.R.
2007-01-01
The Earths surface during the Pleistocene epoch has been repeatedly subjected to glacial cycles that have markedly influenced both the landscape and surface boundary conditions that, in part, governed past evolution of deep-seated Shield groundwater flow domains. As part of the Deep Geologic Repository Technology Programme simulations of the last Laurentide glacial episode have been undertaken with the University of Toronto Glacial System Model (GSM). The purpose of these simulations is to yield constrained predictions of the magnitude and time rate of change of peri-glacial, glacial and boreal regimes that have perturbed Shield flow domains in the geologic past. A detailed model of long timescale climate change has been developed, which is able to make useful predictions of the process of continental glaciation and deglaciation that has occurred in the past due to the small changes in the effective intensity of the Sun at the location of the Earth caused by gravitational many body effects in Solar System evolution. Based upon the success of this model we are able to assert that we have demonstrated a basic understanding of why this process has continually recurred in the past on a timescale of approximately 100 000 years. Continuing work with the Glacial Systems Model and efforts to provide explicit linkage to numerical analyses of sub-surface hydrology are beginning to yield a new understanding of groundwater flow system evolution and response to glacial perturbations. In so doing this understanding is not only providing a reasoned basis on which to examine issues of geosphere stability as relevant to the safety of a hypothetical repository for used nuclear fuel in Shield terrain, but is also offering an improved basis for the integrated interpretation of multi-disciplinary geo-scientific data necessary for development of a descriptive geosphere model that is seen as fundamental to the repository Safety Case. (author)
Energy Technology Data Exchange (ETDEWEB)
Hayat, Tasawar [Quaid-i-Azam Univ., Islamabad (Pakistan). Dept. of Mathematics; King Saud Univ., Riyadh (Saudi Arabia). Dept. of Physics; Iqbal, Zahid [Quaid-i-Azam Univ., Islamabad (Pakistan). Dept. of Mathematics; Qasim, Muhammad [COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan). Dept. of Mathematics; Aldossary, Omar M. [King Saud Univ., Riyadh (Saudi Arabia). Dept. of Physics
2012-05-15
This investigation reports the boundary layer flow and heat transfer characteristics in a couple stress fluid flow over a continuos moving surface with a parallel free stream. The effects of heat generation in the presence of convective boundary conditions are also investigated. Series solutions for the velocity and temperature distributions are obtained by the homotopy analysis method (HAM). Convergence of obtained series solutions are analyzed. The results are obtained and discussed through graphs for physical parameters of interest. (orig.)
Modeling of Hydrophobic Surfaces by the Stokes Problem With the Stick–Slip Boundary Conditions
Czech Academy of Sciences Publication Activity Database
Kučera, R.; Šátek, V.; Haslinger, Jaroslav; Fialová, S.; Pochylý, F.
2017-01-01
Roč. 139, č. 1 (2017), č. článku 011202. ISSN 0098-2202 Institutional support: RVO:68145535 Keywords : algebra * boundary conditions * hydrophobicity * Lagrange multipliers * Navier Stokes equations Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.437, year: 2016 http://fluidsengineering.asmedigitalcollection.asme.org/article.aspx?articleid=2536532
Directory of Open Access Journals (Sweden)
Giovanni Pitari
2017-12-01
Full Text Available Two independent chemistry-transport models with troposphere-stratosphere coupling are used to quantify the different components of the radiative forcing (RF from aircraft emissions of NOx, i.e., the University of L'Aquila climate-chemistry model (ULAQ-CCM and the University of Oslo chemistry-transport model (Oslo-CTM3. The tropospheric NOx enhancement due to aircraft emissions produces a short-term O3 increase with a positive RF (+17.3 mW/m2 (as an average value of the two models. This is partly compensated by the CH4 decrease due to the OH enhancement (−9.4 mW/m2. The latter is a long-term response calculated using a surface CH4 flux boundary condition (FBC, with at least 50 years needed for the atmospheric CH4 to reach steady state. The radiative balance is also affected by the decreasing amount of CO2 produced at the end of the CH4 oxidation chain: an average CO2 accumulation change of −2.2 ppbv/yr is calculated on a 50 year time horizon (−1.6 mW/m2. The aviation perturbed amount of CH4 induces a long-term response of tropospheric O3 mostly due to less HO2 and CH3O2 being available for O3 production, compared with the reference case where a constant CH4 surface mixing ratio boundary condition is used (MBC (−3.9 mW/m2. The CH4 decrease induces a long-term response of stratospheric H2O (−1.4 mW/m2. The latter finally perturbs HOx and NOx in the stratosphere, with a more efficient NOx cycle for mid-stratospheric O3 depletion and a decreased O3 production from HO2+NO in the lower stratosphere. This produces a long-term stratospheric O3 loss, with a negative RF (−1.2 mW/m2, compared with the CH4 MBC case. Other contributions to the net NOx RF are those due to NO2 absorption of UV-A and aerosol perturbations (the latter calculated only in the ULAQ-CCM. These comprise: increasing sulfate due to more efficient oxidation of SO2, increasing inorganic and organic nitrates and the net aerosols indirect effect on warm clouds
Energy Technology Data Exchange (ETDEWEB)
Hayat, T. [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan); Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589 (Saudi Arabia); Iqbal, Z., E-mail: zahidiqbal_qau@yahoo.com [Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000 (Pakistan); Mustafa, M. [Research Centre for Modeling and Simulation, National University of Sciences and Technology, Sector H-12, Islamabad 44000 (Pakistan); Alsaedi, A. [Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589 (Saudi Arabia)
2012-11-15
Highlights: Black-Right-Pointing-Pointer Boundary layer flow of an upper-convected Maxwell (UCM) fluid over a moving surface. Black-Right-Pointing-Pointer Convective boundary conditions have been used. Black-Right-Pointing-Pointer Series solutions are obtained by homotopy analysis method (HAM). Black-Right-Pointing-Pointer Graphical results for various interesting parametric values. - Abstract: This study discusses the flow and heat transfer in an upper-convected Maxwell (UCM) fluid over a moving surface in the presence of a free stream velocity. The convective boundary conditions have been handled. Similarly transformations are invoked to convert the partial differential equations governing the steady flow of a Maxwell fluid into an ordinary differential system. This system is solved by a homotopic approach. The effects of influential parameters such as Deborah number ({beta}), Prandtl number (Pr), Eckert number (Ec), suction parameter (S) and ratio ({lambda}) have been thoroughly examined.
Li, Y.; Epifanio, C.
2017-12-01
In numerical prediction models, the interaction between the Earth's surface and the atmosphere is typically accounted for in terms of surface layer parameterizations, whose main job is to specify turbulent fluxes of heat, moisture and momentum across the lower boundary of the model domain. In the case of a domain with complex geometry, implementing the flux conditions (particularly the tensor stress condition) at the boundary can be somewhat subtle, and there has been a notable history of confusion in the CFD community over how to formulate and impose such conditions generally. In the atmospheric case, modelers have largely been able to avoid these complications, at least until recently, by assuming that the terrain resolved at typical model resolutions is fairly gentle, in the sense of having relatively shallow slopes. This in turn allows the flux conditions to be imposed as if the lower boundary were essentially flat. Unfortunately, while this flat-boundary assumption is acceptable for coarse resolutions, as grids become more refined and the geometry of the resolved terrain becomes more complex, the appproach is less justified. With this in mind, the goal of our present study is to explore the implementation and usage of the full, unapproximated version of the turbulent flux/stress conditions in atmospheric models, thus taking full account of the complex geometry of the resolved terrain. We propose to implement the conditions using a semi-idealized model developed by Epifanio (2007), in which the discretized boundary conditions are reduced to a large, sparse-matrix problem. The emphasis will be on fluxes of momentum, as the tensor nature of this flux makes the associated stress condition more difficult to impose, although the flux conditions for heat and moisture will be considered as well. With the resulotion of 90 meters, some of the results show that the typical differences between flat-boundary cases and full/stress cases are on the order of 10%, with extreme
Directory of Open Access Journals (Sweden)
Ishak Anuar
2011-01-01
Full Text Available Abstract The problem of a steady boundary layer shear flow over a stretching/shrinking sheet in a nanofluid is studied numerically. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique. Two types of nanofluids, namely, Cu-water and Ag-water are used. The effects of nanoparticle volume fraction, the type of nanoparticles, the convective parameter, and the thermal conductivity on the heat transfer characteristics are discussed. It is found that the heat transfer rate at the surface increases with increasing nanoparticle volume fraction while it decreases with the convective parameter. Moreover, the heat transfer rate at the surface of Cu-water nanofluid is higher than that at the surface of Ag-water nanofluid even though the thermal conductivity of Ag is higher than that of Cu.
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P.BalaAnki Reddy
2017-12-01
Full Text Available This paper focuses on a theoretical analysis of a steady two-dimensional magnetohydrodynamic boundary layer flow of a Maxwell fluid over an exponentially stretching surface in the presence of velocity slip and convective boundary condition. This model is used for a nanofluid, which incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear partial differential equations of the governing flow field are converted into a system of coupled non-linear ordinary differential equations by using suitable similarity transformations, and the resultant equations are then solved numerically by using Runge-Kutta fourth order method along with shooting technique. A parametric study is conducted to illustrate the behavior of the velocity, temperature and concentration. The influence of significant parameters on velocity, temperature, concentration, skin friction coefficient and Nusselt number has been studied and numerical results are presented graphically and in tabular form. The reported numerical results are compared with previously published works on various special cases and are found to be an in excellent agreement. It is found that momentum boundary layer thickness decreases with the increase of magnetic parameter. It can also be found that the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters.
Czech Academy of Sciences Publication Activity Database
Svoboda, Jiří; Fischer, F. D.; Klinger, L.; Rabkin, E.
2014-01-01
Roč. 94, č. 30 (2014), s. 3398-3412 ISSN 1478-6435 Institutional support: RVO:68081723 Keywords : grain boundary diffusion * liquid metals * stress analysis * interfacial thermodynamics Subject RIV: BJ - Thermodynamics Impact factor: 1.825, year: 2014
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...... on which boundary condition produces the best results. In this study, various boundary conditions in terms of normal and random incidence absorption coefficients, and normal incidence surface impedances are used in a phased beam tracing model, and simulated results are validated with boundary element...... 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....
Tsang, L.; Lou, S. H.; Chan, C. H.
1991-01-01
The extended boundary condition method is applied to Monte Carlo simulations of two-dimensional random rough surface scattering. The numerical results are compared with one-dimensional random rough surfaces obtained from the finite-element method. It is found that the mean scattered intensity from two-dimensional rough surfaces differs from that of one dimension for rough surfaces with large slopes.
Vergnes, Jean-Pierre; Decharme, Bertrand; Habets, Florence
2014-05-01
Groundwater is a key component of the global hydrological cycle. It sustains base flow in humid climate while it receives seepage in arid region. Moreover, groundwater influences soil moisture through water capillary rise into the soil and potentially affects the energy and water budget between the land surface and the atmosphere. Despite its importance, most global climate models do not account for groundwater and their possible interaction with both the surface hydrology and the overlying atmosphere. This study assesses the impact of capillary rise from shallow groundwater on the simulated water budget over France. The groundwater scheme implemented in the Total Runoff Integrated Pathways (TRIP) river routing model in a previous study is coupled with the Interaction between Soil Biosphere Atmosphere (ISBA) land surface model. In this coupling, the simulated water table depth acts as the lower boundary condition for the soil moisture diffusivity equation. An original parameterization accounting for the subgrid elevation inside each grid cell is proposed in order to compute this fully-coupled soil lower boundary condition. Simulations are performed at high (1/12°) and low (0.5°) resolutions and evaluated over the 1989-2009 period. Compared to a free-drain experiment, upward capillary fluxes at the bottom of soil increase the mean annual evapotranspiration simulated over the aquifer domain by 3.12 % and 1.54 % at fine and low resolutions respectively. This process logically induces a decrease of the simulated recharge from ISBA to the aquifers and contributes to enhance the soil moisture memory. The simulated water table depths are then lowered, which induces a slight decrease of the simulated mean annual river discharges. However, the fully-coupled simulations compare well with river discharge and water table depth observations which confirms the relevance of the coupling formalism.
Zhang, X.; Cornuelle, B. D.; Martin, A.; Weihs, R. R.; Ralph, M.
2017-12-01
We evaluated the merit in coastal precipitation forecasts by inclusion of high resolution sea surface temperature (SST) from blended satellite and in situ observations as a boundary condition (BC) to the Weather Research and Forecast (WRF) mesoscale model through simple perturbation tests. Our sensitivity analyses shows that the limited improvement of watershed scale precipitation forecast is credible. When only SST BC is changed, there is an uncertainty introduced because of artificial model state equilibrium and the nonlinear nature of the WRF model system. With the change of SST on the order of a fraction of a degree centigrade, we found that the part of random perturbation forecast response is saturated after 48 hours when it reaches to the order magnitude of the linear response. It is important to update the SST at a shorter time period, so that the independent excited nonlinear modes can cancel each other. The uncertainty in our SST configuration is quantitatively equivalent to adding to a spatially uncorrelated Guasian noise of zero mean and 0.05 degree of standard deviation to the SST. At this random noise perturbation magnitude, the ensemble average behaves well within a convergent range. It is also found that the sensitivity of forecast changes in response to SST changes. This is measured by the ratio of the spatial variability of mean of the ensemble perturbations over the spatial variability of the corresponding forecast. The ratio is about 10% for surface latent heat flux, 5 % for IWV, and less than 1% for surface pressure.
Quantum cavities with alternating boundary conditions
Facchi, Paolo; Garnero, Giancarlo; Ligabò, Marilena
2018-03-01
We consider the quantum dynamics of a free nonrelativistic particle moving in a cavity and we analyze the effect of a rapid switching between two different boundary conditions. We show that this procedure induces, in the limit of infinitely frequent switchings, a new effective dynamics in the cavity related to a novel boundary condition. We obtain a dynamical composition law for boundary conditions which gives the emerging boundary condition in terms of the two initial ones.
Modelling classroom conditions with different boundary conditions
DEFF Research Database (Denmark)
Marbjerg, Gerd Høy; Jeong, Cheol-Ho; Brunskog, Jonas
2014-01-01
both specular and diffuse reflections with complex-valued acoustical descriptions of the surfaces. In this paper the PARISM model is used to simulate a rectangular room with most of the absorption located in the ceiling. This room configuration is typical for classroom conditions. The simulations...... measures which are important for evaluation of the acoustics in classrooms....
Schobeiri, M. T.; Ozturk, B.; Ashpis, David E.
2007-01-01
The paper experimentally studies the effects of periodic unsteady wake flow and different Reynolds numbers on boundary layer development, separation and re-attachment along the suction surface of a low pressure turbine blade. The experimental investigations were performed on a large scale, subsonic unsteady turbine cascade research facility at Turbomachinery Performance and Flow Research Laboratory (TPFL) of Texas A&M University. The experiments were carried out at Reynolds numbers of 110,000 and 150,000 (based on suction surface length and exit velocity). One steady and two different unsteady inlet flow conditions with the corresponding passing frequencies, wake velocities, and turbulence intensities were investigated. The reduced frequencies chosen cover the operating range of LP turbines. In addition to the unsteady boundary layer measurements, surface pressure measurements were performed. The inception, onset, and the extent of the separation bubble information collected from the pressure measurements were compared with the hot wire measurements. The results presented in ensemble-averaged, and the contour plot forms help to understand the physics of the separation phenomenon under periodic unsteady wake flow and different Reynolds number. It was found that the suction surface displayed a strong separation bubble for these three different reduced frequencies. For each condition, the locations defining the separation bubble were determined carefully analyzing and examining the pressure and mean velocity profile data. The location of the boundary layer separation was dependent of the Reynolds number. It is observed that starting point of the separation bubble and the re-attachment point move further downstream by increasing Reynolds number from 110,000 to 150,000. Also, the size of the separation bubble is smaller when compared to that for Re=110,000.
Integrability and boundary conditions of supersymmetric systems
International Nuclear Information System (INIS)
Yue Ruihong; Liang Hong
1996-01-01
By studying the solutions of the reflection equations, we find out a series of integrable supersymmetric systems with different boundary conditions. The Hamiltonian contains four free parameters which describe the contribution of the boundary terms
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
Boundary conditions of methamphetamine craving.
Lopez, Richard B; Onyemekwu, Chukwudi; Hart, Carl L; Ochsner, Kevin N; Kober, Hedy
2015-12-01
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 2 exploratory studies, we tested the boundary conditions of methamphetamine craving by asking: (a) is craving specific to users' preferred route of administration?, and (b) 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. (PsycINFO Database Record (c) 2015 APA, all rights reserved).
Directory of Open Access Journals (Sweden)
B. R. Rout
2013-01-01
Full Text Available This paper aims to investigate the influence of chemical reaction and the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer MHD heat and mass transfer flow over a moving vertical flat plate. The lower surface of the plate is in contact with a hot fluid while the stream of cold fluid flows over the upper surface with heat source and chemical reaction. The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. The effects of physical parameters on the velocity, temperature, and concentration profiles are illustrated graphically. A table recording the values of skin friction, heat transfer, and mass transfer at the plate is also presented. The discussion focuses on the physical interpretation of the results as well as their comparison with previous studies which shows good agreement as a special case of the problem.
Boundary conditions in random sequential adsorption
Cieśla, Michał; Ziff, Robert M.
2018-04-01
The influence of different boundary conditions on the density of random packings of disks is studied. Packings are generated using the random sequential adsorption algorithm with three different types of boundary conditions: periodic, open, and wall. It is found that the finite size effects are smallest for periodic boundary conditions, as expected. On the other hand, in the case of open and wall boundaries it is possible to introduce an effective packing size and a constant correction term to significantly improve the packing densities.
Bosonization relations as bag boundary conditions
International Nuclear Information System (INIS)
Nadkarni, S.; Nielsen, H.B.; Zahed, I.
1984-10-01
The more sophisticated bag models of hadrons become, the less precisely they seem to determine the bag radius. Idealizing this situation leads to the concept of exact bag models - ''Cheshire Cat'' models, CCM'S - where the physics is completely insensitive to changes in the bag radius. CCM's are constructed explitly in 1+1-dimensions, where exact bosonization relations are known. In the formalism of bag models, these relations appear as boundary conditions which ensure that the shifting of the bag wall has no physical effect. Other notable features of 1+1-dimensional CCM's are: (i) Fermion number, though classically confined, can escape the bag via a vector current anomaly at the surface. (ii) Essentially the same boundary action works for a variety of models and its symmetries determine those of the external boson fields. Remarkably enough, this 1+1-dimensional boundary action has precisely the same form as the one used in 3+1-dimensional chiral bag models, lending support to the belief that the latter are indeed approximateCCM's. These 1+1-dimensional results are expected to provide useful guidelines in the attempt to, at least approximately, besonize 3+1-dimensional QCD. (orig.)
Implementation of Boundary Condition to THALES Code
International Nuclear Information System (INIS)
Jang, Beomjun; Chun, Chong Kuk; Park, Ho Young; Woo, Hae-Seuk
2016-01-01
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
Population models with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Jerome Goddard
2010-09-01
Full Text Available We study a two point boundary-value problem describing the steady states of a Logistic growth population model with diffusion and constant yield harvesting. In particular, we focus on a model when a certain nonlinear boundary condition is satisfied.
Solution of moving boundary problems with implicit boundary condition
International Nuclear Information System (INIS)
Moyano, E.A.
1990-01-01
An algorithm that solves numerically a model for studying one dimensional moving boundary problems, with implicit boundary condition, is described. Landau's transformation is used, in order to work with a fixed number of nodes at each instant. Then, it is necessary to deal with a parabolic partial differential equation, whose diffusive and convective terms have variable coefficients. The partial differential equation is implicitly discretized, using Laasonen's scheme, always stable, instead of employing Crank-Nicholson sheme, as it has been done by Ferris and Hill. Fixed time and space steps (Δt, Δξ) are used, and the iteration is made with variable positions of the interface, i.e. varying δs until a boundary condition is satisfied. The model has the same features of the oxygen diffusion in absorbing tissue. It would be capable of estimating time variant radiation treatments of cancerous tumors. (Author) [es
Second-Order Boundary Value Problem with Integral Boundary Conditions
Directory of Open Access Journals (Sweden)
Nieto JuanJ
2011-01-01
Full Text Available The nonlinear alternative of the Leray Schauder type and the Banach contraction principle are used to investigate the existence of solutions for second-order differential equations with integral boundary conditions. The compactness of solutions set is also investigated.
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
International Nuclear Information System (INIS)
Winicour, Jeffrey
2012-01-01
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') (topical review)
Boundary denoising for open surface meshes
Lee, Wei Zhe; Lim, Wee Keong; Soo, Wooi King
2013-04-01
Recently, applications of open surfaces in 3D have emerged to be an interesting research topic due to the popularity of range cameras such as the Microsoft Kinect. However, surface meshes representing such open surfaces are often corrupted with noises especially at the boundary. Such deformity needs to be treated to facilitate further applications such as texture mapping and zippering of multiple open surface meshes. Conventional methods perform denoising by removing components with high frequencies, thus smoothing the boundaries. However, this may result in loss of information, as not all high frequency transitions at the boundaries correspond to noises. To overcome such shortcoming, we propose a combination of local information and geometric features to single out the noises or unusual vertices at the mesh boundaries. The local shape of the selected mesh boundaries regions, characterized by the mean curvature value, is compared with that of the neighbouring interior region. The neighbouring interior region is chosen such that it is the closest to the corresponding boundary region, while curvature evaluation is independent of the boundary. The smoothing processing is done via Laplacian smoothing with our modified weights to reduce boundary shrinkage. The evaluation of the algorithm is done by noisy meshes generated from controlled model clean meshes. The Hausdorff distance is used as the measurement between the meshes. We show that our method produces better results than conventional smoothing of the whole boundary loop.
Directory of Open Access Journals (Sweden)
G.K. Ramesh
2014-09-01
Full Text Available In this article, heat source/sink effects on the steady boundary layer flow of a Maxwell fluid over a stretching sheet with convective boundary condition in the presence of nanoparticles are reported. An appropriate similarity transformation is employed to transform the governing equations in partial differential equations form to similarity equations in ordinary differential equations form. The resulting equations are then solved numerically using shooting technique. Results for the velocity, temperature and concentration distributions are presented graphically for different values of the pertinent parameters. It is found that the local Nusselt number is smaller and local Sherwood number is higher for Maxwell fluids compared to Newtonian fluids.
Directory of Open Access Journals (Sweden)
J. Y. Tang
2013-02-01
Full Text Available We describe a new top boundary condition (TBC for representing the air–soil diffusive exchange of a generic volatile tracer. This new TBC (1 accounts for the multi-phase flow of a generic tracer; (2 accounts for effects of soil temperature, pH, solubility, sorption, and desorption processes; (3 enables a smooth transition between wet and dry soil conditions; (4 is compatible with the conductance formulation for modeling air–water volatile tracer exchange; and (5 is applicable to site, regional, and global land models.
Based on the new TBC, we developed new formulations for bare-soil resistance and corresponding soil evaporation efficiency. The new soil resistance is predicted as the reciprocal of the harmonic sum of two resistances: (1 gaseous and aqueous molecular diffusion and (2 liquid mass flow resulting from the hydraulic pressure gradient between the soil surface and center of the topsoil control volume. We compared the predicted soil evaporation efficiency with those from several field and laboratory soil evaporation measurements and found good agreement with the typically observed two-stage soil evaporation curves. Comparison with the soil evaporation efficiency equation of Lee and Pielke (1992; hereafter LP92 indicates that their equation can overestimate soil evaporation when the atmospheric resistance is low and underestimate soil evaporation when the soil is dry. Using a synthetic inversion experiment, we demonstrated that using inverted soil resistance data from field measurements to derive empirical soil resistance formulations resulted in large uncertainty because (1 the inverted soil resistance data are always severely impacted by measurement error and (2 the derived empirical equation is very sensitive to the number of data points and the assumed functional form of the resistance.
We expect the application of our new TBC in land models will provide a consistent representation for the diffusive tracer
The surface roughness and planetary boundary layer
Telford, James W.
1980-03-01
Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 24_2004_Article_BF00877766_TeX2GIFE1.gif {σ _w }/{u^* } = ( {2/{9Aa}} )^{{1/4}} ( {1 - 3^{{1/2}{ a/k{d_n }/z{σ _w }/{u^* }z/L} )^{{1/4}} = 1.28(1 - 0.945({{σ _w }/{u^* }}}) {{z/L}})^{{1/4 where u^* = ( {{tau/ρ}}^{{1/2}}, σ w is the standard deviation of the vertical velocity, z is the height and L is the Obukhov scale lenght. The constants a, A, k and d n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these, a and A, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements
Casimir pistons with general boundary conditions
Directory of Open Access Journals (Sweden)
Guglielmo Fucci
2015-02-01
Full Text Available In this work we analyze the Casimir energy and force for a scalar field endowed with general self-adjoint boundary conditions propagating in a higher dimensional piston configuration. The piston is constructed as a direct product I×N, with I=[0,L]⊂R and N a smooth, compact Riemannian manifold with or without boundary. The study of the Casimir energy and force for this configuration is performed by employing the spectral zeta function regularization technique. The obtained analytic results depend explicitly on the spectral zeta function associated with the manifold N and the parameters describing the general boundary conditions imposed. These results are then specialized to the case in which the manifold N is a d-dimensional sphere.
Unconditionally stable perfectly matched layer boundary conditions
De Raedt, H.; Michielsen, K.
2007-01-01
A brief review is given of a systematic, product-formula based approach to construct unconditionally stable algorithms for solving the time-dependent Maxwell equations. The fundamental difficulties that arise when we want to incorporate uniaxial perfectly matched layer boundary conditions into this
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...
Automated Boundary Conditions for Wind Tunnel Simulations
Carlson, Jan-Renee
2018-01-01
Computational fluid dynamic (CFD) simulations of models tested in wind tunnels require a high level of fidelity and accuracy particularly for the purposes of CFD validation efforts. Considerable effort is required to ensure the proper characterization of both the physical geometry of the wind tunnel and recreating the correct flow conditions inside the wind tunnel. The typical trial-and-error effort used for determining the boundary condition values for a particular tunnel configuration are time and computer resource intensive. This paper describes a method for calculating and updating the back pressure boundary condition in wind tunnel simulations by using a proportional-integral-derivative controller. The controller methodology and equations are discussed, and simulations using the controller to set a tunnel Mach number in the NASA Langley 14- by 22-Foot Subsonic Tunnel are demonstrated.
Thermal Simulations, Open Boundary Conditions and Switches
Burnier, Yannis; Florio, Adrien; Kaczmarek, Olaf; Mazur, Lukas
2018-03-01
SU(N) gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by Lüscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.
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.
Molecular Dynamics with Helical Periodic Boundary Conditions
Czech Academy of Sciences Publication Activity Database
Kessler, Jiří; Bouř, Petr
2014-01-01
Roč. 35, č. 21 (2014), s. 1552-1559 ISSN 0192-8651 R&D Projects: GA ČR GAP208/11/0105; GA MŠk(CZ) LH11033 Grant - others:GA AV ČR(CZ) M200551205; GA MŠk(CZ) LM2010005 Institutional support: RVO:61388963 Keywords : periodic boundary conditions * helical symmetry * molecular dynamics * protein structure * amyloid fibrils Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.589, year: 2014
Numerical experiment with upstream boundary conditions
Huml, Jaroslav; Kozel, Karel
2012-04-01
The work deals with a numerical solution of subsonic and transonic flows described by the system of Euler equations in 2D and 3D flows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the flows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel flows.
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 of ...... diffuser showed good agreement with the experimentally obtained results although differences were observed in the flow far from the inlet. None of the investigated models of the heated surface did provide satisfactory results....
Riemann surfaces with boundaries and string theory
International Nuclear Information System (INIS)
Morozov, A.Yu.; Roslyj, A.A.
1989-01-01
A consideration of the cutting and joining operations for Riemann surfaces permits one to express the functional integral on a Riemann surface in terms of integrals over its pieces which are suarfaces with boundaries. This yields an expression for the determinant of the Laplacian on a Riemann surface in terms of Krichever maps for its pieces. Possible applications of the methods proposed to a study of the string perturbation theory in terms of an universal moduli space are mentioned
Quantum quench with hard wall boundary conditions
Goldstein, Garry; Andrei, Natan
2015-03-01
In this work we present analysis of a quench for the Lieb Liniger gas contained in a large box with hard wall boundary conditions. We study the time average of local correlation functions. We show that both the quench action logic and the GGE are applicable. We show that the time average of the system corresponds to an eigenstate of the Lieb Liniger Hamiltonian. We show that this eigenstate is related to an eigenstate of a Lieb Liniger Hamiltonian with periodic boundary conditions on an interval of twice the length and with twice as many particles (a doubled system). We further show that local operators with support far away from the boundaries of the hard wall Lieb Liniger gas have the same expectation values as corresponding operators for the doubled system. We present an example of a quench where the Lieb Liniger gas is initially confined in several traps and then released into a bigger container, an approximate description of the Newton cradle experiment. This research was supported by NSF Grant DMR 1006684 and Rutgers CMT fellowship.
Canonical group quantization and boundary conditions
International Nuclear Information System (INIS)
Jung, Florian
2012-01-01
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.
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.
Numerical experiment with upstream boundary conditions
Directory of Open Access Journals (Sweden)
Huml Jaroslav
2012-04-01
Full Text Available The work deals with a numerical solution of subsonic and transonic ﬂows described by the system of Euler equations in 2D and 3D ﬂows in a channel. Authors used Lax-Wendroff and the multistage Runge-Kutta scheme to numerically solve the ﬂows in a 2D G AMM channel and an extended 3D channel. Authors compare the results achieved by two different upstream boundary conditions in 2D and also in 3D transonic channel ﬂows.
International Nuclear Information System (INIS)
Itagaki, M.; Brebbia, C.A.
1991-01-01
This paper reports on the boundary element method used to generate energy-dependent matrix-type boundary conditions along core/reflector interfaces and along baffle-plate surfaces of pressurized water reactors. This method enables one to deal with all types of boundary geometries including convex and concave corners. The method is applicable to neutron diffusion problems with more than two energy groups and also can be used to model a reflector with or without a baffle plate. Excellent eigenvalue and flux shape results can be obtained when the boundary conditions generated by this technique are coupled with core-only finite difference calculations
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...
Fractional partial differential equations with boundary conditions
Baeumer, Boris; Kovács, Mihály; Sankaranarayanan, Harish
2018-01-01
We identify the stochastic processes associated with one-sided fractional partial differential equations on a bounded domain with various boundary conditions. This is essential for modelling using spatial fractional derivatives. We show well-posedness of the associated Cauchy problems in C0 (Ω) and L1 (Ω). In order to do so we develop a new method of embedding finite state Markov processes into Feller processes on bounded domains and then show convergence of the respective Feller processes. This also gives a numerical approximation of the solution. The proof of well-posedness closes a gap in many numerical algorithm articles approximating solutions to fractional differential equations that use the Lax-Richtmyer Equivalence Theorem to prove convergence without checking well-posedness.
Tieleman, D.P; Berendsen, H.J.C.
1996-01-01
We compared molecular dynamics simulations of a bilayer of 128 fully hydrated phospholipid (DPPC) molecules, using different parameters and macroscopic boundary conditions. The same system was studied under constant pressure, constant volume, and constant surface tension boundary conditions, with
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.
On the boundary conditions in cylindrical cell approximation
International Nuclear Information System (INIS)
Altiparmakov, D.V.
1980-01-01
A solution of the integral transport equation for an arbitrary boundary condition is obtained by solving the integral transport equation for homogeneous (vacuum) boundary condition and using the neutron balance condition. An effective boundary condition satisfying the zero gradient of the neutron flux on the cell boundary is assumed. The numerical solution is obtained by using a pointwise approximation based on a polynomial flux approximation. Disadvantage factor calculations of the Thie lattice cells are carried out. Comparisons are performed with the results obtained for the actual cells by two-dimensional methods as well as their cylindrical approximations applying various boundary conditions. It is obvious from the results shown here that the proposed boundary condition has advantages in respect to others. The errors introduced by the proposed boundary condition are of the lower order in respect to the inaccuracy of the existing transport methods. Thus, the applications of the two-dimensional methods for regular lattice calculations is unnecessary. (author)
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...
Boundary and initial conditions in protostar calculations
International Nuclear Information System (INIS)
Disney, M.J.
1976-01-01
On first fragmentation protostars probably form part of a larger protocluster cloud already in a state of dynamic collapse. In that case it is argued that the protostar boundary is initially collapsing at supersonic speed relative to the core. This prevents information from the boundary reaching the core and calls into question models like Larson's, which start homogeneously but become centrally condensed due to the propagation of a rarefaction wave from the boundary. (author)
Long-time behaviour of absorbing boundary conditions
Engquist, B.; Halpern, L.
1990-01-01
A new class of computational far-field boundary conditions for hyperbolic partial differential equations was recently introduced by the authors. These boundary conditions combine properties of absorbing conditions for transient solutions and properties of far-field conditions for steady states. This paper analyses the properties of the wave equation coupled with these new boundary conditions: well-posedness, dissipativity and convergence in time.
Directory of Open Access Journals (Sweden)
Garg P.
2016-12-01
Full Text Available This paper studies the mathematical implications of the two dimensional viscous steady laminar combined free-forced convective flow of an incompressible fluid over a semi infinite fixed vertical porous plate embedded in a porous medium. It is assumed that the left surface of the plate is heated by convection from a hot fluid which is at a temperature higher than the temperature of the fluid on the right surface of the vertical plate. To achieve numerical consistency for the problem under consideration, the governing non linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity variable and then solved numerically under conditions admitting similarity solutions. The effects of the physical parameters of both the incompressible fluid and the vertical plate on the dimensionless velocity and temperature profiles are studied and analysed and the results are depicted both graphically and in a tabular form. Finally, algebraic expressions and the numerical values are obtained for the local skin-friction coefficient and the local Nusselt number.
Slarti: A boundary condition editor for a coupled climate model
Mickelson, S. A.; Jacob, R. L.; Pierrehumbert, R.
2006-12-01
One of the largest barriers to making climate models more flexible is the difficulty in creating new boundary conditions, especially for "deep time" paleoclimate cases where continents are in different positions. Climate models consist of several mutually-interacting component models and the boundary conditions must be consistent between them. We have developed a program called Slarti which uses a Graphical User Interface and a set of consistency rules to aid researchers in creating new, consistent, boundary condition files for the Fast Ocean Atmosphere Model (FOAM). Users can start from existing mask, topography, or bathymetry data or can build a "world" entirely from scratch (e.g. a single island continent). Once a case has been started, users can modify mask, vegetation, bathymetry, topography, and river flow fields by drawing new data through a "paint" interface. Users activate a synchronization button which goes through the fields to eliminate inconsistencies. When the changes are complete and save is selected, Slarti creates all the necessary files for an initial run of FOAM. The data is edited at the highest resolution (the ocean-land surface in FOAM) and then interpolated to the atmosphere resolution. Slarti was implemented in Java to maintain portability across platforms. We also relied heavily on Java Swing components to create the interface. This allowed us to create an object-oriented interface that could be used on many different systems. Since Slarti allows users to visualize their changes, they are able to see areas that may cause problems when the model is ran. Some examples would be lakes from the river flow field and narrow trenches within the bathymetry. Through different checks and options available through its interface, Slarti makes the process of creating new boundary conditions for FOAM easier and faster while reducing the chance for user errors.
Experimental verification of free-space singular boundary conditions in an invisibility cloak
International Nuclear Information System (INIS)
Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Zhang, Baile; Chen, Huanyang
2016-01-01
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. (paper)
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.
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...... of full-scale experiments in a room ventilated by the mixing principle have been performed for validation of the models. The experimental results include measurements of temperature as well as measurements of velocity and turbulence by Laser Doppler Anemometry (LDA). A simple model of the complex inlet...
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...
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.
Nonlinear solution for radiation boundary condition of heat transfer process in human eye.
Dehghani, A; Moradi, A; Dehghani, M; Ahani, A
2011-01-01
In this paper we propose a new method based on finite element method for solving radiation boundary condition of heat equation inside the human eye and other applications. Using this method, we can solve heat equation inside human eye without need to model radiation boundary condition to a robin boundary condition. Using finite element method we can obtain a nonlinear equation, and finally we use nonlinear algorithm to solve it. The human eye is modeled as a composition of several homogeneous regions. The Ritz method in the finite element method is used for solving heat differential equation. Applying the boundary conditions, the heat radiation condition and the robin condition on the cornea surface of the eye and on the outer part of sclera are used, respectively. Simulation results of solving nonlinear boundary condition show the accuracy of the proposed method.
Surface roughness effects on the hypersonic turbulent boundary layer
Energy Technology Data Exchange (ETDEWEB)
Berg, D.E.
1977-09-01
An experimental investigation of the response of a hypersonic turbulent boundary layer to a step change in surface roughness has been performed. The boundary layer on a flat nozzle wall of a Mach 6 wind tunnel was subjected to abrupt changes in surface roughness and its adjustment to the new surface conditions was examined. Both mean and fluctuating flow properties were acquired for smooth-to-rough and rough-to-smooth surface configurations. The boundary layer was found to respond gradually and to attain new equilibrium profiles, for both the mean and the fluctuating properties, some 10 to 25 delta downstream of the step change. Mean flow self-similarity was the first to establish itself, followed by the mass flux fluctuations, followed in turn by the total temperature fluctuations. Use of a modified Van Driest transformation resulted in good correlations of smooth and rough wall data in the form of the incompressible law of the wall. This is true even in the nonequilibrium vicinity of the step for small roughness heights. The present data are found to correlate well with previously published roughness effect data from low and high speed flows when the roughnesses are characterized by an equivalent sand grain roughness height.
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....
Scattering through a straight quantum waveguide with combined boundary conditions
Czech Academy of Sciences Publication Activity Database
Briet, Ph.; Dittrich, Jaroslav; Soccorsi, E.
2014-01-01
Roč. 55, č. 11 (2014), s. 112104 ISSN 0022-2488 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : quantum waveguide * scattering * Dirichlet boundary condition * Neumann boundary condition Subject RIV: BE - Theoretical Physics Impact factor: 1.243, year: 2014
Curved planar quantum wires with Dirichlet and Neumann boundary conditions
Czech Academy of Sciences Publication Activity Database
Dittrich, Jaroslav; Kříž, J.
2002-01-01
Roč. 35, - (2002), s. 269-275 ISSN 0305-4470 R&D Projects: GA AV ČR IAA1048101; GA AV ČR KSK1010104 Keywords : quantum wires * laplace operation * Dirichlet boundary conditions * Neumann boundary conditions Subject RIV: BE - Theoretical Physics Impact factor: 1.406, year: 2002
Divergence-Free Wavelets on the Hypercube : General Boundary Conditions
Stevenson, R.
2016-01-01
On the n-dimensional hypercube, for given k∈N, wavelet Riesz bases are constructed for the subspace of divergence-free vector fields of the Sobolev space Hk((0,1)n)n with general homogeneous Dirichlet boundary conditions, including slip or no-slip boundary conditions. Both primal and suitable dual
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
Periodic Boundary Conditions in the ALEGRA Finite Element Code
International Nuclear Information System (INIS)
Aidun, John B.; Robinson, Allen C.; Weatherby, Joe R.
1999-01-01
This document describes the implementation of periodic boundary conditions in the ALEGRA finite element code. ALEGRA is an arbitrary Lagrangian-Eulerian multi-physics code with both explicit and implicit numerical algorithms. The periodic boundary implementation requires a consistent set of boundary input sets which are used to describe virtual periodic regions. The implementation is noninvasive to the majority of the ALEGRA coding and is based on the distributed memory parallel framework in ALEGRA. The technique involves extending the ghost element concept for interprocessor boundary communications in ALEGRA to additionally support on- and off-processor periodic boundary communications. The user interface, algorithmic details and sample computations are given
The effects of external conditions in turbulent boundary layers
Brzek, Brian G.
The effects of multiple external conditions on turbulent boundary layers were studied in detail. These external conditions include: surface roughness, upstream turbulence intensity, and pressure gradient. Furthermore, the combined effects of these conditions show the complicated nature of many realistic flow conditions. It was found that the effects of surface roughness are difficult to generalize, given the importance of so many parameters. These parameters include: roughness geometry, roughness regime, roughness height to boundary layer thickness, (k/delta), roughness parameter, ( k+), Reynolds number, and roughness function (Delta B+). A further complication, is the difficulty in computing the wall shear stress, tauw/rho. For the sand grain type roughness, the mean velocity and Reynolds stresses were studied in inner and outer variables, as well as, boundary layer parameters, anisotropy tensor, production term, and viscous stress and form drag contributions. To explore the effects of roughness and Reynolds number dependence in the boundary layer, a new experiment was carefully designed to properly capture the x-dependence of the single-point statistics. It was found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the skin friction due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction, near-wall roughness parameters, and inner velocity profiles as k + increases into the fully rough regime. However, in the transitionally rough regime, (i.e., 5 component shows the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables show self-similarity for fixed experimental conditions. However, as the roughness parameter, k +, increases, all Reynolds stress
Entropy Stability and the No-Slip Wall Boundary Condition
Svärd, Magnus
2018-01-18
We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an L bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.
Monopole Giant Resonances and TDHF boundary conditions
International Nuclear Information System (INIS)
Stevenson, P.D.; Almehed, D.; Reinhard, P.-G.; Maruhn, J.A.
2007-01-01
Using time-dependent Hartree-Fock, we induce isoscalar and isovector monopole vibrations and follow the subsequent vibrations of both the same and opposite isospin nature in the N Z nucleus 132 Sn. By suitable scaling of the proton and neutron parts of the excitation operators, the coupling between the modes is studied, and the approximate normal modes found. Chaotic dynamics are then analysed in the isoscalar giant monopole resonance by using reflecting boundaries in a large space to build up a large number of 0 + states whose spacings are then analysed. A Wigner-like distribution is found
Silent inflow condition for turbulent boundary layers
Gloerfelt, X.; Robinet, J.-C.
2017-12-01
The generation of a turbulent inflow is a tricky problem. In the framework of aeroacoustics, another important constraint is that the numerical strategy used to reach a turbulent state induces a spurious noise which is lower than the acoustic field of interest. For the study of noise radiated directly by a turbulent boundary layer on a flat plate, this constraint is severe since wall turbulence is a very inefficient source. That is why a method based on a transition by modal interaction using a base flow with an inflection point is proposed to cope with that. The base flow must be a solution of the equations so we use a profile behind a backward-facing step representative of experimental trip bands. A triad of resonant waves is selected by a local stability analysis of the linearized compressible equations and is added with a weak amplitude in the inlet plane. The compressible stability calculation allows the specification of the thermodynamic quantities at the inlet, which turns out to be fundamental to ensure a quiet inflow. A smooth transition is achieved with the rapid formation of Λ -shape vortices in a staggered organization as in subharmonic transition. The dominance of oblique waves promotes a rapid breakdown by the liftup mechanism of low-speed streaks. The quality of the fully turbulent state is assessed and the direct noise radiation from a turbulent boundary layer at Mach 0.5 is obtained with a very low level of spurious noise.
Minimization of heat slab nodes with higher order boundary conditions
International Nuclear Information System (INIS)
Solbrig, C.W.
1992-01-01
The accuracy of a numerical solution can be limited by the numerical approximation to the boundary conditions rather than the accuracy of the equations which describe the interior. The study presented in this paper compares the results from two different numerical formulations of the convective boundary condition on the face of a heat transfer slab. The standard representation of the boundary condition in a test problem yielded an unacceptable error even when the heat transfer slab was partitioned into over 300 nodes. A higher order boundary condition representation was obtained by using a second order approximation for the first derivative at the boundary and combining it with the general equation used for inner nodes. This latter formulation produced reasonable results when as few as ten nodes were used
System and method for free-boundary surface extraction
Algarni, Marei
2017-10-26
A method of extracting surfaces in three-dimensional data includes receiving as inputs three-dimensional data and a seed point p located on a surface to be extracted. The method further includes propagating a front outwardly from the seed point p and extracting a plurality of ridge curves based on the propagated front. A surface boundary is detected based on a comparison of distances between adjacent ridge curves and the desired surface is extracted based on the detected surface boundary.
Boundary conditions of normal and anomalous diffusion from thermal equilibrium.
Korabel, Nickolay; Barkai, Eli
2011-05-01
Infiltration of diffusing particles from one material to another, where the diffusion mechanism is either normal or anomalous, is a widely observed phenomenon. Starting with an underlying continuous-time random-walk model, we derive the boundary conditions for the diffusion equations describing this problem. We discuss a simple method showing how the boundary conditions can be determined from equilibrium experiments. When the diffusion processes are close to thermal equilibrium, the boundary conditions are determined by a thermal Boltzmann factor, which in turn controls the solution of the problem.
Crucial effect of boundary conditions on the buckling of shells
International Nuclear Information System (INIS)
Combescure, A.
1989-01-01
We want to show here that the boundary conditions can have a drastic effect on the prediction of buckling loads and that this influence can even be more drastic that the initial imperfection in some cases. This is a very important feature because the design rules in case of buckling take into account the effect of initial imperfections but do not consider the effect of unknown boundary conditions. We shall first give two examples showing this drastic effect and then develop a methodology to prevent the designer against over estimation of buckling loads due to a non conservative choice of boundary conditions
Existence results for nonlinear boundary-value problems with integral boundary conditions
Directory of Open Access Journals (Sweden)
Mouffak Benchohra
2005-01-01
Full Text Available In this paper, we investigate the existence of solutions for a second order nonlinear boundary-value problem with integral boundary conditions. By using suitable fixed point theorems, we study the cases when the right hand side has convex and nonconvex values.
Behavior of the reversed field pinch with nonideal boundary conditions
International Nuclear Information System (INIS)
Ho, Yung-Lung.
1988-11-01
The linear and nonlinear magnetohydrodynamic stability of current-driven modes are studied for a reversed field pinch with nonideal boundary conditions. The plasma is bounded by a thin resistive shell surrounded by a vacuum region out to a radius at which a perfectly conducting wall is situated. The distant wall and the thin shell problems are studied by removing either the resistive shell or the conducting wall. Linearly, growth rates of tearing modes and kink modes are calculated by analytical solutions based on the modified Bessel function model for the equilibrium. The effects of variation of the shell resistivity and wall proximity on the growth rates are investigated. The modes that may be important in different parameter regimes and with different boundary conditions are identified. The nonlinear behaviors are studied with a three-dimensional magnetohydrodynamics code. The fluctuations generally rise with increasing distance between the conducting wall and the plasma. The enhanced fluctuation induced v x b electric field primarily oppose toroidal current; hence, loop voltage must increase to sustain the constant. Quasilinear interaction between modes typically associated with the dynamo action is identified as the most probable nonlinear destabilization mechanism. The helicity and energy balance properties of the simulation results are discussed. The interruption of current density along field lines intersecting the resistive shell is shown to lead to surface helicity leakage. This effect is intimately tied to stability, as fluctuation induced v x b electric field is necessary to transport the helicity to the surface. In this manner, all aspects of helicity balance, i.e., injection, transport, and dissipation, are considered self-consistently. The importance of the helicity and energy dissipation by the mean components of the magnetic field and current density is discussed. 88 refs., 41 figs., 3 tabs
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.
Facilitating conditions for boundary-spanning behavior in governance networks
Meerkerk, Ingmar; 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 organizational literature on facilitative and servant leadership, we examine two potential conditions: a facilitative project management style and executive support. We conducted survey research among p...
Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions
Directory of Open Access Journals (Sweden)
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.
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.
Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition
Directory of Open Access Journals (Sweden)
Exequiel Mallea-Zepeda
2018-01-01
Full Text Available We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient 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.
Open boundary condition, Wilson flow and the scalar glueball mass
International Nuclear Information System (INIS)
Chowdhury, Abhishek; Harindranath, A.; Maiti, Jyotirmoy
2014-01-01
A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV≤(1/a)≤5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV≤(1/a)≤5.7 GeV.
SurfCut: Free-Boundary Surface Extraction
Algarni, Marei Saeed Mohammed
2016-09-15
We present SurfCut, an algorithm for extracting a smooth simple surface with unknown boundary from a noisy 3D image and a seed point. In contrast to existing approaches that extract smooth simple surfaces with boundary, our method requires less user input, i.e., a seed point, rather than a 3D boundary curve. Our method is built on the novel observation that certain ridge curves of a front propagated using the Fast Marching algorithm are likely to lie on the surface. Using the framework of cubical complexes, we design a novel algorithm to robustly extract such ridge curves and form the surface of interest. Our algorithm automatically cuts these ridge curves to form the surface boundary, and then extracts the surface. Experiments show the robustness of our method to errors in the data, and that we achieve higher accuracy with lower computational cost than comparable methods. © Springer International Publishing AG 2016.
Asymptotic boundary conditions for dissipative waves: General theory
Hagstrom, Thomas
1990-01-01
An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Asymptotic boundary conditions for dissipative waves - General theory
Hagstrom, Thomas
1991-01-01
An outstanding issue in computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.
Directory of Open Access Journals (Sweden)
Qingkai Kong
2012-02-01
Full Text Available In this paper, we study the existence and multiplicity of positive solutions of a class of nonlinear fractional boundary value problems with Dirichlet boundary conditions. By applying the fixed point theory on cones we establish a series of criteria for the existence of one, two, any arbitrary finite number, and an infinite number of positive solutions. A criterion for the nonexistence of positive solutions is also derived. Several examples are given for demonstration.
Quasisteady primitive equations with associated upper boundary conditions
International Nuclear Information System (INIS)
Gordon, P.
1979-01-01
This paper presents another approach to the problem of modeling large scale atmospheric flow. The major thrust of the method is to search for quasi-steady-state phenomena. This leads to sets of diagnostic and predictive equations that differ from those presently in use. Another important feature of the analysis is the introduction of a slowly floating upper boundary. In addition to simplifying the question of boundary conditions at the upper boundary, the floating top requires a highly significant change in the set of diagnostic variables. Two possible upper boundary conditions are derived in conjunction with the floating top. The first assumes continuous flow at the upper boundary, while the second assumes a compression-wave type discontinuity. Two specific criteria are formulated for checking the validity of the quasi-steady-state model. One is a scale assumption, between the physical scale and the time scale. The other is the requirement that the solution of the diagnostic equations be the steady-state limit of the original time-dependent equations. Various examples are given in order to attempt to clarify the techniques and philosophy of this approach. In addition, a specific test case is solved numerically with three models: The fixed top quasi-steady-state model, the floating top quasi-steady-state model, and a hydrostatic model. At the same time various upper boundary conditions are tested and compared. The results of the investigation indicate several significant advantages in favor of the floating top quasi-steady-state model
Nonlinear interaction of the surface waves at a plasma boundary
International Nuclear Information System (INIS)
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
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)
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.
Transport synthetic acceleration with opposing reflecting boundary conditions
International Nuclear Information System (INIS)
Zika, M.R.; Adams, M.L.
2000-01-01
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
Transport Synthetic Acceleration with Opposing Reflecting Boundary Conditions
International Nuclear Information System (INIS)
Zika, Michael R.; Adams, Marvin L.
2000-01-01
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
Critical effects of downstream boundary conditions on vortex breakdown
Kandil, Osama; Kandil, Hamdy A.; Liu, C. H.
1992-01-01
The unsteady, compressible, full Navier-Stokes (NS) equations are used to study the critical effects of the downstream boundary conditions on the supersonic vortex breakdown. The present study is applied to two supersonic vortex breakdown cases. In the first case, quasi-axisymmetric supersonic swirling flow is considered in a configured circular duct, and in the second case, quasi-axisymmetric supersonic swirling jet, that is issued from a nozzle into a supersonic jet of lower Mach number, is considered. For the configured duct flow, four different types of downstream boundary conditions are used, and for the swirling jet flow from the nozzle, two types of downstream boundary conditions are used. The solutions are time accurate which are obtained using an implicit, upwind, flux-difference splitting, finite-volume scheme.
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
Directory of Open Access Journals (Sweden)
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.
Boundary properties of solutions of equations of minimal surface kind
Miklyukov, V. M.
2001-10-01
Generalized solutions of equations of minimal-surface type are studied. It is shown that a solution makes at most countably many jumps at the boundary. In particular, a solution defined in the exterior of a disc extends by continuity to the boundary circle everywhere outside a countable point set. An estimate of the sum of certain non-local characteristics of the jumps of a solution at the boundary is presented. A result similar to Fatou's theorem on angular boundary values is proved.
Nonlinear Elliptic Boundary Value Problems at Resonance with Nonlinear Wentzell Boundary Conditions
Directory of Open Access Journals (Sweden)
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.
Change of Surface Roughness and Planetary Boundary Layer
DEFF Research Database (Denmark)
Jensen, Niels Otto
1978-01-01
The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent ...
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
Simulations of QCD and QED with C* boundary conditions
Hansen, Martin; Lucini, Biagio; Patella, Agostino; Tantalo, Nazario
2017-01-01
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 prim...
Optimal control problems for impulsive systems with integral boundary conditions
Directory of Open Access Journals (Sweden)
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.
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.
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...
The height of the atmospheric boundary layer during unstable conditions
Energy Technology Data Exchange (ETDEWEB)
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
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.
The Ablowitz-Ladik system with linearizable boundary conditions
Biondini, Gino; Bui, Anh
2015-09-01
The boundary value problem (BVP) for the Ablowitz-Ladik (AL) system on the natural numbers with linearizable boundary conditions is studied. In particular: (i) a discrete analogue is derived of the Bäcklund transformation that was used to solved similar BVPs for the nonlinear Schrödinger equation; (ii) an explicit proof is given that the Bäcklund-transformed solution of AL remains within the class of solutions that can be studied by the inverse scattering transform; (iii) an explicit linearizing transformation for the Bäcklund transformation is provided; (iv) explicit relations are obtained among the norming constants associated with symmetric eigenvalues; (v) conditions for the existence of self-symmetric eigenvalues are obtained. The results are illustrated by several exact soliton solutions, which describe the soliton reflection at the boundary with or without the presence of self-symmetric eigenvalues. This article is dedicated to Mark Ablowitz on the occasion of his seventieth birthday.
Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals
DEFF Research Database (Denmark)
Kuroda, Mitsutoshi; Tvergaard, Viggo
2009-01-01
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...... 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...
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 ...
The Hardy inequality with boundary or intermediate conditions
Czech Academy of Sciences Publication Activity Database
Kufner, Alois
2017-01-01
Roč. 8, č. 2 (2017), s. 105-109 ISSN 2077-9879 Institutional support: RVO:67985840 Keywords : Hardy's inequality * boundary conditions Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics http://www.mathnet.ru/ php /archive.phtml?wshow=paper&jrnid=emj&paperid=259&option_lang=eng
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
Directory of Open Access Journals (Sweden)
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.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
http://www.ias.ac.in/article/fulltext/reso/009/04/0050-0060. Keywords. No-slip boundary condition; Navier-Stokes equations; Poiseuille flow; flow resistance. Author Affiliations. Sandeep Prabhakara1 M D Deshpande2. Indian Institute of Technology, Kharagpur 721 302, India. CTFD Division National Aerospace Laboratories ...
Boundary conditions for open quantum systems driven far from equilibrium
Frensley, William R.
1990-07-01
This is a study of simple kinetic models of open systems, in the sense of systems that can exchange conserved particles with their environment. The system is assumed to be one dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time reversible, exponentially growing (unphysical) solutions are introduced into the time dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and its continuum formulations, are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.
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.
Frequency and Time Domain Modeling of Acoustic Liner Boundary Conditions
Bliss, Donald B.
1982-01-01
reacting layers as described in Reference [2], was extended to apply to a broad range of liner types. This method included the effect of local gradients along the liner surface, and was particularly appropriate for situations with flow over the liner and grazing incidence acoustic fields. In order to utilize time domain computational methods to solve for the propfan acoustic field, corresponding liner boundary conditions were developed for time domain solutions rather than frequency domain solutions.
On time boundary of functional metal properties maintainance under extreme conditions
Directory of Open Access Journals (Sweden)
Zhabyka L.V.
2012-08-01
Full Text Available There are established the boundaries of conserving functional properties of metals at dynamic failure under extreme conditions (longevity range t ∼10−6÷10−10s. The methods of non-linear physics made it possible to determine universal attributes of non-equilibrium systems evolution conditioned by collective effects and phenomena of self-organization in the appearing dissipative structures. In the paper there is presented a universal failure surface that allows simulation of metals behavior under laboratory conditions and forecast of time boundary of functional properties conservation.
Euclidean pseudoduality and boundary conditions in sigma models
Energy Technology Data Exchange (ETDEWEB)
Sar Latin-Small-Letter-Dotless-I saman, Mustafa, E-mail: msarisaman@ku.edu.tr [Department of Mathematics, Koc University, 34450 Sar Latin-Small-Letter-Dotless-I yer, Istanbul (Turkey)
2013-03-01
We discuss pseudoduality transformations in two-dimensional conformally invariant classical sigma models, and extend our analysis to a given boundaries of world-sheet, which gives rise to an appropriate framework for the discussion of the pseudoduality between D-branes. We perform analysis using the Euclidean spacetime and show that structures on the target space can be transformed into pseudodual manifold identically. This map requires that torsions and curvatures related to individual spaces are the same when connections are Riemannian. Boundary pseudoduality imposes locality condition.
The boundary conditions for point transformed electromagnetic invisibility cloaks
International Nuclear Information System (INIS)
Weder, Ricardo
2008-01-01
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, ∂K + , and at the inside, ∂K - , 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 ∂K + -which is always true-and that the normal components of the curl of the electric and the magnetic fields have to vanish at ∂K - . 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 ∂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 above. As these boundary conditions have to be satisfied for exact transformation
Most general AdS{sub 3} boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Grumiller, Daniel; Riegler, Max [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstr. 8-10/136, A-1040 Vienna (Austria)
2016-10-06
We consider the most general asymptotically anti-de Sitter boundary conditions in three-dimensional Einstein gravity with negative cosmological constant. The metric contains in total twelve independent functions, six of which are interpreted as chemical potentials (or non-normalizable fluctuations) and the other half as canonical boundary charges (or normalizable fluctuations). Their presence modifies the usual Fefferman-Graham expansion. The asymptotic symmetry algebra consists of two sl(2){sub k} current algebras, the levels of which are given by k=ℓ/(4G{sub N}), where ℓ is the AdS radius and G{sub N} the three-dimensional Newton constant.
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
Nonlinear Vibration Analysis of Moving Strip with Inertial Boundary Condition
Directory of Open Access Journals (Sweden)
Chong-yi Gao
2015-01-01
Full Text Available According to the movement mechanism of strip and rollers in tandem mill, the strip between two stands was simplified to axially moving Euler beam and the rollers were simplified to the inertial component on the fixed axis rotation, namely, inertial boundary. Nonlinear vibration mechanical model of Euler beam with inertial boundary conditions was established. The transverse and longitudinal motion equations were derived based on Hamilton’s principle. Kantorovich averaging method was employed to discretize the motion equations and the inertial boundary equations, and the solutions were obtained using the modified iteration method. Depending on numerical calculation, the amplitude-frequency responses of Euler beam were determined. The axial velocity, tension, and rotational inertia have strong influences on the vibration characteristics. The results would provide an important theoretical reference to control and analyze the vertical vibration of moving strip in continuous rolling process.
On the Derivation of Boundary Conditions for Continuum Dislocation Dynamics
Directory of Open Access Journals (Sweden)
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.
Matrix albedo for discrete ordinates infinite-medium boundary condition
International Nuclear Information System (INIS)
Mathews, K.; Dishaw, J.
2007-01-01
Discrete ordinates problems with an infinite exterior medium (reflector) can be more efficiently computed by eliminating grid cells in the exterior medium and applying a matrix albedo boundary condition. The albedo matrix is a discretized bidirectional reflection distribution function (BRDF) that accounts for the angular quadrature set, spatial quadrature method, and spatial grid that would have been used to model a portion of the exterior medium. The method is exact in slab geometry, and could be used as an approximation in multiple dimensions or curvilinear coordinates. We present an adequate method for computing albedo matrices and demonstrate their use in verifying a discrete ordinates code in slab geometry by comparison with Ganapol's infinite medium semi-analytic TIEL benchmark. With sufficient resolution in the spatial and angular grids and iteration tolerance to yield solutions converged to 6 digits, the conventional (scalar) albedo boundary condition yielded 2-digit accuracy at the boundary, but the matrix albedo solution reproduced the benchmark scalar flux at the boundary to all 6 digits. (authors)
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.
Matrix factorisations for rational boundary conditions by defect fusion
International Nuclear Information System (INIS)
Behr, Nicolas; Fredenhagen, Stefan
2015-01-01
A large class of two-dimensional N=(2,2) superconformal field theories can be understood as IR fixed-points of Landau-Ginzburg models. In particular, there are rational conformal field theories that also have a Landau-Ginzburg description. To understand better the relation between the structures in the rational conformal field theory and in the Landau-Ginzburg theory, we investigate how rational B-type boundary conditions are realised as matrix factorisations in the SU(3)/U(2) Grassmannian Kazama-Suzuki model. As a tool to generate the matrix factorisations we make use of a particular interface between the Kazama-Suzuki model and products of minimal models, whose fusion can be realised as a simple functor on ring modules. This allows us to formulate a proposal for all matrix factorisations corresponding to rational boundary conditions in the SU(3)/U(2) model.
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.
Bound states in waveguides with complex Robin boundary conditions
Czech Academy of Sciences Publication Activity Database
Novák, Radek
2016-01-01
Roč. 96, 3-4 (2016), s. 251-281 ISSN 0921-7134 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : non-self-adjointness * waveguide * Robin boundary conditions * spectral analysis * essential spectrum * weak coupling * Birman-Schwinger principle * reality of the spectrum Subject RIV: BE - Theoretical Physics Impact factor: 0.933, year: 2016
Eigenvalue inequalities for the Laplacian with mixed boundary conditions
Czech Academy of Sciences Publication Activity Database
Lotoreichik, Vladimir; Rohleder, J.
2017-01-01
Roč. 263, č. 1 (2017), s. 491-508 ISSN 0022-0396 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : Laplace operator * mixed boundary conditions * eigenvalue inequality * polyhedral domain * Lipschitz domain Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.988, year: 2016
New boundary conditions for oil reservoirs with fracture
Andriyanova, Elena; Astafev, Vladimir
2017-06-01
Based on the fact that most of oil fields are on the late stage of field development, it becomes necessary to produce hard-to-extract oil, which can be obtained only by use of enhance oil recovery methods. For example many low permeable or shale formations can be developed only with application of massive hydraulic fracturing technique. In addition, modern geophysical researches show that mostly oil bearing formations are complicated with tectonic faults of different shape and permeability. These discontinuities exert essential influence on the field development process and on the well performance. For the modeling of fluid flow in the reservoir with some area of different permeability, we should determine the boundary conditions. In this article for the first time the boundary conditions for the problem of fluid filtration in the reservoir with some discontinuity are considered. This discontinuity represents thin but long area, which can be hydraulic fracturing of tectonic fault. The obtained boundary condition equations allow us to take into account pressure difference above and below the section and different values of permeability.
Electromagnetic transitions between states satisfying free-boundary conditions
International Nuclear Information System (INIS)
Nikolopoulos, L. A. A.
2006-01-01
We address the problem of calculating electromagnetic transition matrix elements between states of a particle in spherically symmetrical potentials with no assumed boundary conditions at finite distance (free-boundary-condition method). For this, the Schroedinger equation is solved in a finite box of radius R and bound and continuum states, appropriately normalized, are numerically represented, through a variational finite-basis-set (B-spline) approach. The equivalence between the three transition operator forms (length, velocity, acceleration), within this approach, is discussed, and bound-continuum and continuum-continuum matrix elements are calculated in all three gauges. Results for the strong electromagnetic radiation of hydrogen are presented through the calculation of two-photon ionization cross sections and photoelectron angular distributions. It is demonstrated that the present approach is well suited for the calculation of multiphoton transitions when ionization in the continuum is allowed (above-threshold ionization). With the free-boundary-condition method complete control over the density of scattering states is feasible and, as the result of that, the degeneracy in the continuum between partial waves is preserved
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.
Time-resolved PIV measurements of the atmospheric boundary layer over wind-driven surface waves
Markfort, Corey; Stegmeir, Matt
2017-11-01
Complex interactions at the air-water interface result in two-way coupling between wind-driven surface waves and the atmospheric boundary layer (ABL). Turbulence generated at the surface plays an important role in aquatic ecology and biogeochemistry, exchange of gases such as oxygen and carbon dioxide, and it is important for the transfer of energy and controlling evaporation. Energy transferred from the ABL promotes the generation and maintenance of waves. A fraction of the energy is transferred to the surface mixed layer through the generation of turbulence. Energy is also transferred back to the ABL by waves. There is a need to quantify the details of the coupled boundary layers of the air-water system to better understand how turbulence plays a role in the interactions. We employ time-resolved PIV to measure the detailed structure of the air and water boundary layers under varying wind and wave conditions in the newly developed IIHR Boundary-Layer Wind-Wave Tunnel. The facility combines a 30-m long recirculating water channel with an open-return boundary layer wind tunnel. A thick turbulent boundary layer is developed in the 1 m high air channel, over the water surface, allowing for the study of boundary layer turbulence interacting with a wind-driven wave field.
Hydromagnetic conditions near the core-mantle boundary
Backus, George E.
1995-01-01
The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.
Directory of Open Access Journals (Sweden)
Syahira Mansur
2016-10-01
Full Text Available The unsteady boundary layer flow of a nanofluid past a stretching/shrinking sheet with a convective surface boundary condition is studied. The effects of the unsteadiness parameter, stretching/shrinking parameter, convective parameter, Brownian motion parameter and thermophoresis parameter on the local Nusselt number are investigated. Numerical solutions to the governing equations are obtained using a shooting method. The results for the local Nusselt number are presented for different values of the governing parameters. The local Nusselt number decreases as the stretching/shrinking parameter increases. The local Nusselt number is consistently higher for higher values of the convective parameter but lower for higher values of the unsteadiness parameter, Brownian motion parameter and thermophoresis parameter.
Supersymmetric Boundary Conditions in mathcal{N}=4 Super Yang-Mills Theory
Gaiotto, Davide; Witten, Edward
2009-06-01
We study boundary conditions in {N}=4 super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a "pole" at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm's equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.
High Energy Boundary Conditions for a Cartesian Mesh Euler Solver
Pandya, Shishir A.; Murman, Scott M.; Aftosmis, Michael J.
2004-01-01
Inlets and exhaust nozzles are often omitted or fared over in aerodynamic simulations of aircraft due to the complexities involving in the modeling of engine details such as complex geometry and flow physics. However, the assumption is often improper as inlet or plume flows have a substantial effect on vehicle aerodynamics. A tool for specifying inlet and exhaust plume conditions through the use of high-energy boundary conditions in an established inviscid flow solver is presented. The effects of the plume on the flow fields near the inlet and plume are discussed.
Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology
Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.
2017-12-01
The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.
Repulsive Casimir force from fractional Neumann boundary conditions
International Nuclear Information System (INIS)
Lim, S.C.; Teo, L.P.
2009-01-01
This Letter studies the finite temperature Casimir force acting on a rectangular piston associated with a massless fractional Klein-Gordon field at finite temperature. Dirichlet boundary conditions are imposed on the walls of a d-dimensional rectangular cavity, and a fractional Neumann condition is imposed on the piston that moves freely inside the cavity. The fractional Neumann condition gives an interpolation between the Dirichlet and Neumann conditions, where the Casimir force is known to be always attractive and always repulsive respectively. For the fractional Neumann boundary condition, the attractive or repulsive nature of the Casimir force is governed by the fractional order which takes values from zero (Dirichlet) to one (Neumann). When the fractional order is larger than 1/2, the Casimir force is always repulsive. For some fractional orders that are less than but close to 1/2, it is shown that the Casimir force can be either attractive or repulsive depending on the aspect ratio of the cavity and the temperature.
Boundary conditions for Kerr-AdS perturbations
Dias, Óscar J. C.; Santos, Jorge E.
2013-10-01
The Teukolsky master equation and its associated spin-weighted spheroidal harmonic decomposition simplify considerably the study of linear gravitational perturbations of the Kerr(-AdS) black hole. However, the formulation of the problem is not complete before we assign the physically relevant boundary conditions. We find a set of two Robin boundary conditions (BCs) that must be imposed on the Teukolsky master variables to get perturbations that are asymptotically global AdS, i.e. that asymptotes to the Einstein Static Universe. In the context of the AdS/CFT correspondence, these BCs allow a non-zero expectation value for the CFT stress-energy tensor while keeping fixed the boundary metric. When the rotation vanishes, we also find the gauge invariant differential map between the Teukolsky and the Kodama-Ishisbashi (Regge-Wheeler-Zerilli) formalisms. One of our Robin BCs maps to the scalar sector and the other to the vector sector of the Kodama-Ishisbashi decomposition. The Robin BCs on the Teukolsky variables will allow for a quantitative study of instability timescales and quasinormal mode spectrum of the Kerr-AdS black hole. As a warm-up for this programme, we use the Teukolsky formalism to recover the quasinormal mode spectrum of global AdS-Schwarzschild, complementing previous analysis in the literature.
Allowed wavevectors under the application of incommensurate periodic boundary conditions
International Nuclear Information System (INIS)
Boykin, Timothy B; Kharche, Neerav; Klimeck, Gerhard
2006-01-01
While the energy bands of solids are often thought of as continuous functions of the wavevector, k, they are in fact discrete functions, due to the periodic boundary conditions applied over a finite number of primitive cells. The traditional approach enforces periodicity over a volume containing N i primitive unit cells along the direction of the primitive lattice vector a i . While this method yields a simple formula for the allowed k, it can be problematic computer programs for lattices such as face-centred cubic (FCC) where the boundary faces of the primitive cell are not orthogonal. The fact that k is discrete is of critical importance for supercell calculations since they include only a finite number of unit cells, which determines the number of wavevectors, and have a given geometry, which determines their spacing. Rectangular supercells, with the faces orthogonal to the Cartesian axes, are computationally simplest but are not commensurate with the FCC unit cell, so that the traditional approach for determining the allowed k-values is no longer useful. Here, we present a simple method for finding the allowed k-values when periodic boundary conditions are applied over a rectangular supercell, answering the question in both its practical and pedagogical aspects
Electrostatics of solvated systems in periodic boundary conditions
Andreussi, Oliviero; Marzari, Nicola
2014-12-01
Continuum solvation methods can provide an accurate and inexpensive embedding of quantum simulations in liquid or complex dielectric environments. Notwithstanding a long history and manifold applications to isolated systems in open boundary conditions, their extension to materials simulations, typically entailing periodic boundary conditions, is very recent, and special care is needed to address correctly the electrostatic terms. We discuss here how periodic boundary corrections developed for systems in vacuum should be modified to take into account solvent effects, using as a general framework the self-consistent continuum solvation model developed within plane-wave density-functional theory [O. Andreussi et al., J. Chem. Phys. 136, 064102 (2012), 10.1063/1.3676407]. A comprehensive discussion of real- and reciprocal-space corrective approaches is presented, together with an assessment of their ability to remove electrostatic interactions between periodic replicas. Numerical results for zero- and two-dimensional charged systems highlight the effectiveness of the different suggestions, and underline the importance of a proper treatment of electrostatic interactions in first-principles studies of charged systems in solution.
Boundary surface and microstructure analysis of ceramic materials
International Nuclear Information System (INIS)
Woltersdorf, J.; Pippel, E.
1992-01-01
The article introduces the many possibilities of high voltage (HVEM) and high resolution electron microscopy (HREM) for boundary surface and microstructure analysis of ceramic materials. The investigations are limited to ceramic long fibre composites and a ceramic fibre/glass matrix system. (DG) [de
Influence of rigid boundary on the propagation of torsional surface ...
Indian Academy of Sciences (India)
Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer. Shishir Gupta. ∗. , Rehena Sultana and Santimoy Kundu. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826 004, India. ∗. Corresponding author. e-mail: shishir ism@yahoo.com. The present work ...
Body surface adaptations to boundary-layer dynamics
Videler, J.J.
1995-01-01
Evolutionary processes have adapted nektonic animals to interact efficiently with the water that surrounds them. Not all these adaptations serve the same purpose. This paper concentrates on reduction of drag due to friction in the boundary layer close to the body surface. Mucus, compliant skins,
Efficient enforcement of far-field boundary conditions in the Transformed Field Expansions method
Nicholls, David P.
2011-09-01
The Method of Transformed Field Expansions (TFE) has been demonstrated to be a robust and highly accurate numerical scheme for simulating solutions of boundary value and free boundary problems from the sciences and engineering. As a Boundary Perturbation Method it builds highly accurate solutions based upon exact solutions in a simple, canonical, geometry and corrects these via Taylor series to fit the actual geometry at hand. The TFE method has significantly enhanced stability properties when compared with other Boundary Perturbation approaches, however, this comes at the cost of requiring a full volumetric discretization as opposed the surface formulation that other methods can realize. In this paper we outline two techniques for ameliorating this shortcoming, first by employing a Legendre Spectral Element Method to implement efficient, graded meshes, and second by utilizing an Artificial Boundary with a Transparent Boundary Condition placed quite close to the boundary of the domain. In this contribution we focus on the specific problem of simulating the Dirichlet-Neumann operator associated to Laplace's equation on a periodic cell (which arises in the water wave problem). While the details of our results are specific to this problem, the general conclusions are valid for the wider class of problems to which the TFE method can be applied. For each technique we discuss implementation details and display numerical results which support the conclusion that each of these techniques can greatly reduce the computational cost of using the TFE method.
Viscous boundary lubrication of hydrophobic surfaces by mucin.
Yakubov, Gleb E; McColl, James; Bongaerts, Jeroen H H; Ramsden, Jeremy J
2009-02-17
The lubricating behavior of the weakly charged short-side-chain glycoprotein mucin "Orthana" (Mw=0.55 MDa) has been investigated between hydrophobic and hydrophilic PDMS substrates using soft-contact tribometry. It was found that mucin facilitates lubrication between hydrophobic PDMS surfaces, leading to a 10-fold reduction in boundary friction coefficient for rough surfaces. The presence of mucin also results in a shift of the mixed lubrication regime to lower entrainment speeds. The observed boundary lubrication behavior of mucin was found to depend on the bulk concentration, and we linked this to the structure and dynamics of the adsorbed mucin films, which are assessed using optical waveguide light spectroscopy. We observe a composite structure of the adsorbed mucin layer, with its internal structure governed by entanglement. The film thickness of this adsorbed layer increases with concentration, while the boundary friction coefficient for rough surfaces was found to be inversely proportional to the thickness of the adsorbed film. This link between lubrication and structure of the film is consistent with a viscous boundary lubrication mechanism, i.e., a thicker adsorbed film, at a given sliding speed, results in a lower local shear rate and, hence, in a lower local shear stress. The estimated local viscosities of the adsorbed layer, derived from the friction measurements and the polymer layer density, are in agreement with each other.
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.
Evolution of passive movement in advective environments: General boundary condition
Zhou, Peng; Zhao, Xiao-Qiang
2018-03-01
In a previous work [16], Lou et al. studied a Lotka-Volterra competition-diffusion-advection system, where two species are supposed to differ only in their advection rates and the environment is assumed to be spatially homogeneous and closed (no-flux boundary condition), and showed that weaker advective movements are more beneficial for species to win the competition. In this paper, we aim to extend this result to a more general situation, where the environmental heterogeneity is taken into account and the boundary condition at the downstream end becomes very flexible including the standard Dirichlet, Neumann and Robin type conditions as special cases. Our main approaches are to exclude the existence of co-existence (positive) steady state and to provide a clear picture on the stability of semi-trivial steady states, where we introduced new ideas and techniques to overcome the emerging difficulties. Based on these two aspects and the theory of abstract competitive systems, we achieve a complete understanding on the global dynamics.
Thermal properties of nuclear matter under the periodic boundary condition
International Nuclear Information System (INIS)
Otuka, Naohiko; Ohnishi, Akira
1999-01-01
We present the thermal properties of nuclear matter under the periodic boundary condition by the use of our hadronic nucleus-nucleus cascade model (HANDEL) which is developed to treat relativistic heavy-ion collisions from BNL-AGS to CERN-SPS. We first show some results of p-p scattering calculation in our new version which is improved in order to treat isospin ratio and multiplicity more accurately. We then display the results of calculation of nuclear matter with baryon density ρ b = 0.77 fm 3 at some energy densities. Time evolution of particle abundance and temperature are shown. (author)
The Casimir effect for pistons with transmittal boundary conditions
Fucci, Guglielmo
2017-11-01
This work focuses on the analysis of the Casimir effect for pistons subject to transmittal boundary conditions. In particular we consider, as piston configuration, a direct product manifold of the type I × N where I is a closed interval of the real line and N is a smooth compact Riemannian manifold. By utilizing the spectral zeta function regularization technique, we compute the Casimir energy of the system and the Casimir force acting on the piston. Explicit results for the force are provided when the manifold N is a d-dimensional sphere.
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.
Boundary layer for non-newtonian fluids on curved surfaces
International Nuclear Information System (INIS)
Stenger, N.
1981-04-01
By using the basic equation of fluid motion (conservation of mass and momentum) the boundary layer parameters for a Non-Newtonian, incompressible and laminar fluid flow, has been evaluated. As a test, the flat plate boundary layer is first analized and afterwards, a case with pressure gradient, allowing separation, is studied. In the case of curved surfaces, the problem is first developed in general and afterwards particularized to a circular cylinder. Finally suction and slip in the flow interface are examined. The power law model is used to represent the stress strain relationship in Non-Newtonian flow. By varying the fluid exponent one can then, have an idea of how the Non-Newtonian behavior of the flow influences the parameters of the boundary layer. Two equations, in an appropriate coordinate system have been obtained after an order of magnitude analysis of the terms in the equations of motion is performed. (Author) [pt
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.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
. 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......For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important...... to the atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented...
Identification of boundary heat flux on the continuous casting surface
Directory of Open Access Journals (Sweden)
E. Majchrzak
2008-12-01
Full Text Available In the paper the numerical solution of the inverse problem consisting in the identification of the heat flux on the continuous casting surface is presented. The additional information results from the measured surface or interior temperature histories. In particular the sequential function specification method using future time steps is applied. On the stage of numerical computations the 1st scheme of the boundary element method for parabolic equations is used. Because the problem is strongly non-linear the additional procedure 'linearizing' the task discussed is introduced. This procedure is called the artificial heat source method. In the final part of the paper the examples of computations are shown.
Theory of a curved planar waveguide with Robin boundary conditions.
Olendski, O; Mikhailovska, L
2010-03-01
A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Lambda , with Lambda being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Lambda at the opposite interfaces. Various transport properties of the film
Conditions on holographic entangling surfaces in higher curvature gravity
Energy Technology Data Exchange (ETDEWEB)
Erdmenger, Johanna; Flory, Mario; Sleight, Charlotte [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805, Munich (Germany)
2014-06-17
We study the extremal surfaces of functionals recently proposed for the holographic calculation of entanglement entropy in general higher curvature theories, using New Massive gravity and Gauss-Bonnet gravity as concrete examples. We show that the entropy functionals admit closed extremal surfaces, which for black hole backgrounds can encircle the event horizon of the black hole. In the examples considered, such closed surfaces correspond to a lower value of the entropy functional than expected from CFT calculations, implying a seeming mismatch between the bulk and boundary calculations. For Lorentzian settings we show that this problem can be resolved by imposing a causality constraint on the extremal surfaces. The possibility of deriving conditions from an alternative conical boundary condition method as proposed by Lewkowycz and Maldacena is explored.
Homogenized boundary conditions and resonance effects in Faraday cages
Hewitt, I. J.
2016-01-01
We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called ‘Faraday cage effect’). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. PMID:27279775
Boundary lubrication of heterogeneous surfaces and the onset of cavitation in frictional contacts.
Savio, Daniele; Pastewka, Lars; Gumbsch, Peter
2016-03-01
Surfaces can be slippery or sticky depending on surface chemistry and roughness. We demonstrate in atomistic simulations that regular and random slip patterns on a surface lead to pressure excursions within a lubricated contact that increase quadratically with decreasing contact separation. This is captured well by a simple hydrodynamic model including wall slip. We predict with this model that pressure changes for larger length scales and realistic frictional conditions can easily reach cavitation thresholds and significantly change the load-bearing capacity of a contact. Cavitation may therefore be the norm, not the exception, under boundary lubrication conditions.
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Ideas leading to the resolution of the problem of no-slip condition for fluid velocity at a solid surface are traced in this concluding part of the article. In the continuum limit velocity slip being zero is established beyond any doubt now. Even turbulent flows which have a large velocity gradient near a wall have to satisfy the ...
Subjective surfaces: a geometric model for boundary completion
Energy Technology Data Exchange (ETDEWEB)
Sarti, Alessandro; Malladi, Ravi; Sethian, J.A.
2000-06-01
We present a geometric model and a computational method for segmentation of images with missing boundaries. In many situations, the human visual system fills in missing gaps in edges and boundaries, building and completing information that is not present. Boundary completion presents a considerable challenge in computer vision, since most algorithms attempt to exploit existing data. A large body of work concerns completion models, which postulate how to construct missing data; these models are often trained and specific to particular images. In this paper, we take the following, alternative perspective: we consider a reference point within an image as given, and then develop an algorithm which tries to build missing information on the basis of the given point of view and the available information as boundary data to the algorithm. Starting from this point of view, a surface is constructed. It is then evolved with the mean curvature flow in the metric induced by the image until a piecewise constant solution is reached. We test the computational model on modal completion, amodal completion, texture, photo and medical images. We extend the geometric model and the algorithm to 3D in order to extract shapes from low signal/noise ratio medical volumes. Results in 3D echocardiography and 3D fetal echography are presented.
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
DEFF Research Database (Denmark)
Johannessen, Kim
2014-01-01
The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...
Vibration modes of a single plate with general boundary conditions
Directory of Open Access Journals (Sweden)
Phamová L.
2016-06-01
Full Text Available This paper deals with free flexural vibration modes and natural frequencies of a thin plate with general boundary conditions — a simply supported plate connected to its surroundings with torsional springs. Vibration modes were derived on the basis of the Rajalingham, Bhat and Xistris approach. This approach was originally used for a clamped thin plate, so its adaptation was needed. The plate vibration function was usually expressed as a single partial differential equation. This partial differential equation was transformed into two ordinary differential equations that can be solved in the simpler way. Theoretical background of the computations is briefly described. Vibration modes of the supported plate with torsional springs are presented graphically and numerically for three different values of stiffness of torsional springs.
Unsteady Squeezing Flow of Carbon Nanotubes with Convective Boundary Conditions.
Directory of Open Access Journals (Sweden)
Tasawar Hayat
Full Text Available Unsteady flow of nanofluids squeezed between two parallel plates is discussed in the presence of viscous dissipation. Heat transfer phenomenon is disclosed via convective boundary conditions. Carbon nanotubes (single-wall and multi-wall are used as nanoparticles which are homogeneously distributed in the base fluid (water. A system of non-linear differential equations for the flow is obtained by utilizing similarity transformations through the conservation laws. Influence of various emerging parameters on the velocity and temperature profiles are sketched graphically and discussed comprehensively. Analyses of skin fraction coefficient and Nusselt number are also elaborated numerically. It is found out that velocity is smaller for squeezing parameter in the case of multi-wall carbon nanotubes when compared with single-wall carbon nanotubes.
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.
Yang, Chuan-Fu
Inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions. We give formulations of the associated inverse problems such as Titchmarsh-Weyl theorem, Hochstadt-Lieberman theorem and Mochizuki-Trooshin theorem, and prove corresponding uniqueness theorems. The obtained results are generalizations of the similar results for the classical Sturm-Liouville operator on a finite interval.
Scalar field dynamics in a BTZ background with generic boundary conditions
International Nuclear Information System (INIS)
Garbarz, Alan; La Madrid, Joan; Leston, Mauricio
2017-01-01
We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4 ≤ m e 2 l 2 < 0 can be well defined within a one-parametric family of distinct boundary conditions (-3/4 being the conformally coupled case), while for m e 2 l 2 ≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m e 2 l 2 < -1, and also it is shown that in the range m e 2 l 2 element of [-1, -3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. (orig.)
Scalar field dynamics in a BTZ background with generic boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Garbarz, Alan; La Madrid, Joan [UBA y IFIBA, CONICET, Departamento de Fisica, FCEyN, Buenos Aires (Argentina); Leston, Mauricio [Pabellon IAFE-CONICET, Instituto de Astronomia y Fisica del Espacio, Buenos Aires (Argentina)
2017-11-15
We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4 ≤ m{sub e}{sup 2}l{sup 2} < 0 can be well defined within a one-parametric family of distinct boundary conditions (-3/4 being the conformally coupled case), while for m{sub e}{sup 2}l{sup 2} ≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m{sub e}{sup 2}l{sup 2} < -1, and also it is shown that in the range m{sub e}{sup 2}l{sup 2} element of [-1, -3/4) there is a U(1) family of allowed boundary conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved. (orig.)
Streamline Patterns and their Bifurcations near a wall with Navier slip Boundary Conditions
DEFF Research Database (Denmark)
Tophøj, Laust; Møller, Søren; Brøns, Morten
2006-01-01
We consider the two-dimensional topology of streamlines near a surface where the Navier slip boundary condition applies. Using transformations to bring the streamfunction in a simple normal form, we obtain bifurcation diagrams of streamline patterns under variation of one or two external parameters....... Topologically, these are identical with the ones previously found for no-slip surfaces. We use the theory to analyze the Stokes flow inside a circle, and show how it can be used to predict new bifurcation phenomena. ©2006 American Institute of Physics...
Surfaces of Constant Mean Curvature in Euclidean 3-space Orthogonal to a Plane along its Boundary
Directory of Open Access Journals (Sweden)
HINOJOSA PEDRO A.
2002-01-01
Full Text Available We consider compact surfaces with constant nonzero mean curvature whose boundary is a convex planar Jordan curve. We prove that if such a surface is orthogonal to the plane of the boundary, then it is a hemisphere.
Scalar field dynamics in a BTZ background with generic boundary conditions
Garbarz, Alan; La Madrid, Joan; Leston, Mauricio
2017-11-01
We revisit the dynamics of a massive scalar field in a Banados, Teitelboim, and Zanelli background taking into account the lack of global hyperbolicity of the spacetime. We approach this issue using the strategy of Ishibashi and Wald which finds a unique smooth solution as the causal evolution of initial data, each possible evolution corresponding to a positive self-adjoint extension of certain operator in a Hilbert space on the initial surface. Moreover, solutions obtained this way are the most general ones satisfying a few physically sensible requirements. This procedure is intimately related to the choice of boundary conditions and the existence of bound states. We find that the scalar field dynamics in the (effective) mass window -3/4≤ m_e^2ℓ ^2conditions (-3/4 being the conformally coupled case), while for m_e^2ℓ ^2≥ 0 the boundary condition is unique (only one self-adjoint extension is possible). It is argued that there is no sensible evolution possible for m_e^2ℓ ^2conditions, however, the positivity of the self-adjoint extensions is only motivated but not proven. We focus mainly on describing the dynamics of such evolutions given the initial data and all possible boundary conditions, and in particular we show the energy is always positive and conserved.
A Case Study of Offshore Advection of Boundary Layer Rolls over a Stably Stratified Sea Surface
DEFF Research Database (Denmark)
Svensson, Nina; Sahlée, Erik; Bergström, Hans
2017-01-01
originate from boundary layer rolls generated over the convective air above Swedish mainland, also supported by visual satellite images showing the typical signature cloud streets. The simulations indicate that the rolls are advected and maintained at least 30–80 km off the coast, in agreement...... with the streaks observed by the SAR images. During evening when the convective conditions over land diminish, the streaky structures over the sea are still seen in the horizontal wind field; however, the vertical component is close to zero. Thus advected feature from a land surface can affect the wind field...... considerably for long times and over large areas in coastal regions. Although boundary layer rolls are a well-studied feature, no previous study has presented results concerning their persistence during situations with advection to a strongly stratified boundary layer. Such conditions are commonly encountered...
Energy Technology Data Exchange (ETDEWEB)
Biondini, Gino [Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260 (United States); Kovačič, Gregor [Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2014-03-15
The inverse scattering transform for the focusing nonlinear Schrödinger equation with non-zero boundary conditions at infinity is presented, including the determination of the analyticity of the scattering eigenfunctions, the introduction of the appropriate Riemann surface and uniformization variable, the symmetries, discrete spectrum, asymptotics, trace formulae and the so-called theta condition, and the formulation of the inverse problem in terms of a Riemann-Hilbert problem. In addition, the general behavior of the soliton solutions is discussed, as well as the reductions to all special cases previously discussed in the literature.
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.
Boundary layer flow of nanofluid over an exponentially stretching surface
Nadeem, Sohail; Lee, Changhoon
2012-01-01
The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.
Boundary layer flow of nanofluid over an exponentially stretching surface.
Nadeem, Sohail; Lee, Changhoon
2012-01-30
The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.
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
A Note on Fractional Differential Equations with Fractional Separated Boundary Conditions
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2012-01-01
Full Text Available We consider a new class of boundary value problems of nonlinear fractional differential equations with fractional separated boundary conditions. A connection between classical separated and fractional separated boundary conditions is developed. Some new existence and uniqueness results are obtained for this class of problems by using standard fixed point theorems. Some illustrative examples are also discussed.
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.
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
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 ...
Boundary conditions for a composite model of leptons and quarks
International Nuclear Information System (INIS)
Mainland, G B
2015-01-01
Because the existence of families of elements and hadrons was ultimately understood by the realization that atoms and hadrons are composite, an obvious approach to explaining the existence of lepton and quark families is to assume that the particles in these families are also composite. The mass and spin spectra of leptons and quarks suggest that if these particles are composite, they are most likely bound states of a scalar and spin-1/2 fermion interacting via electrodynamics. However, if they are composite, the bound states must be highly relativistic since in each family the least massive member has a small mass compared with the others. Also, composite leptons and quarks must be extremely tightly bound since no internal structure has ever been conclusively detected. Highly relativistic, bound-state, Bethe- Salpeter solutions of a scalar and a spin-1/2 fermion bound by minimal electrodynamics are discussed. These specific solutions cannot describe leptons or quarks as bound states because the magnitude of the charges of the constituents are an order of magnitude larger than e. The boundary conditions, however, allow solutions when the constituents have charges with magnitudes on the order of e. (paper)
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.
Nested Bethe Ansatz for Spin Ladder Model with Open Boundary Conditions
International Nuclear Information System (INIS)
Wu Junfang; Zhang Chunmin; Yue Ruihong; Li Runling
2005-01-01
The nested Bethe ansatz (BA) method is applied to find the eigenvalues and the eigenvectors of the transfer matrix for spin-ladder model with open boundary conditions. Based on the reflection equation, we find the general diagonal solution, which determines the general boundary interaction in the Hamiltonian. We introduce the spin-ladder model with open boundary conditions. By finding the solution K ± of the reflection equation which determines the nontrivial boundary terms in the Hamiltonian, we diagonalize the transfer matrix of the spin-ladder model with open boundary conditions in the framework of nested BA.
Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains
International Nuclear Information System (INIS)
Ferraro, N.M.; Jardin, S.C.; Luo, X.
2010-01-01
The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.
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.
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.
Edery, Ariel; Graham, Noah; MacDonald, Ilana
2009-06-01
Under dimensional reduction, a system in D spacetime dimensions will not necessarily yield its D-1-dimensional analog version. Among other things, this result will depend on the boundary conditions and the dimension D of the system. We investigate this question for scalar and Abelian gauge fields under boundary conditions that obey the symmetries of the action. We apply our findings to the Casimir piston, an ideal system for detecting boundary effects. Our investigation is not limited to extra dimensions and we show that the original piston scenario proposed in 2004, a toy model involving a scalar field in 3D (2+1) dimensions, can be obtained via dimensional reduction from a more realistic 4D electromagnetic (EM) system. We show that for perfect conductor conditions, a D-dimensional EM field reduces to a D-1 scalar field and not its lower-dimensional version. For Dirichlet boundary conditions, no theory is recovered under dimensional reduction and the Casimir pressure goes to zero in any dimension. This “zero Dirichlet” result is useful for understanding the EM case. We then identify two special systems where the lower-dimensional version is recovered in any dimension: systems with perfect magnetic conductor (PMC) and Neumann boundary conditions. We show that these two boundary conditions can be obtained from a variational procedure in which the action vanishes outside the bounded region. The fields are free to vary on the surface and have zero modes, which survive after dimensional reduction.
A Monge–Ampere Equation with an Unusual Boundary Condition
Directory of Open Access Journals (Sweden)
Marc Sedjro
2015-11-01
Full Text Available We consider a class of Monge–Ampere equations where the convex conjugate of the unknown function is prescribed on a boundary of its domain yet to be determined. We show the existence of a weak solution.
Effect of inlet conditions for numerical modelling of the urban boundary layer
Gnatowska, Renata
2018-01-01
The paper presents the numerical results obtained with the use of the ANSYS FLUENT commercial code for analysing the flow structure around two rectangular inline surface-mounted bluff bodies immersed in a boundary layer. The effects of the inflow boundary layer for the accuracy of the numerical modelling of the flow field around a simple system of objects are described. The analysis was performed for two concepts. In the former case, the inlet velocity profile was defined using the power law, whereas the kinetic and dissipation energy was defined from the equations according to Richards and Hoxey [1]. In the latter case, the inlet conditions were calculated for the flow over the rough area composed of the rectangular components.
Hejranfar, Kazem; Parseh, Kaveh
2017-09-01
The preconditioned characteristic boundary conditions based on the artificial compressibility (AC) method are implemented at artificial boundaries for the solution of two- and three-dimensional incompressible viscous flows in the generalized curvilinear coordinates. The compatibility equations and the corresponding characteristic variables (or the Riemann invariants) are mathematically derived and then applied as suitable boundary conditions in a high-order accurate incompressible flow solver. The spatial discretization of the resulting system of equations is carried out by the fourth-order compact finite-difference (FD) scheme. In the preconditioning applied here, the value of AC parameter in the flow field and also at the far-field boundary is automatically calculated based on the local flow conditions to enhance the robustness and performance of the solution algorithm. The code is fully parallelized using the Concurrency Runtime standard and Parallel Patterns Library (PPL) and its performance on a multi-core CPU is analyzed. The incompressible viscous flows around a 2-D circular cylinder, a 2-D NACA0012 airfoil and also a 3-D wavy cylinder are simulated and the accuracy and performance of the preconditioned characteristic boundary conditions applied at the far-field boundaries are evaluated in comparison to the simplified boundary conditions and the non-preconditioned characteristic boundary conditions. It is indicated that the preconditioned characteristic boundary conditions considerably improve the convergence rate of the solution of incompressible flows compared to the other boundary conditions and the computational costs are significantly decreased.
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.
Analysis of the susceptibility in a fluid system with Neumann – plus boundary conditions
Directory of Open Access Journals (Sweden)
Djondjorov Peter
2018-01-01
Full Text Available The behaviour of the local and total susceptibilities of a fluid system bounded by different surfaces is studied in the framework of the Ginsburg-Landau Ising type model. The case of a plain geometry, Neumann-infinity boundary conditions under variations of the temperature and an external ordering field is considered. Exact analytic expressions for the order parameter, local and total susceptibilities in such a system are presented. They are used to analyse the phase behaviour of fluids confined in regions close to the bulk critical point of the respective infinite system.
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...... though: the full variability with the perpendicular wind speed and horizontal rain intensity should be preserved, where feasible, for improved estimations of the moisture transfer in building components. In the concluding section, it is moreover shown that the dependence of the surface moisture transfer...
Modeling of microdevices for SAW-based acoustophoresis - A study of boundary conditions
DEFF Research Database (Denmark)
Skov, Nils Refstrup; Bruus, Henrik
2016-01-01
We present a finite-element method modeling of acoustophoretic devices consisting of a single, long, straight, water-filled microchannel surrounded by an elastic wall of either borosilicate glass (pyrex) or the elastomer polydimethylsiloxane (PDMS) and placed on top of a piezoelectric transducer...... that actuates the device by surface acoustic waves (SAW). We compare the resulting acoustic fields in these full solid-fluid models with those obtained in reduced fluid models comprising of only a water domain with simplified, approximate boundary conditions representing the surrounding solids. The reduced...
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.
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
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.
Directory of Open Access Journals (Sweden)
Laraqi Najib
2017-01-01
Full Text Available Heat conduction in solids subjected to non-homogenous boundary conditions leads to singularities in terms of heat flux density. That kind of issues can be also encountered in various scientists’ fields as electromagnetism, electrostatic, electrochemistry and mechanics. These problems are difficult to solve by using the classical methods such as integral transforms or separation of variables. These methods lead to solving of dual integral equations or Fredholm integral equations, which are not easy to use. The present work addresses the calculation of thermal resistance of a finite medium submitted to conjugate surface Neumann and Dirichlet conditions, which are defined by a band-shape heat source and a uniform temperature. The opposite surface is subjected to a homogeneous boundary condition such uniform temperature, or insulation. The proposed solving process is based on simple and accurate correlations that provide the thermal resistance as a function of the ratio of the size of heat source and the depth of the medium. A judicious scale analysis is performed in order to fix the asymptotic behaviour at the limits of the value of the geometric parameter. The developed correlations are very simple to use and are valid regardless of the values of the defined geometrical parameter. The performed validations by comparison with numerical modelling demonstrate the relevant agreement of the solutions to address singularity calculation issues.
Beutner, Thomas J.; Celik, Zeki Z.; Roberts, Leonard
1992-01-01
A computational study has been undertaken to investigate method of modeling solid and porous wall boundary conditions in computational fluid dynamics (CFD) codes. The procedure utilizes experimental measurements at the walls to develop a flow field solution based on the method of singularities. This flow field solution is then imposed as a boundary condition in a CFD simulation of the internal flow field. The effectiveness of this method in describing the boundary conditions at the wind tunnel walls using only sparse experimental measurements has been investigated. Position and refinement of experimental measurement locations required to describe porous wall boundary conditions has also been considered.
Quaas, Alexander; Rodríguez, Andrei
2018-02-01
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data C1 up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary.
Liu, Biyue; Zheng, Jie; Bach, Richard; Tang, Dalin
2015-01-01
inlet and the outlet did not have significant effect on the spatial distribution patterns of the PD, the WPG and the WSS on the lumen surface, regarding the locations of the maximum and the minimum of each quantity. The observations from this study indicated that the ways how pressure and velocity boundary conditions are imposed in computational models have considerable impact on flow velocity and shear stress predictions. Accuracy of in vivo measurements of blood pressure and velocity is of great importance for reliable model predictions.
Evolution of the lower planetary boundary layer over strongly contrasting surfaces
International Nuclear Information System (INIS)
Coulter, R.L.; Gao, W.; Martin, T.J.; Shannon, J.D.; Doran, J.C.; Hubbe, J.M.; Shaw, W.M.
1992-01-01
In a multilaboratory field study held near Boardman in northeastern Oregon in June 1991, various properties of the surface and lower atmospheric boundary layer over heavily irrigated cropland and adjacent desert steppe were investigated in the initial campaign of the Atmospheric Radiation Measurement (ARM) program. The locale was selected because its disparate characteristics over various spatial scales stress the ability of general circulation models (GCMS) to describe lower boundary conditions, particularly across the discontinuity between desert (in which turbulent flux of heat must be primarily as sensible heat) and large irrigated tracts (in which turbulent flux of latent heat should be the larger term). This campaign of ARM seeks to increase knowledge in three critical areas: (1) determination of the relationships between surface heat fluxes measured over multiple scales and the controlling surface parameters within each scale, (2) integration of local and nearly local heat flux estimates to produce estimates appropriate for GCM grid cells of 100-200 km horizontal dimension, and (3) characterization of the growth and development of the atmospheric boundary layer near transitions between surfaces with strongly contrasting moisture availabilities
International Nuclear Information System (INIS)
Teles, V.; Maugis, P.; Mouche, E.; Brulhet, J.; Wendling, J.; Vigneron, G.
2007-01-01
The Callovo-Oxfordian formation in the Eastern part of France was recognized as a potential nuclear waste repository layer. The ANDRA (National Agency for Nuclear Waste Management) has launched a few years ago a research program that aims to define the mechanisms of importance in the impact of the surface environment evolution on the site hydrogeology. Based on mapping and dating results, ANDRA has quantified the geomorphological evolution of the Meuse/Haute-Marne site in the past and has estimated the future evolution over 1 million years. The Callovo-Oxfordian boundary conditions depend on the hydraulic heads in the two surrounding aquifers, the Oxfordian limestone above, and the Dogger one, below. Both aquifer outcrops are modified over the next million years. For the present study, the geo-morphologic evolution is considered independently of other processes and translated in the hydrogeological model in terms of changes in the hydraulic boundary conditions at the surface. The hydrodynamic simulations have been performed with the code Cast3M (implemented by CEA (Atomic Energy Commissariat)) using a mixed hybrid finite-element formulation. For these groundwater flow simulations, three modelled stages are presented: the Present, 500,000 years (500 Ky) and 10 6 years (1 Ma) in the future. The landscape evolution is merely considered through the use of three different topographies on which the boundary conditions are applied. According to ANDRA predictions, at the Meuse/Haute-Marne site, the valley incisions on the Bure plateau will locally reach the Oxfordian limestone. Thus, the Oxfordian aquifer exhibits more changes due to topographic evolution than the Dogger aquifer. Hydrodynamic simulations show a significant impact of the valley incisions on the groundwater flow by the creation of local outlets to the Oxfordian limestone aquifer in the North of the area for the 1 My topography. It induces local perturbations of the saturation level. The global erosion of the
Stress and mixed boundary conditions for two-dimensional ...
Indian Academy of Sciences (India)
decagonal quasi-crystal (QC) media, the reciprocal theorem and the general solution for. QCs are applied in a novel ... flat plates consists of an interior component significant throughout the plates and a boundary layer component (in ..... important, but whose minimum distance ˜d from E to ˜E is positive and independent of h.
Airborne Measurement of Insolation Impact on the Atmospheric Surface Boundary Layer
Jacob, Jamey; Chilson, Phil; Houston, Adam; Detweiler, Carrick; Bailey, Sean; Cloud-Map Team
2017-11-01
Atmospheric surface boundary layer measurements of wind and thermodynamic parameters are conducted during variable insolation conditions, including the 2017 eclipse, using an unmanned aircraft system. It is well known that the air temperatures can drop significantly during a total solar eclipse as has been previously observed. In past eclipses, these observations have primarily been made on the ground. We present results from airborne measurements of the near surface boundary layer using a small unmanned aircraft with high temporal resolution wind and thermodynamic observations. Questions that motivate the study include: How does the temperature within the lower atmospheric boundary vary during an eclipse? What impact does the immediate removal of radiative heating on the ground have on the lower ABL? Do local wind patterns change during an eclipse event and if so why? Will there be a manifestation of the nocturnal boundary layer wind maximum? Comparisons are made with the DOE ARM SGP site that experiences a lower but still significant insolation. Supported by the National Science Foundation under Award Number 1539070.
International Nuclear Information System (INIS)
Agrawal, Nilesh; Ali, Seik Mansoor; Balasubramaniyan, V.
2015-01-01
A Passive Auto-catalytic recombiners (PAR) consists of an array of vertical catalyst coated plates. Hydrogen rich gas mixture flows between the plates and reacts exothermically leading to high plate temperature. This can lead to PAR induced deflagration which is a major safety concern. PAR induced deflagration can be avoided if heat transfer from the plates of a PAR is enhanced. Thus, numerical studies are carried out for reactive flow of gas mixture within one vertical channel with heat transfer controlled boundaries. Four different heat transfer boundary conditions, namely, adiabatic, natural convection, forced convection and pool boiling heat transfer boundary conditions are considered. The results show that the catalyst surface temperature can be controlled using enhanced heat transfer from the surface. Pool boiling heat transfer is especially very effective in controlling the temperature and ensuring high rate of reactions. The results may be useful in designing better PARs in the future. (author)
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.
A mixed-grid finite element method with PML absorbing boundary conditions for seismic wave modelling
International Nuclear Information System (INIS)
Liu, Shaolin; Li, Xiaofan; Liu, Youshan; Wang, Wenshuai
2014-01-01
We have developed a mixed-grid finite element method (MGFEM) to simulate seismic wave propagation in 2D structurally complex media. This method divides the physical domain into two subdomains. One subdomain covering the major part of the physical domain is divided by regular quadrilateral elements, while the other subdomain uses triangular elements to correctly fit a rugged free surface topography. The local stiffness matrix of any quadrilateral element is identical and matrix-vector production is calculated using an element-by-element technique, which avoids assembling a huge global stiffness matrix. As only a few triangular elements exist in the subdomain containing the rugged free surface topography, the memory requirements for storing the assembled subdomain global stiffness matrix are significantly reduced. To eliminate artificial boundary reflections, the MGFEM is also implemented to solve the system equations of PML absorbing boundary conditions (PML ABC). The accuracy and efficiency of the MGFEM is tested in numerical experiments by comparing it with conventional methods, and numerical comparisons also indicate its tremendous ability to describe rugged surfaces. (paper)
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
Generating wind fluctuations for Large Eddy Simulation inflow boundary condition
International Nuclear Information System (INIS)
Bekele, S.A.; Hangan, H.
2004-01-01
Large Eddy Simulation (LES) studies of flows over bluff bodies immersed in a boundary layer wind environment require instantaneous wind characteristics. The influences of the wind environment on the building pressure distribution are a well-established fact in the experimental study of wind engineering. Measured wind data of full or model scale are available only at a limited number of points. A method of obtaining instantaneous wind data at all mesh points of the inlet boundary for LES computation is necessary. Herein previous and new wind inflow generation techniques are presented. The generated wind data is then applied to a LES computation of a channel flow. The characteristics of the generated wind fluctuations in comparison to the measured data and the properties of the flow field computed from these two wind data are discussed. (author)
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.
Effect of boundary conditions on radial mode structure of whistlers
International Nuclear Information System (INIS)
Boswell, R.W.
1983-01-01
The dispersion of the radical eigen modes of a cylindrical m=1 whistler wave with Ωsub(i) << ω << Ωsub(e) << ωsub(pe) are investigated for both conducting and insulating boundaries, where Ωsub(e) and Ωsub(i) are the electron and ion gyro frequencies, Ωsub(pe) is the electron plasma frequency. The effects of electron inertia and resistivity on the modes are discussed
Korbly, L.
1980-01-01
The exchange of stabilities is demonstrated for a system with harmonic boundary conditions. The motion of fluid in the presence of temperatures gradients is described. It is shown that this principle holds under free, but not rigid or semirigid, boundary conditions.
Trickle-down boundary conditions in aeolian dune-field pattern formation
Ewing, R. C.; Kocurek, G.
2015-12-01
One the one hand, wind-blown dune-field patterns emerge within the overarching boundary conditions of climate, tectonics and eustasy implying the presence of these signals in the aeolian geomorphic and stratigraphic record. On the other hand, dune-field patterns are a poster-child of self-organization, in which autogenic processes give rise to patterned landscapes despite remarkable differences in the geologic setting (i.e., Earth, Mars and Titan). How important are climate, tectonics and eustasy in aeolian dune field pattern formation? Here we develop the hypothesis that, in terms of pattern development, dune fields evolve largely independent of the direct influence of 'system-scale' boundary conditions, such as climate, tectonics and eustasy. Rather, these boundary conditions set the stage for smaller-scale, faster-evolving 'event-scale' boundary conditions. This 'trickle-down' effect, in which system-scale boundary conditions indirectly influence the event scale boundary conditions provides the uniqueness and richness of dune-field patterned landscapes. The trickle-down effect means that the architecture of the stratigraphic record of dune-field pattern formation archives boundary conditions, which are spatially and temporally removed from the overarching geologic setting. In contrast, the presence of an aeolian stratigraphic record itself, reflects changes in system-scale boundary conditions that drive accumulation and preservation of aeolian strata.
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.
The effect of external boundary conditions on condensation heat transfer in rotating heat pipes
Daniels, T. C.; Williams, R. J.
1979-01-01
Experimental evidence shows the importance of external boundary conditions on the overall performance of a rotating heat pipe condenser. Data are presented for the boundary conditions of constant heat flux and constant wall temperature for rotating heat pipes containing either pure vapor or a mixture of vapor and noncondensable gas as working fluid.
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.
Gnoffo, Peter A.; Johnston, Christopher O.
2011-01-01
Implementations of a model for equilibrium, steady-state ablation boundary conditions are tested for the purpose of providing strong coupling with a hypersonic flow solver. The objective is to remove correction factors or film cooling approximations that are usually applied in coupled implementations of the flow solver and the ablation response. Three test cases are considered - the IRV-2, the Galileo probe, and a notional slender, blunted cone launched at 10 km/s from the Earth's surface. A successive substitution is employed and the order of succession is varied as a function of surface temperature to obtain converged solutions. The implementation is tested on a specified trajectory for the IRV-2 to compute shape change under the approximation of steady-state ablation. Issues associated with stability of the shape change algorithm caused by explicit time step limits are also discussed.
Structural acoustic control of plates with variable boundary conditions: design methodology.
Sprofera, Joseph D; Cabell, Randolph H; Gibbs, Gary P; Clark, Robert L
2007-07-01
A method for optimizing a structural acoustic control system subject to variations in plate boundary conditions is provided. The assumed modes method is used to build a plate model with varying levels of rotational boundary stiffness to simulate the dynamics of a plate with uncertain edge conditions. A transducer placement scoring process, involving Hankel singular values, is combined with a genetic optimization routine to find spatial locations robust to boundary condition variation. Predicted frequency response characteristics are examined, and theoretically optimized results are discussed in relation to the range of boundary conditions investigated. Modeled results indicate that it is possible to minimize the impact of uncertain boundary conditions in active structural acoustic control by optimizing the placement of transducers with respect to those uncertainties.
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.
Water Surface Ripples Generated by the Turbulent Boundary Layer of a Surface-Piercing Moving Wall
Washuta, N.; Masnadi, N.; Duncan, J. H.
2014-11-01
Free surface ripples created by subsurface turbulence along a surface-piercing moving wall are studied experimentally. In this experiment, a meter-wide stainless steel belt travels horizontally in a loop around two rollers with vertically oriented axes, which are separated by 7.5 meters. One of the two 7.5-m-long belt sections between the rollers is in contact with the water in a large open-surface water tank and the water level is adjusted so that the top of the belt pierces the water free surface. The belt is launched from rest with a 3 g acceleration in order to quickly reach a steady state velocity. This belt motion creates a temporally evolving boundary layer analogous to the spatially evolving boundary layer created along the side of a ship hull moving at the belt velocity, with a length equivalent to the length of belt that has passed the measurement region. The water surface ripples generated by the subsurface turbulence are measured in a plane normal to the belt using a cinematic LIF technique. It is found that the overall RMS surface fluctuations increase linearly with belt speed and that the spatial distributions of the fluctuations show a sharp increase near the wall. The support of the Office of Naval Research is gratefully acknowledged.
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.)
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.
A Case Study of Offshore Advection of Boundary Layer Rolls over a Stably Stratified Sea Surface
Directory of Open Access Journals (Sweden)
Nina Svensson
2017-01-01
Full Text Available Streaky structures of narrow (8-9 km high wind belts have been observed from SAR images above the Baltic Sea during stably stratified conditions with offshore winds from the southern parts of Sweden. Case studies using the WRF model and in situ aircraft observations indicate that the streaks originate from boundary layer rolls generated over the convective air above Swedish mainland, also supported by visual satellite images showing the typical signature cloud streets. The simulations indicate that the rolls are advected and maintained at least 30–80 km off the coast, in agreement with the streaks observed by the SAR images. During evening when the convective conditions over land diminish, the streaky structures over the sea are still seen in the horizontal wind field; however, the vertical component is close to zero. Thus advected feature from a land surface can affect the wind field considerably for long times and over large areas in coastal regions. Although boundary layer rolls are a well-studied feature, no previous study has presented results concerning their persistence during situations with advection to a strongly stratified boundary layer. Such conditions are commonly encountered during spring in coastal regions at high latitudes.
Drag reduction using wrinkled surfaces in high Reynolds number laminar boundary layer flows
Raayai-Ardakani, Shabnam; McKinley, Gareth H.
2017-09-01
Inspired by the design of the ribbed structure of shark skin, passive drag reduction methods using stream-wise riblet surfaces have previously been developed and tested over a wide range of flow conditions. Such textures aligned in the flow direction have been shown to be able to reduce skin friction drag by 4%-8%. Here, we explore the effects of periodic sinusoidal riblet surfaces aligned in the flow direction (also known as a "wrinkled" texture) on the evolution of a laminar boundary layer flow. Using numerical analysis with the open source Computational Fluid Dynamics solver OpenFOAM, boundary layer flow over sinusoidal wrinkled plates with a range of wavelength to plate length ratios ( λ / L ), aspect ratios ( 2 A / λ ), and inlet velocities are examined. It is shown that in the laminar boundary layer regime, the riblets are able to retard the viscous flow inside the grooves creating a cushion of stagnant fluid that the high-speed fluid above can partially slide over, thus reducing the shear stress inside the grooves and the total integrated viscous drag force on the plate. Additionally, we explore how the boundary layer thickness, local average shear stress distribution, and total drag force on the wrinkled plate vary with the aspect ratio of the riblets as well as the length of the plate. We show that riblets with an aspect ratio of close to unity lead to the highest reduction in the total drag, and that because of the interplay between the local stress distribution on the plate and stream-wise evolution of the boundary layer the plate has to exceed a critical length to give a net decrease in the total drag force.
Inferring Lower Boundary Driving Conditions Using Vector Magnetic Field Observations
Schuck, Peter W.; Linton, Mark; Leake, James; MacNeice, Peter; Allred, Joel
2012-01-01
Low-beta coronal MHD simulations of realistic CME events require the detailed specification of the magnetic fields, velocities, densities, temperatures, etc., in the low corona. Presently, the most accurate estimates of solar vector magnetic fields are made in the high-beta photosphere. Several techniques have been developed that provide accurate estimates of the associated photospheric plasma velocities such as the Differential Affine Velocity Estimator for Vector Magnetograms and the Poloidal/Toroidal Decomposition. Nominally, these velocities are consistent with the evolution of the radial magnetic field. To evolve the tangential magnetic field radial gradients must be specified. In addition to estimating the photospheric vector magnetic and velocity fields, a further challenge involves incorporating these fields into an MHD simulation. The simulation boundary must be driven, consistent with the numerical boundary equations, with the goal of accurately reproducing the observed magnetic fields and estimated velocities at some height within the simulation. Even if this goal is achieved, many unanswered questions remain. How can the photospheric magnetic fields and velocities be propagated to the low corona through the transition region? At what cadence must we observe the photosphere to realistically simulate the corona? How do we model the magnetic fields and plasma velocities in the quiet Sun? How sensitive are the solutions to other unknowns that must be specified, such as the global solar magnetic field, and the photospheric temperature and density?
Second order bounce back boundary condition for the lattice Boltzmann fluid simulation
International Nuclear Information System (INIS)
Kim, In Chan
2000-01-01
A new bounce back boundary method of the second order in error is proposed for the lattice Boltzmann fluid simulation. This new method can be used for the arbitrarily irregular lattice geometry of a non-slip boundary. The traditional bounce back boundary condition for the lattice Boltzmann simulation is of the first order in error. Since the lattice Boltzmann method is the second order scheme by itself, a boundary technique of the second order has been desired to replace the first order bounce back method. This study shows that, contrary to the common belief that the bounce back boundary condition is unilaterally of the first order, the second order bounce back boundary condition can be realized. This study also shows that there exists a generalized bounce back technique that can be characterized by a single interpolation parameter. The second order bounce back method can be obtained by proper selection of this parameter in accordance with the detailed lattice geometry of the boundary. For an illustrative purpose, the transient Couette and the plane Poiseuille flows are solved by the lattice Boltzmann simulation with various boundary conditions. The results show that the generalized bounce back method yields the second order behavior in the error of the solution, provided that the interpolation parameter is properly selected. Coupled with its intuitive nature and the ease of implementation, the bounce back method can be as good as any second order boundary method
Schaefer, Marius; Bugnion, Louis
2013-06-01
We present results of detailed velocity profile measurements in a large series of granular flow experiments in a dam-break setup. The inclination angle, bead size, and roughness of the running surface were varied. In all experiments, the downstream velocity profiles changed continuously from the head to the tail of the avalanches. On rough running surfaces, an inflection point developed in the velocity profiles. These velocity profiles cannot be modeled by the large class of constitutive laws which relate the shear stress to a power law of the strain rate. The velocity profile shape factor increased from the head to the tail of the avalanches. Its maximum value grew with increasing roughness of the running surface. We conclude that flow features such as velocity profiles are strongly influenced by the boundary condition at the running surface, which depends on the ratio of bead size to the typical roughness length of the surface. Furthermore, we show that varying velocity profile shape factors inside gravitationally driven finite-mass flows give rise to an additional term in the depth-averaged momentum equation, which is normally solved in the simulation software of hazardous geophysical flows. We therefore encourage time dependent velocity profile measurements inside hazardous geophysical flows, to learn about the importance of this "new" term in the mathematical modeling of these flows.
RamReddy, Ch.; Venkata Rao, Ch.
2017-12-01
In this paper, a numerical analysis is performed to investigate the effects of double dispersion and convective boundary condition on natural convection flow over vertical frustum of a cone in a nanofluid saturated non-Darcy porous medium. In addition, Brownian motion and thermophoresis effects have taken into consideration, and the uniform wall nanoparticle condition is replaced with the zero nanoparticle mass flux boundary condition to execute physically applicable results. For this complex problem, the similarity solution does not exist and hence suitable non-similarity transformations are used to transform the governing equations along with the boundary conditions into non-dimensional form. The Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM) is used to solve the reduced non-similar, coupled partial differential equations. To test the accuracy of proposed method, the error analysis and convergence tests are conducted. The effect of flow influenced parameters on non-dimensional velocity, temperature, nanoparticle volume fraction, regular concentration field as well as on the surface drag, heat transfer, nanoparticle and regular mass transfer rates are analyzed.
An approximate method for solving a melting problem with periodic boundary conditions
Directory of Open Access Journals (Sweden)
Qu Liang-Hui
2014-01-01
Full Text Available An effective thermal diffusivity method is used to solve one-dimensional melting problem with periodic boundary conditions in a semi-infinite domain. An approximate analytic solution showing the functional relation between the location of the moving boundary and time is obtained by using Laplace transform. The evolution of the moving boundary and the temperature field in the phase change domain are simulated numerically, and the numerical results are compared with previous results in open literature.
Nanoscale roughness effect on Maxwell-like boundary conditions for the Boltzmann equation
Energy Technology Data Exchange (ETDEWEB)
Brull, S., E-mail: Stephane.Brull@math.u-bordeaux.fr; Charrier, P., E-mail: Pierre.Charrier@math.u-bordeaux.fr; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux.fr [University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33400 Talence (France)
2016-08-15
It is well known that the roughness of the wall has an effect on microscale gas flows. This effect can be shown for large Knudsen numbers by using a numerical solution of the Boltzmann equation. However, when the wall is rough at a nanometric scale, it is necessary to use a very small mesh size which is much too expansive. An alternative approach is to incorporate the roughness effect in the scattering kernel of the boundary condition, such as the Maxwell-like kernel introduced by the authors in a previous paper. Here, we explain how this boundary condition can be implemented in a discrete velocity approximation of the Boltzmann equation. Moreover, the influence of the roughness is shown by computing the structure scattering pattern of mono-energetic beams of the incident gas molecules. The effect of the angle of incidence of these molecules, of their mass, and of the morphology of the wall is investigated and discussed in a simplified two-dimensional configuration. The effect of the azimuthal angle of the incident beams is shown for a three-dimensional configuration. Finally, the case of non-elastic scattering is considered. All these results suggest that our approach is a promising way to incorporate enough physics of gas-surface interaction, at a reasonable computing cost, to improve kinetic simulations of micro- and nano-flows.
Discrete Boltzmann Method with Maxwell-Type Boundary Condition for Slip Flow
Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua
2018-01-01
The rarefied effect of gas flow in microchannel is significant and cannot be well described by traditional hydrodynamic models. It has been known that discrete Boltzmann model (DBM) has the potential to investigate flows in a relatively wider range of Knudsen number because of its intrinsic kinetic nature inherited from Boltzmann equation. It is crucial to have a proper kinetic boundary condition for DBM to capture the velocity slip and the flow characteristics in the Knudsen layer. In this paper, we present a DBM combined with Maxwell-type boundary condition model for slip flow. The tangential momentum accommodation coefficient is introduced to implement a gas-surface interaction model. Both the velocity slip and the Knudsen layer under various Knudsen numbers and accommodation coefficients can be well described. Two kinds of slip flows, including Couette flow and Poiseuille flow, are simulated to verify the model. To dynamically compare results from different models, the relation between the definition of Knudsen number in hard sphere model and that in BGK model is clarified. Support of National Natural Science Foundation of China under Grant Nos. 11475028, 11772064, and 11502117 Science Challenge Project under Grant Nos. JCKY2016212A501 and TZ2016002
Boundary Conditions for a New Type of Design Task
DEFF Research Database (Denmark)
McAloone, Tim C.
2011-01-01
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......Manufacturing companies have traditionally focused their efforts on developing and producing physical products for the market. Currently, however, many companies are rethinking their business strategies, from selling products to providing services. In place of the product alone, the activity...... object and research paradigm, studying service‐oriented approaches to product development and seeking to understand how to spell the systematic development of these so-called Product/Service‐Systems (PSS). When considering the shift towards PSS in the domain of engineering, it is in...
On problems with displacement in boundary conditions for hyperbolic equation
Directory of Open Access Journals (Sweden)
Elena A. Utkina
2016-03-01
Full Text Available We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat problem is replaced by nonlocal condition on the relevant characteristic. Non-local conditions are the linear combinations of the normal derivatives at points on opposite characteristics. In case of replacement of one condition we solve the problem by reduction to the Goursat problem for which it exists and is unique. To find the unknown Goursat condition author receives the integral equation, rewrite it in operational form and finds its unique solvability cases. To prove the unique solvability of the equation, the author shows the continuous linear operator and the fact, that some degree of the resulting operator is a contraction mapping. It is known that in this case the required Goursat condition can be written as Neumann series. We considered in detail only one of the tasks, but for both the unique solvability theorems are formulated. If the two conditions are changed, the uniqueness of the solution on the assumption that it exists, is proved by the method of a priori estimates. For this purpose, the inner product and the norm in $L_2$ are used. As a result, the conditions were obtained for the coefficients of a hyperbolic equation that ensure the uniqueness of the solution. An example is given, confirming that these conditions are essential. Namely, constructed an equation whose coefficients do not satisfy the conditions of the last theorem, given the conditions on the characteristics and nontrivial solution is built.
The refined analytic torsion and a well-posed boundary condition for the odd signature operator
Huang, Rung-Tzung; Lee, Yoonweon
2018-03-01
In this paper we discuss the refined analytic torsion on an odd dimensional compact oriented Riemannian manifold with boundary under some assumption. For this purpose we introduce two boundary conditions which are complementary to each other and well-posed for the odd signature operator B in the sense of Seeley. We then show that the zeta-determinants of B2 and eta-invariants of B subject to these boundary conditions are well defined by using the method of the asymptotic expansions of the traces of the heat kernels. We use these facts to define the refined analytic torsion on a compact manifold with boundary and show that it is invariant on the change of metrics in the interior of the manifold. We finally describe the refined analytic torsion under these boundary conditions as an element of the determinant line.
The PPP model of alternant cyclic polyenes with modified boundary conditions
International Nuclear Information System (INIS)
Bendazzoli, G.L.; Evangelisti, S.
1995-01-01
The extension of the PPP Hamiltonian for alternant cyclic polyenes to noninteger values of the pseudomomentum by imposing modified boundary conditions is discussed in detail. It is shown that a computer program for periodic boundary conditions can be easily adapted to the new boundary conditions. Full CI computations are carried out for some low-lying states of the PPP model of alternant cyclic polyenes (CH) N (N even) at half-filling. The energy values obtained by using periodic (Bloch) and antiperiodic (Moebius) orbitals are used to perform energy extrapolations for N → ∞. 38 refs., 2 figs., 5 tabs
Existence and regularity of solutions to the Leray-alpha model with Navier slip boundary conditions
Directory of Open Access Journals (Sweden)
Hani Ali
2016-08-01
Full Text Available We establish the existence and regularity of a unique weak solution to turbulent flows in a bounded domain $\\Omega\\subset\\mathbb R^3$ governed by the Leray-$\\alpha$ model with Navier slip boundary condition for the velocity. Furthermore, we show that when the filter coefficient $\\alpha$ tends to zero, these weak solutions converge to a suitable weak solution to the incompressible Navier Stokes equations subject to the Navier boundary conditions. Finally, we discuss the relation between the Leray-$\\alpha$ model and the Navier-Stokes equations with homogeneous Dirichlet boundary condition.
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...... simulations of two-dimensional Ising systems with various system shapes and boundary conditions....
An effective absorbing layer for the boundary condition in acoustic seismic wave simulation
Yao, Gang; da Silva, Nuno V.; Wu, Di
2018-04-01
Efficient numerical simulation of seismic wavefields generally involves truncating the Earth model in order to keep computing time and memory requirements down. Absorbing boundary conditions, therefore, are applied to remove the boundary reflections caused by this truncation, thereby allowing for accurate modeling of wavefields. In this paper, we derive an effective absorbing boundary condition for both acoustic and elastic wave simulation, through the simplification of the damping term of the split perfectly matched layer (SPML) boundary condition. This new boundary condition is accurate, cost-effective, and easily implemented, especially for high-performance computing. Stability analysis shows that this boundary condition is effectively as stable as normal (non-absorbing) wave equations for explicit time-stepping finite differences. We found that for full-waveform inversion (FWI), the strengths of the effective absorbing layer—a reduction of the computational and memory cost coupled with a simplistic implementation—significantly outweighs the limitation of incomplete absorption of outgoing waves relative to the SPML. More importantly, we demonstrate that this limitation can easily be overcome through the use of two strategies in FWI, namely variable cell size and model extension thereby fully compensating for the imperfectness of the proposed absorbing boundary condition.
Heat conduction in a plate-type fuel element with time-dependent boundary conditions
International Nuclear Information System (INIS)
Faya, A.J.G.; Maiorino, J.R.
1981-01-01
A method for the solution of boundary-value problems with variable boundary conditions is applied to solve a heat conduction problem in a plate-type fuel element with time dependent film coefficient. The numerical results show the feasibility of the method in the solution of this class of problems. (Author) [pt
Heat flow in functionally graded pipes with isothermal boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Dryden, John [University of Western Ontario, Department of Mechanical and Materials Engineering, London, ON (Canada)
2009-06-15
The steady state two-dimensional temperature field within a functionally graded pipe having isothermal inner and outer surfaces is calculated. The analysis is based upon the theory of complex variables. An expression, which depends upon the spatial variation of the conductivity, is suggested for the equivalent homogeneous thermal conductivity. (orig.)
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).
The OSMOSIS Model of the Wind-Driven Ocean Surface Boundary Layer.
Grant, A. L.; Belcher, S. E.; Pearson, B.; Polton, J.
2016-02-01
In the wind-driven ocean surface boundary layer (OSBL) the vertical velocity variance is observed to be larger than in shear driven turbulence. The observed variances are consistent with the results from large-eddy simulations (LES) which parametrize the interaction between the Stokes drift of the surface waves and vorticity. The resulting flow is known as Langmuir turbulence and the close connection between winds and waves suggests that Langmuir turbulence is common in the OSBL. This poster describes a model of the OSBL, developed as part of the OSMOSIS project, in which mixing is by Langmuir turbulence. The transports of momentum, heat and salinity are represented by a first-order closure scheme with flux-gradient relationships that include non-gradient contributions. In this the model is similar to the KPP scheme which uses flux-gradient relationships with non-gradient contributions to represent scalar transports. The flux-gradient relationships are derived from an analysis of the turbulent flux budgets of momentum and scalars (heat) obtained from LES. The non-gradient terms represent the contributions to the turbulent flux by the terms in the turbulent flux budget that represent the effects of the Stokes shear, buoyancy and turbulent transport. The eddy viscosity, diffusivities and non-gradient components are represented by similarity profiles. The depth of the boundary layer is determined by a prognostic equation, which represents the time variation of the boundary layer depth in both unstable and stable conditions. It is based on the equation for the depth integrated potential energy combined with a parametrization of the turbulent kinetic energy budget. The use of the prognostic equation allows the effects of Langmuir turbulence on boundary layer depth to be explicitly represented in the model. Comparison with the results from LES of the diurnal cycle of the OSBL are presented as a test for the model.
Boundary Conditions and the Aeolian Sediment State of the Olympia Undae Dune Field, Mars
Middlebrook, W.; Ewing, R. C.; Ayoub, F.; Bridges, N. T.; Smith, I.; Spiga, A.
2015-05-01
We evaluate the boundary conditions in Olympia Undae. We map two and three dimensional dune parameters from two locations proximal and distal to Planum Boreum and constrain sediment fluxes. We compare our results with a mesoscale atmospheric model.
International Nuclear Information System (INIS)
Tang, X. Z.
2000-01-01
Subtleties of implementing the standard perfectly conducting wall boundary condition in a general toroidal geometry are clarified for a mixed scalar magnetic field representation. An iterative scheme based on Ohm's law is given
Ou, Dayi; Mak, Cheuk Ming
2011-06-01
Several prediction methods have recently been developed for systematically studying the effects of general boundary conditions on the sound transmission loss (STL) of plate-like structures. But corresponding experimental validation studies remain scarce owing to the difficulty of obtaining accurate boundary conditions for practical structures. This paper presents a convincing experiment conducted on a baffled plate system to validate the STL prediction model in a previous paper by Yu et al. [Noise Control Eng. J. 58(2), 187-200, 2010]. A method is proposed to determine the boundary conditions of this system, and experimental STL compares well with the predictions based on the identified boundary condition. © 2011 Acoustical Society of America
Upper and lower solutions method for differential inclusions with integral boundary conditions
Directory of Open Access Journals (Sweden)
Abdelghani Ouahab
2006-03-01
Full Text Available A nonlinear alternative of the Leray-Schauder type for multivalued maps combined with upper and lower solutions is used to investigate the existence of solutions for second-order differential inclusions with integral boundary conditions.
Enhancement of single mode operation in coaxial optical waveguide using DB boundary conditions
Lohia, Pooja; Prajapati, Y.; Saini, J. P.; Rai, B. S.
2014-11-01
In this study, a competent numerical strategy to compute the dispersion of optical waveguides is presented and propagation of electromagnetic waves in a coaxial optical waveguide with DB boundary conditions is instigated. For this intend, cylindrical coordinates are here being used to derive the DB boundary conditions and to obtain field components for the modes. The propagation constant for the waveguide to be studied is determined by solving the Bessel and the modified Bessel functions. The cutoff frequencies for various lower order modes have been calculated and their dispersion characteristics are plotted correspondingly. The behavior of the coaxial optical waveguide under DB boundary conditions is shown to be significantly different from that of coaxial optical waveguide and conventional optical waveguide under traditional or tangential boundary conditions. Finally, the effect of waveguide dimensions on the mode cutoff frequencies and fabrication issues are also addressed.
Stokes flow with slip and Kuwabara boundary conditions
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
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 shape from a sphere is also investigated. The explicit expression for the stream function is obtained to the ...
The No-Slip Boundary Condition in Fluid Mechanics
Indian Academy of Sciences (India)
Historical Development. A brief and excellent review of this problem of velocity slip in fluid flow is given in the book by Goldstein [1]. We freely borrow from this book adding some explanations and supple- ments based on the earlier discussion in Part 1. We saw that Newton tacitly assumed the no-slip condition in the.
Chevron defect at the intersection of grain boundaries with free surfaces in Au
International Nuclear Information System (INIS)
Radetic, T.; Lancon, F.; Dahmen, U.
2002-01-01
We have identified a new defect at the intersection between grain boundaries and surfaces in Au using atomic resolution transmission electron microscopy. At the junction line of 90 deg. tilt grain boundaries of (110)-(001) orientation with the free surface, a small segment of the grain boundary, about 1 nm in length, dissociates into a triangular region with a chevronlike stacking disorder and a distorted hcp structure. The structure and stability of these defects are confirmed by atomistic simulations, and we point out the relationship with the one-dimensional incommensurate structure of the grain boundary
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.
International Nuclear Information System (INIS)
Seki, Yohji; Kawamura, Hiroshi
2005-01-01
Direct numerical simulation (DNS) have been performed for the turbulent heat transfer in a channel flow. In the present study, effect of thermal boundary condition is examined. DNS has been carried out for streamwisely thermal boundary conditions (Re τ =180) with Pγ=0.71 to obtain statistical mean temperatures, temperature variances, budget terms and time scale ratios etc. The obtained results have indicated that the time scale ratio varies along a streamwise. (author)
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.
Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation
International Nuclear Information System (INIS)
Yan-Yan, Chen; Hua-Bing, Li; Hou-Hui, Yi
2008-01-01
The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density (bulk pressure). If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows
Schrödinger functional boundary conditions and improvement for N > 3
DEFF Research Database (Denmark)
Hietanen, A.; Karavirta, T.; Vilaseca, P.
2014-01-01
The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N ) gauge theory is based on the Schrodinger functional (SF). In this paper we construct a family of boundary fields for general values of N which enter the standard definition of the SF coupling. We...... provide spatial boundary conditions for fermions in several representations which reduce the condition number of the squared Dirac operator. In addition, we calculate the improvement coefficients for N > 3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects...
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.
Effects of Uncertainties in Electric Field Boundary Conditions for Ring Current Simulations
Chen, Margaret W.; O'Brien, T. Paul; Lemon, Colby L.; Guild, Timothy B.
2018-01-01
Physics-based simulation results can vary widely depending on the applied boundary conditions. As a first step toward assessing the effect of boundary conditions on ring current simulations, we analyze the uncertainty of cross-polar cap potentials (CPCP) on electric field boundary conditions applied to the Rice Convection Model-Equilibrium (RCM-E). The empirical Weimer model of CPCP is chosen as the reference model and Defense Meteorological Satellite Program CPCP measurements as the reference data. Using temporal correlations from a statistical analysis of the "errors" between the reference model and data, we construct a Monte Carlo CPCP discrete time series model that can be generalized to other model boundary conditions. RCM-E simulations using electric field boundary conditions from the reference model and from 20 randomly generated Monte Carlo discrete time series of CPCP are performed for two large storms. During the 10 August 2000 storm main phase, the proton density at 10 RE at midnight was observed to be low (Dst index is bounded by the simulated Dst values. In contrast, the simulated Dst values during the recovery phases of the 10 August 2000 and 31 August 2005 storms tend to underestimate systematically the observed late Dst recovery. This suggests a need to improve the accuracy of particle loss calculations in the RCM-E model. Application of this technique can aid modelers to make efficient choices on either investing more effort on improving specification of boundary conditions or on improving descriptions of physical processes.
A damping boundary condition for atomistic-continuum coupling
International Nuclear Information System (INIS)
Zhang Jie; Tieu, Kiet; Michal, Guillaume; Zhu Hongtao; Zhang Liang; Su Lihong; Deng Guanyu; Wang Hui
2017-01-01
The minimization of spurious wave reflection is a challenge in multiscale coupling due to the difference of spatial resolution between atomistic and continuum regions. In this study, a new damping condition is presented for eliminating spurious wave reflection at the interface between atomistic and continuum regions. This damping method starts by a coarse–fine decomposition of the atomic velocity based on the bridging scale method. The fine scale velocity of the atoms in the damping region is reduced by applying nonlinear damping coefficients. The effectiveness of this damping method is verified by one- and two- dimensional simulations. (paper)
Surface description of QCD with fermionic quark boundaries
International Nuclear Information System (INIS)
Burden, C.J.
1983-01-01
The flux sheet description of pure gauge theories proposed by Bardakci and Greensite is extended to include fermionic quark fields defined on the sheet boundaries. The quark fields are sources and sinks of colour flux and the action remains gauge invariant. It is shown that the partition function contains colour singlet contributions with the quantum numbers of mesons, baryons and exotics. (author)
Improving bottom-boundary conditions for SVAT simulations in shallow-groundwater systems
Morris, Paul J.; Verhoef, Anne; Macdonald, David M. J.; Gardner, Cate M.; Punalekar, Suvarna M.; Tatarenko, Irina; Gowing, David
2013-04-01
A well documented disparity exists between models that simulate: i) groundwater hydrological processes; and ii) soil-vegetation-atmosphere transfers (SVAT) of water and energy. This is particularly pertinent in shallow groundwater systems, such as lowland floodplains, where the domains of surface water and groundwater necessarily overlap. Consideration of either SVAT or groundwater processes in shallow groundwater systems necessitates a robust understanding of their bi-directional interactions. The hydrological bottom-boundary conditions of SVAT models can be driven using continuous groundwater data from dipwells. However, where such data are not available the bottom boundary must be simulated. We sought to develop a simple empirical model of subsurface fluxes of water between a floodplain soil column and its adjoining river, without the additional cost and complication of a fully linked surface water-groundwater model. We conducted our research at Yarnton Mead, a floodplain meadow on the River Thames in Oxfordshire, UK. We used in-situ soil-physical, hydrological and meteorological data to generate an empirical relationship between floodplain water-table position, and rate and direction of subsurface water fluxes between the floodplain soil and the river. We estimated rates of subsurface water flux into and out of our instrumented soil column as the residual term of a water balance equation. We then fitted a linear model to describe the rate and direction of subsurface flux as a function of water-table position. Although the level of explanation of the linear model is not high (r-squared = 0.39), the relationship is highly significant (p validated the model's simulated water tables against dipwell measurements. The simulated water tables fitted well to observed data with root mean square error of 0.13 m and r-squared = 0.71. The fit could be improved further by optimising the slope and intercept of the linear model. Our results are highly promising and suggest
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.
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.
Jun, Li; Huicheng, Yin
2018-05-01
The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.
Critical dense polymers with Robin boundary conditions, half-integer Kac labels and Z4 fermions
Directory of Open Access Journals (Sweden)
Paul A. Pearce
2014-12-01
Full Text Available For general Temperley–Lieb loop models, including the logarithmic minimal models LM(p,p′ with p,p′ coprime integers, we construct an infinite family of Robin boundary conditions on the strip as linear combinations of Neumann and Dirichlet boundary conditions. These boundary conditions are Yang–Baxter integrable and allow loop segments to terminate on the boundary. Algebraically, the Robin boundary conditions are described by the one-boundary Temperley–Lieb algebra. Solvable critical dense polymers is the first member LM(1,2 of the family of logarithmic minimal models and has loop fugacity β=0 and central charge c=−2. Specialising to LM(1,2 with our Robin boundary conditions, we solve the model exactly on strips of arbitrary finite size N and extract the finite-size conformal corrections using an Euler–Maclaurin formula. The key to the solution is an inversion identity satisfied by the commuting double row transfer matrices. This inversion identity is established directly in the Temperley–Lieb algebra. We classify the eigenvalues of the double row transfer matrices using the physical combinatorics of the patterns of zeros in the complex spectral parameter plane and obtain finitised characters related to spaces of coinvariants of Z4 fermions. In the continuum scaling limit, the Robin boundary conditions are associated with irreducible Virasoro Verma modules with conformal weights Δr,s−12=132(L2−4 where L=2s−1−4r, r∈Z, s∈N. These conformal weights populate a Kac table with half-integer Kac labels. Fusion of the corresponding modules with the generators of the Kac fusion algebra is examined and general fusion rules are proposed.
Rustic, G. T.; Polissar, P. J.; Ravelo, A. C.; White, S. M.
2017-12-01
The El Niño Southern Oscillation (ENSO) plays a dominant role in Earth's climate variability. Paleoceanographic evidence suggests that ENSO has changed in the past, and these changes have been linked to large-scale climatic shifts. While a close relationship between ENSO evolution and climate boundary conditions has been predicted, testing these predictions remains challenging. These climate boundary conditions, including insolation, the mean surface temperature gradient of the tropical Pacific, global ice volume, and tropical thermocline depth, often co-vary and may work together to suppress or enhance the ocean-atmosphere feedbacks that drive ENSO variability. Furthermore, suitable paleo-archives spanning multiple climate states are sparse. We have aimed to test ENSO response to changing climate boundary conditions by generating new reconstructions of mixed-layer variability from sedimentary archives spanning the last three glacial-interglacial cycles from the Central Tropical Pacific Line Islands, where El Niño is strongly expressed. We analyzed Mg/Ca ratios from individual foraminifera to reconstruct mixed-layer variability at discrete time intervals representing combinations of climatic boundary conditions from the middle Holocene to Marine Isotope Stage (MIS) 8. We observe changes in the mixed-layer temperature variability during MIS 5 and during the previous interglacial (MIS 7) showing significant reductions in ENSO amplitude. Differences in variability during glacial and interglacial intervals are also observed. Additionally, we reconstructed mixed-layer and thermocline conditions using multi-species Mg/Ca and stable isotope measurements to more fully characterize the state of the Central Tropical Pacific during these intervals. These reconstructions provide us with a unique view of Central Tropical Pacific variability and water-column structure at discrete intervals under varying boundary climate conditions with which to assess factors that shape ENSO
International Nuclear Information System (INIS)
Follin, S.
1999-06-01
The SR 97 project presents a performance assessment (PA) of the overall safety of a hypothetical deep repository at three sites in Sweden arbitrarily named Aberg, Beberg and Ceberg. One component of this PA assesses the uncertainties in the hydrogeological modelling. This study focuses on uncertainties in boundary settings (size of model domain and boundary conditions) in the regional and site-scale hydrogeological modelling of the three sites used to simulating the possible transport of radionuclides from the emplacement waste packages through the host rock to the accessible environment. Model uncertainties associated with, for instance, parameter heterogeneity and structural interpretations are addressed in other studies. This study concludes that the regional modelling of the SR 97 project addresses uncertainties in the choice of boundary conditions and size of model domain differently at each site, although the overall handling is acceptable and in accordance with common modelling practice. For example, the treatment of uncertainties with regard to the ongoing post-glacial flushing of the Baltic Shield is creditably addressed although not exhaustive from a modelling point of view. A significant contribution of the performed modelling is the study of nested numerical models, i.e., the numerical interplay between regional and site-scale numerical models. In the site-scale modelling great efforts are made to address problems associated with (i) the telescopic mesh refinement (TMR) technique with regard to the stochastic continuum approach, and (ii) the transfer of boundary conditions between variable-density flow systems and flow systems that are constrained to treat uniform density flow. This study concludes that the efforts made to handle these problems are acceptable with regards to the objectives of the SR 97 project
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.
Dynamical structure of the turbulent boundary layer on rough surface
Czech Academy of Sciences Publication Activity Database
Uruba, Václav; Jonáš, Pavel; Hladík, Ondřej
2011-01-01
Roč. 11, č. 1 (2011), s. 603-604 ISSN 1617-7061 R&D Projects: GA ČR GA101/08/1112; GA ČR GAP101/10/1230 Institutional research plan: CEZ:AV0Z20760514 Keywords : turbulent boundary layer * rough wall * hairpin vortex Subject RIV: BK - Fluid Dynamics http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110291/abstract
The unified method: II. NLS on the half-line with t-periodic boundary conditions
International Nuclear Information System (INIS)
Lenells, J; Fokas, A S
2012-01-01
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this general method to this particular class of problems yields the solution in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the complex k-plane (the Fourier plane), which has a jump matrix with explicit (x, t)-dependence involving four scalar functions of k, called spectral functions. Two of these functions depend on the initial data, whereas the other two depend on all boundary values. The most difficult step of the new method is the characterization of the latter two spectral functions in terms of the given initial and boundary data, i.e. the elimination of the unknown boundary values. For certain boundary conditions, called linearizable, this can be achieved by simply using algebraic manipulations. Here, we first present an effective characterization of the spectral functions in terms of the given initial and boundary data for the general case of non-linearizable boundary conditions. This characterization is based on the analysis of the so-called global relation and on the introduction of the so-called Gelfand–Levitan–Marchenko representations of the eigenfunctions defining the spectral functions. We then concentrate on the physically significant case of t-periodic Dirichlet boundary data. After presenting certain heuristic arguments which suggest that the Neumann boundary values become periodic as t → ∞, we show that for the case of the NLS with a sine-wave as Dirichlet data, the asymptotics of the Neumann boundary values can be computed explicitly at least up to third order in a perturbative expansion and indeed at least up to this order are asymptotically periodic. (paper)
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.
Fayssal, Iyad A; Moukalled, Fadl; Alam, Samir; Isma'eel, Hussain
2018-04-01
This paper reports on a new boundary condition formulation to model the total coronary myocardial flow and resistance characteristics of the myocardial vascular bed for any specific patient when considered for noninvasive diagnosis of ischemia. The developed boundary condition model gives an implicit representation of the downstream truncated coronary bed. Further, it is based on incorporating patient-specific physiological parameters that can be noninvasively extracted to account for blood flow demand to the myocardium at rest and hyperemic conditions. The model is coupled to a steady three-dimensional (3D) collocated pressure-based finite volume flow solver and used to characterize the "functional significance" of a patient diseased coronary artery segment without the need for predicting the hemodynamics of the entire arterial system. Predictions generated with this boundary condition provide a deep understanding of the inherent challenges behind noninvasive image-based diagnostic techniques when applied to human diseased coronary arteries. The overall numerical method and formulated boundary condition model are validated via two computational-based procedures and benchmarked with available measured data. The newly developed boundary condition is used via a designed computational methodology to (a) confirm the need for incorporating patient-specific physiological parameters when modeling the downstream coronary resistance, (b) explain the discrepancies presented in the literature between measured and computed fractional flow reserve (FFRCT), and (c) discuss the current limitations and future challenges in shifting to noninvasive assessment of ischemia.
Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
International Nuclear Information System (INIS)
Fagotti, Maurizio; Calabrese, Pasquale
2011-01-01
We consider the Rényi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher–Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(l -1 ) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary
Energy Technology Data Exchange (ETDEWEB)
van Milligen, B. Ph. [Asociacion EURATOM-CIEMAT; Calvo, Ivan [CIEMAT, Madrid; Sanchez, Raul [ORNL
2008-01-01
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behavior of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
Energy Technology Data Exchange (ETDEWEB)
Milligen, B Ph van; Calvo, I [Asociacion EURATOM-CIEMAT para Fusion, Avda. Complutense 22, 28040 Madrid (Spain); Sanchez, R [Fusion Energy Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States)], E-mail: boudewijn.vanmilligen@ciemat.es
2008-05-30
The present work studies continuous time random walks (CTRWs) in a finite domain. A broad class of boundary conditions, of which absorbing and reflecting boundaries are particular cases, is considered. It is shown how any CTRW in this class can be mapped to a CTRW in an infinite domain. This may allow applying well-known techniques for infinite CTRWs to the problem of obtaining the fluid limit for finite domain CTRWs, where the fluid limit (or hydrodynamic limit) refers to the partial differential equation describing the long time and large distance behaviour of the system. As an illustration, the fluid limit equation and its propagator are obtained explicitly in the case of purely reflecting boundaries. We also derive the modification of the Riemann-Liouville fractional differential operators implementing the reflecting boundary conditions.
Stabilizing local boundary conditions for two-dimensional shallow water equations
Dia, Ben Mansour
2018-03-27
In this article, we present a sub-critical two-dimensional shallow water flow regulation. From the energy estimate of a set of one-dimensional boundary stabilization problems, we obtain a set of polynomial equations with respect to the boundary values as a requirement for the energy decrease. Using the Riemann invariant analysis, we build stabilizing local boundary conditions that guarantee the stability of the hydrodynamical state around a given steady state. Numerical results for the controller applied to the nonlinear problem demonstrate the performance of the method.
Surface transition on ice induced by the formation of a grain boundary.
Directory of Open Access Journals (Sweden)
Christian Pedersen
Full Text Available Interfaces between individual ice crystals, usually referred to as grain boundaries, play an important part in many processes in nature. Grain boundary properties are, for example, governing the sintering processes in snow and ice which transform a snowpack into a glacier. In the case of snow sintering, it has been assumed that there are no variations in surface roughness and surface melting, when considering the ice-air interface of an individual crystal. In contrast to that assumption, the present work suggests that there is an increased probability of molecular surface disorder in the vicinity of a grain boundary. The conclusion is based on the first detailed visualization of the formation of an ice grain boundary. The visualization is enabled by studying ice crystals growing into contact, at temperatures between -20°C and -15°C and pressures of 1-2 Torr, using Environmental Scanning Electron Microscopy. It is observed that the formation of a grain boundary induces a surface transition on the facets in contact. The transition does not propagate across facet edges. The surface transition is interpreted as the spreading of crystal dislocations away from the grain boundary. The observation constitutes a qualitatively new finding, and can potentially increase the understanding of specific processes in nature where ice grain boundaries are involved.
Gowdy waves as a test-bed for constraint-preserving boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Bona, Carles; Bona-Casas, Carles, E-mail: cbona@uib.e [Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca, Spain Institute for Applied Computation with Community Code (IAC3) (Spain)
2010-05-01
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.
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.
Directory of Open Access Journals (Sweden)
Samira Hamani
2010-01-01
Full Text Available In this article, the authors establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential inclusions involving the Caputo fractional derivative and nonlinear integral conditions. Both cases of convex and nonconvex valued right hand sides are considered. The topological structure of the set of solutions also examined.
Winkler boundary conditions for three-point bending tests on 1D nanomaterials
International Nuclear Information System (INIS)
Gangadean, D; McIlroy, David N; Faulkner, Brian E; Eric Aston, D
2010-01-01
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.
Directory of Open Access Journals (Sweden)
K. Schäfer
2012-07-01
Full Text Available Measurements of land-surface emission rates of greenhouse and other gases at large spatial scales (10 000 m^{2} are needed to assess the spatial distribution of emissions. This can be readily done using spatial-integrating micro-meteorological methods like flux-gradient methods which were evaluated for determining land-surface emission rates of trace gases under stable boundary layers. Non-intrusive path-integrating measurements are utilized. Successful application of a flux-gradient method requires confidence in the gradients of trace gas concentration and wind, and in the applicability of boundary-layer turbulence theory; consequently the procedures to qualify measurements that can be used to determine the flux is critical. While there is relatively high confidence in flux measurements made under unstable atmospheres with mean winds greater than 1 m s^{−1}, there is greater uncertainty in flux measurements made under free convective or stable conditions. The study of N_{2}O emissions of flat grassland and NH_{3} emissions from a cattle lagoon involves quality-assured determinations of fluxes under low wind, stable or night-time atmospheric conditions when the continuous "steady-state" turbulence of the surface boundary layer breaks down and the layer has intermittent turbulence. Results indicate that following the Monin-Obukhov similarity theory (MOST flux-gradient methods that assume a log-linear profile of the wind speed and concentration gradient incorrectly determine vertical profiles and thus flux in the stable boundary layer. An alternative approach is considered on the basis of turbulent diffusivity, i.e. the measured friction velocity as well as height gradients of horizontal wind speeds and concentrations without MOST correction for stability. It is shown that this is the most accurate of the flux-gradient methods under stable conditions.
Highly stable superhydrophobic surfaces under flow conditions
Lee, Moonchan; Yim, Changyong; Jeon, Sangmin
2015-01-01
We synthesized hydrophobic anodic aluminum oxide nanostructures with pore diameters of 35, 50, 65, and 80 nm directly on quartz crystal microresonators, and the stability of the resulting superhydrophobicity was investigated under flow conditions by measuring changes in the resonance frequency and dissipation factor. When the quartz substrates were immersed in water, their hydrophobic surfaces did not wet due to the presence of an air interlayer. The air interlayer was gradually replaced by water over time, which caused decreases in the resonance frequency (i.e., increases in mass) and increases in the dissipation factor (i.e., increases in viscous damping). Although the water contact angles of the nanostructures increased with increasing pore size, the stability of their superhydrophobicity increased with decreasing pore size under both static conditions (without flow) and dynamic conditions (with flow); this increase can be attributed to an increase in the solid surface area that interacts with the air layer above the nanopores as the pore size decreases. Further, the effects of increasing the flow rate on the stability of the superhydrophobicity were quantitatively determined.
Space-like surfaces with free boundary in the Lorentz-Minkowski space
International Nuclear Information System (INIS)
López, R; Pyo, J
2012-01-01
We investigate a variational problem in the Lorentz-Minkowski space L 3 whose critical points are space-like surfaces with a constant mean curvature and making a constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of space-like hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space L n+1 . (paper)
Effects of various thermal boundary conditions on natural convection in porous cavities
Cheong, H. T.; Sivasankaran, S.; Bhuvaneswari, M.; Siri, Z.
2015-10-01
The present work analyzes numerically the effects of various thermal boundary conditions and the geometry of the cavity on natural convection in cavities with fluid-saturated porous medium. Cavity of square, right-angled trapezium and right-angled triangle shapes are considered. The different temperature profiles are imposed on the left wall of the cavity and the right wall is maintained at a lower constant temperature. The top and bottom walls are adiabatic. The Darcy model is adopted for the porous medium. The finite difference method is used to solve the governing equations and boundary conditions over a range of Darcy-Rayleigh numbers. Streamlines, isotherms and Nusselt numbers are used for presenting the results. The heat transfer of the square cavity is more enhanced at high Darcy-Rayleigh number for all the thermal boundary conditions considered.
Heat kernel for the elliptic system of linear elasticity with boundary conditions
Taylor, Justin; Kim, Seick; Brown, Russell
2014-10-01
We consider the elliptic system of linear elasticity with bounded measurable coefficients in a domain where the second Korn inequality holds. We construct heat kernel of the system subject to Dirichlet, Neumann, or mixed boundary condition under the assumption that weak solutions of the elliptic system are Hölder continuous in the interior. Moreover, we show that if weak solutions of the mixed problem are Hölder continuous up to the boundary, then the corresponding heat kernel has a Gaussian bound. In particular, if the domain is a two dimensional Lipschitz domain satisfying a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary condition, then we show that the heat kernel has a Gaussian bound. As an application, we construct Green's function for elliptic mixed problem in such a domain.
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.
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.
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.
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.
Boundary condition effect on response modification factor of X-braced steel frames
Directory of Open Access Journals (Sweden)
Walid A. Attia
2018-04-01
Full Text Available Design of the structures to resist seismic force depends on the theory of dissipation in elastic 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 braced steel frame structures and that effects on R-factor. This study is an attempt to assess overstrength, ductility and response modification factor of X-braced steel frame under change in boundary conditions, as change in the direction of strong axis of column and connection support type of column besides variation in storey and bays numbers to be 21 frames and each frame has 8 different boundary conditions as sum of 168 cases for analysis. These frames were analyzed by using nonlinear static “pushover” analysis. As results of this study change in support type and direction of strong axis of column give large change in value of R-factor; the minimum value was 4.37 and maximum value 10.97. Minimum value is close to code value that’s mean the code is more conservative in suggesting of R-factor and gives a large factor of safety. Change in the location of bracing gives change in value of R-factor for all boundary conditions. Change in direction of strong axis of columns and support type didn’t give change in value of fundamental period, all boundary conditions. Keywords: Response modification factor, Ductility reduction factor, Overstrength factor, Boundary conditions, Brace frame, Nonlinear static analysis “Pushover”
International Nuclear Information System (INIS)
Paul, O.P.K.
1978-01-01
An approach to simulate the flux vanishing boundary condition in solving the two group coupled neutron diffusion equations in three dimensions (x, y, z) employed to calculate the flux distribution and keff of the reactor is summarised. This is of particular interest when the flux vanishing boundary in x, y, z directions is not an integral multiple of the mesh spacings in these directions. The method assumes the flux to be negative, hypothetically at the mesh points lying outside the boundary and thus the finite difference formalism for Laplacian operator, taking into account six neighbours of a mesh point in a square mesh arrangement, is expressed in a general form so as to account for the boundary mesh points of the system. This approach has been incorporated in a three dimensional diffusion code similar to TAPPS23 and has been used for IRT-2000 reactor and the results are quite satisfactory. (author)
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.
A representation of the boundary condition for the macroscopic magnetic field intensity
International Nuclear Information System (INIS)
Delecki, Z.A.
1989-01-01
An explicit formula is derived for the surface-current density in terms of the constitutive parameters of the dielectric media adjacent to both sides of the boundary surface. The concepts of the transverse-longitudinal decomposition of electromagnetic fields and the intrinsic impedance for a homogeneous medium are used. The limiting procedure is applied to represent the transverse fields and currents at the interface of two different media
Wang, Lingquan; Zeng, Zhong; Zhang, Liangqi; Qiao, Long; Zhang, Yi; Lu, Yiyu
2018-04-01
Navier-Stokes (NS) equations with no-slip boundary conditions fail to realistically describe micro-flows with considering nanoscale phenomena. Particularly, in kerogen pores, slip-flow and surface diffusion are important. In this study, we propose a new slip boundary scheme for the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the slip-flow considering surface diffusion effect. Meanwhile, the second-order slip velocity can be taken into account. The predicted characteristics in a two-dimensional micro-flow, including slip-velocity, velocity distribution along the flow direction with/without surface diffusion are present. The results in this study are compared with available analytical and reference results, and good agreements are achieved.
Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading
Directory of Open Access Journals (Sweden)
T.Y. Ng
1998-01-01
Full Text Available In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.
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Aifeng Wang
2016-01-01
Full Text Available We investigate the step-type contrast structure for high dimensional Tikhonov system with Neumann boundary conditions. We not only propose a key condition with the existence of the number of mutually independent first integrals under which there exists a step-type contrast structure, but also determine where an internal transition time is. Using the method of boundary function, we construct the formal asymptotic solution and give the analytical expression for the higher order terms. At the same time, the uniformly valid asymptotic expansion and the existence of such an available step-type contrast structure are obtained by sewing connection method.
International Nuclear Information System (INIS)
Ozgener, B.; Ozgener, H.A.
2005-01-01
A multiregion, multigroup collision probability method with white boundary condition is developed for thermalization calculations of light water moderated reactors. Hydrogen scatterings are treated by Nelkin's kernel while scatterings from other nuclei are assumed to obey the free-gas scattering kernel. The isotropic return (white) boundary condition is applied directly by using the appropriate collision probabilities. Comparisons with alternate numerical methods show the validity of the present formulation. Comparisons with some experimental results indicate that the present formulation is capable of calculating disadvantage factors which are closer to the experimental results than alternative methods
International Nuclear Information System (INIS)
Lu Jianming; Ouyang Guangyao; Zhang Ping; Rong Bojun
2012-01-01
Combining the advantages of the finite element software in temperature field analyzing with the multivariate function optimization arithmetic, a feasibility method based on the exterior temperature was proposed to get the thermal boundary conditions, which was required in temperature field analyzing. The thermal boundary conditions can be obtained only by some temperature measurement values. Taking the identification of the convection heat transfer coefficient of a high power density diesel engine cylinder head as an example, the calculation result shows that when the temperature measurement error was less than 0.5℃, the maximum relative error was less than 2%. It is shown that the new method was feasible (authors)
On the physical solutions to the heat equation subjected to nonlinear boundary conditions
International Nuclear Information System (INIS)
Gama, R.M.S. da.
1990-01-01
This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)
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.
Rate-Independent Processes with Linear Growth Energies and Time-Dependent Boundary Conditions
Czech Academy of Sciences Publication Activity Database
Kružík, Martin; Zimmer, J.
2012-01-01
Roč. 5, č. 3 (2012), s. 591-604 ISSN 1937-1632 R&D Projects: GA AV ČR IAA100750802 Grant - others:GA ČR(CZ) GAP201/10/0357 Institutional research plan: CEZ:AV0Z10750506 Keywords : concentrations * oscillations * time-dependent boundary conditions * rate-independent evolution Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2011/MTR/kruzik-rate-independent processes with linear growth energies and time-dependent boundary conditions.pdf
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.
Influences of the boundary layer evolution on surface ozone ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... A chemical box model simulation indicates about 17% reduction in the daytime ozone levels during the conditions of suppressed PBL in comparison with those of higher PBL conditions. On a few occasions, substantially elevated ozone levels (as high as 90 ppbv) were observed during late evening hours, ...
International Nuclear Information System (INIS)
Ramiere, I.
2006-09-01
This work is dedicated to the introduction of two original fictitious domain methods for the resolution of elliptic problems (mainly convection-diffusion problems) with general and eventually mixed boundary conditions: Dirichlet, Robin or Neumann. The originality lies in the approximation of the immersed boundary by an approximate interface derived from the fictitious domain Cartesian mesh, which is generally not boundary-fitted to the physical domain. The same generic numerical scheme is used to impose the embedded boundary conditions. Hence, these methods require neither a surface mesh of the immersed boundary nor the local modification of the numerical scheme. We study two modelling of the immersed boundary. In the first one, called spread interface, the approximate immersed boundary is the union of the cells crossed by the physical immersed boundary. In the second one, called thin interface, the approximate immersed boundary lies on sides of mesh cells. Additional algebraic transmission conditions linking both flux and solution jumps through the thin approximate interface are introduced. The fictitious problem to solve as well as the treatment of the embedded boundary conditions are detailed for the two methods. A Q1 finite element scheme is implemented for the numerical validation of the spread interface approach while a new cell-centered finite volume scheme is derived for the thin interface approach with immersed jumps. Each method is then combined to multilevel local mesh refinement algorithms (with solution or flux residual) to increase the precision of the solution in the vicinity of the immersed interface. A convergence analysis of a Q1 finite element method with non-boundary fitted meshes is also presented. This study proves the convergence rates of the present methods. Among the various industrial applications, the simulation on a model of heat exchanger in french nuclear power plants enables us to appreciate the performances of the fictitious domain
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.
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Joao Fialho
2017-02-01
Full Text Available This paper is concerned with the existence of bounded or unbounded solutions to regular and singular second order boundary value problem on the half-line with functional boundary conditions. These functional boundary conditions generalize the usual boundary assumptions and may be applied to a broad number of cases, such as, nonlocal, integro-differential, with delays, with maximum or minimum arguments... The arguments are based on the Schauder fixed point theorem and lower and upper solutions method.
Miao, Yucong; Guo, Jianping; Liu, Shuhua; Zhao, Chun; Li, Xiaolan; Zhang, Gen; Wei, Wei; Ma, Yanjun
2018-05-01
The northeastern China frequently experiences severe aerosol pollution in winter under unfavorable meteorological conditions. How and to what extent the meteorological factors affect the air quality there are not yet clearly understood. Thus, this study investigated the impacts of synoptic patterns on the aerosol transport and planetary boundary layer (PBL) structure in Shenyang from 1 to 3 December 2016, using surface observations, sounding measurements, satellite data, and three-dimensional simulations. Results showed that the aerosol pollution occurred in Shenyang was not only related to the local emissions, but also contributed by trans-boundary transport of aerosols from the Beiijng-Tianjin-Hebei (BTH) region. In the presence of the westerly and southwesterly synoptic winds, the aerosols emitted from BTH could be brought to Shenyang. From December 2 to 3, the aerosols emitted from BTH accounted for ∼20% of near-surface PM2.5 in Shenyang. In addition, the large-scale synoptic forcings could affect the vertical mixing of pollutants through modulating the PBL structure in Shenyang. The westerly and southwesterly synoptic winds not only brought the aerosols but also the warmer air masses from the southwest regions to Shenyang. The strong warm advections above PBL could enhance the already existing thermal inversion layers capping over PBL in Shenyang, leading to the suppressions of PBL. Both the trans-boundary transport of aerosols and the suppressions of PBL caused by the large-scale synoptic forcings should be partly responsible for the poor air quality in Shenyang, in addition to the high pollutant emissions. The present study revealed the physical mechanisms underlying the aerosol pollution in Shenyang, which has important implications for better forecasting and controlling the aerosols pollution.
International Nuclear Information System (INIS)
Steitz, Roland; Schemmel, Sebastian; Shi Hongwei; Findenegg, Gerhard H
2005-01-01
The boundary layer of aqueous surfactants and amphiphilic triblock copolymers against flat solid surfaces of different degrees of hydrophobicity was investigated by neutron reflectometry (NR), grazing incidence small angle neutron scattering (GISANS) and atomic force microscopy (AFM). Solid substrates of different hydrophobicities were prepared by appropriate surface treatment or by coating silicon wafers with polymer films of different chemical natures. For substrates coated with thin films (20-30 nm) of deuterated poly(styrene) (water contact angle θ w ∼ 90), neutron reflectivity measurements on the polymer/water interface revealed a water depleted liquid boundary layer of 2-3 nm thickness and a density about 90% of the bulk water density. No pronounced depletion layer was found at the interface of water against a less hydrophobic polyelectrolyte coating (θ w ∼ 63). It is believed that the observed depletion layer at the hydrophobic polymer/water interface is a precursor of the nanobubbles which have been observed by AFM at this interface. Decoration of the polymer coatings by adsorbed layers of nonionic C m E n surfactants improves their wettability by the aqueous phase at surfactant concentrations well below the critical micellar concentration (CMC) of the surfactant. Here, GISANS experiments conducted on the system SiO 2 /C 8 E 4 /D 2 O reveal that there is no preferred lateral organization of the C 8 E 4 adsorption layers. For amphiphilic triblock copolymers (PEO-PPO-PEO) it is found that under equilibrium conditions they form solvent-swollen brushes both at the air/water and the solid/water interface. In the latter case, the brushes transform to uniform, dense layers after extensive rinsing with water and subsequent solvent evaporation. The primary adsorption layers maintain properties of the precursor brushes. In particular, their thickness scales with the number of ethylene oxide units (EO) of the block copolymer. In the case of dip-coating without
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
Laminar boundary layer response to rotation of a finite diameter surface patch
International Nuclear Information System (INIS)
Klewicki, J.C.; Hill, R.B.
2003-01-01
The responses of the flat plate laminar boundary layer to perturbations generated by rotating a finite patch of the bounding surface are explored experimentally. The size of the surface patch was of the same order as the boundary layer thickness. The displacement thickness Reynolds number range of the boundary layers explored was 72-527. The rotation rates of the surface patch ranged from 2.14 to 62.8 s-1. Qualitative flow visualizations and quantitative molecular tagging velocimetry measurements revealed that rotation of a finite surface patch generates an asymmetric loop-like vortex. Significant features of this vortex include that, (i) the sign of the vorticity in the vortex head is opposite that of the boundary layer vorticity regardless of the sign of the input rotation, (ii) one leg of the vortex exhibits motion akin to solid body rotation while the other leg is best characterized as a spanwise shear layer, (iii) the vortex leg exhibiting near solid body rotation lifts more rapidly from the surface than the leg more like a shear layer, and (iv) the vortex leg exhibiting near solid body rotation always occurs on the side of the surface patch experiencing downstream motion. These asymmetries switch sides depending on the sign of the input rotation. The present results are interpreted and discussed relative to analytical solutions for infinite geometries. By way of analogy, plausible connections are drawn between the present results and the influences of wall normal vortices in turbulent boundary layer flows
''Free-space'' boundary conditions for the time-dependent wave equation
International Nuclear Information System (INIS)
Lindman, E.L.
1975-01-01
Boundary conditions for the discrete wave equation which act like an infinite region of free space in contact with the computational region can be constructed using projection operators. Propagating and evanescent waves coming from within the computational region generate no reflected waves as they cross the boundary. At the same time arbitrary waves may be launched into the computational region. Well known projection operators for one-dimensional waves may be used for this purpose in one dimension. Extensions of these operators to higher dimensions along with numerically efficient approximations to them are described for higher-dimensional problems. The separation of waves into ingoing and outgoing waves inherent in these boundary conditions greatly facilitates diagnostics
Directory of Open Access Journals (Sweden)
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.
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.
Steady Boundary Layer Disturbances Created By Two-Dimensional Surface Ripples
Kuester, Matthew
2017-11-01
Multiple experiments have shown that surface roughness can enhance the growth of Tollmien-Schlichting (T-S) waves in a laminar boundary layer. One of the common observations from these studies is a ``wall displacement'' effect, where the boundary layer profile shape remains relatively unchanged, but the origin of the profile pushes away from the wall. The objective of this work is to calculate the steady velocity field (including this wall displacement) of a laminar boundary layer over a surface with small, 2D surface ripples. The velocity field is a combination of a Blasius boundary layer and multiple disturbance modes, calculated using the linearized Navier-Stokes equations. The method of multiple scales is used to include non-parallel boundary layer effects of O (Rδ- 1) ; the non-parallel terms are necessary, because a wall displacement is mathematically inconsistent with a parallel boundary layer assumption. This technique is used to calculate the steady velocity field over ripples of varying height and wavelength, including cases where a separation bubble forms on the leeward side of the ripple. In future work, the steady velocity field will be the input for stability calculations, which will quantify the growth of T-S waves over rough surfaces. The author would like to acknowledge the support of the Kevin T. Crofton Aerospace & Ocean Engineering Department at Virginia Tech.
A Multigrid Algorithm for an Elliptic Problem with a Perturbed Boundary Condition
Bonito, Andrea
2013-01-01
We discuss the preconditioning of systems coupling elliptic operators in Ω⊂Rd, d=2,3, with elliptic operators defined on hypersurfaces. These systems arise naturally when physical phenomena are affected by geometric boundary forces, such as the evolution of liquid drops subject to surface tension. The resulting operators are sums of interior and boundary terms weighted by parameters. We investigate the behavior of multigrid algorithms suited to this context and demonstrate numerical results which suggest uniform preconditioning bounds that are level and parameter independent.
Influence of solid boundary conditions on the evolution of free and wall-bounded turbulent flows
International Nuclear Information System (INIS)
D'Addio, Paolo; Sassun, David; Orlandi, Paolo; Flores, Oscar
2014-01-01
The effect of the boundary conditions on the organization of vortex clusters is analyzed in two separate cases: rough channel flow and grid-generated turbulence. The aim is to understand how far the fluid structures are affected by the presence of roughness and the geometry of the grid. The grid-turbulence cases show that the single- and multi-scale geometries generate a flow strongly dominated by the shear at the beginning. The shear is initially caused by the presence of the body and, for the multi-scale grids, subsequently by the large differences between the scales. Further downstream from the grid these shear-dominated structures break up and form more isotropic clusters, whose dimensions seem to depend little on the particular geometry of the grid. For fractal grids, clusters are formed right downstream of the grid, resulting in a flow with less inhomogeneities than for single- and multi-scale grids. Eight different rough surfaces have been analyzed. In the smooth channel, both attached and detached clusters have been found and, depending on the geometry, the roughness affects the attached structures. Roughnesses made of aligned obstacles with a large separation seem to reduce the number of these structures in the flow. When the roughness elements are closely packed, both for transverse and aligned obstacles, the attached clusters are not able to reach within the roughness elements, and they seem to be anchored to the plane of the crests.
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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.
Modeling Turbulence Generation in the Atmospheric Surface and Boundary Layers
2015-10-01
ZT ). The initial acceleration of the rising buoyant air will be a = g∆T/TA. This is simply Archimedes ’ principle applied to the buoyant air. The... applications . 1 Various rules are employed to model C2n in the surface layer, but a key question is how to extend this estimation technique into the lower...in terms of wind turbulence the structure of the fluctuations produces a Reynolds stress tensor whose principle axes are not equal, meaning that at the
DEFF Research Database (Denmark)
Langen, Peter Lang; Vinther, Bo Møllesøe
2009-01-01
The response in northern hemisphere atmospheric circulation and the resulting changes in moisture sources for Greenland precipitation to glacial boundary conditions are studied in NCAR's CCM3 atmospheric general circulation model fitted with a moisture tracking functionality. We employ both...... seasonality, condensation temperatures and source temperatures are assessed. Udgivelsesdato: June 2009...
Boundary conditions in Ginsburg Landau theory and critical temperature of high-T superconductors
Lykov, A. N.
2008-06-01
New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature ( T) of high- T superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T of cuprate superconductors.
Boundary conditions in Ginsburg-Landau theory and critical temperature of high-Tc superconductors
International Nuclear Information System (INIS)
Lykov, A.N.
2008-01-01
New mixed boundary conditions to the Ginsburg-Landau equations are found to limit the critical temperature (T c ) of high-T c superconductors. Moreover, the value of the pseudogap in these superconductors can be explained by using the method. As a result, the macroscopic approach is proposed to increase T c of cuprate superconductors
DEFF Research Database (Denmark)
Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.
2007-01-01
A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...
Directory of Open Access Journals (Sweden)
Mabrouk Bragdi
2013-01-01
Full Text Available We discuss the existence of solutions for a class of some separated boundary differential inclusions of fractional orders 2<α<3 involving the Caputo derivative. In order to obtain necessary conditions for the existence result, we apply the fixed point technique, fractional calculus, and multivalued analysis.
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.|info:eu-repo/dai/nl/311474748; van de Schootbrugge, B.|info:eu-repo/dai/nl/376758562; Sinninghe Damsté, J.S.|info:eu-repo/dai/nl/07401370X; Brinkhuis, H.|info:eu-repo/dai/nl/095046097
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
Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions
Directory of Open Access Journals (Sweden)
M. U. Malakeeva
2012-01-01
Full Text Available The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints.
Construction of the Nuclear Effective Interaction from Energy Eigenstates and Boundary Conditions
McElvain, Kenneth; Haxton, Wick
2017-01-01
The original Harmonic Oscillator Based Effective Theory (HOBET) work by Haxton and Luu reduced H = T +VNN , with VNN a realistic potential, to Heff in a small basis defined by projection operator P while correctly including all scattering by H through an excluded space Q. Scattering by T is analytically included to all orders, leaving the ET expansion focused on the short range VNN. Results do not depend on the size P as the effect of scattering through Q is fully included, also distinguishing HOBET from other methods. In this talk we abandon VNN and determine the LECs of the ET expansion from energy levels and boundary conditions. In the infinite volume continuum case every energy is an eigenvalue of H with an associated scattering state. In the LQCD context boundary conditions are periodic. In either case the ET LECs can be determined from energy, boundary condition pairs. We show that the Cartesian HO ET LECs can be expressed in terms of the spherical ones, giving a spherical, infinite volume ET, bypassing the use of Luscher's method. The approach cleanly isolates operator mixing induced by the finite box, sequestering effects that vanish in the continuum limit in a Green's function constrained to match the boundary conditions. Supported by the DOE under contracts DE-SC00046548 and DE-AC02-98CH10886.
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Cornelis van der Mee
2005-01-01
Full Text Available We present the complete version including proofs of the results announced in [van der Mee C., Pivovarchik V.: A Sturm-Liouville spectral problem with boundary conditions depending on the spectral parameter. Funct. Anal. Appl. 36 (2002, 315–317 [Funkts. Anal. Prilozh. 36 (2002, 74–77 (Russian
In-plane vibration analysis of annular plates with arbitrary boundary conditions.
Shi, Xianjie; Shi, Dongyan; Qin, Zhengrong; Wang, Qingshan
2014-01-01
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.
In-Plane Vibration Analysis of Annular Plates with Arbitrary Boundary Conditions
Directory of Open Access Journals (Sweden)
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.
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,...
Kelvin--Helmholtz-like instability of a shear layer subject to free boundary conditions
International Nuclear Information System (INIS)
Mjolsness, R.C.
1979-01-01
For free boundary conditions a shear layer with linear velocity profile supports irrotational disturbances, one mode being unstable when its wavelength lambda>2.619 times the thickness h of the shear layer. For long wavelengths the dispersion relation of the mode approaches the Kelvin--Helmholtz form
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...
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...
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)
Mouffak Benchohra
2012-01-01
Full Text Available The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
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.
DEFF Research Database (Denmark)
Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John
2015-01-01
In this work the stability properties of a partial differential equation (PDE) with state-dependent parameters and asymmetric boundary conditions are investigated. The PDE describes the temperature distribution inside foodstuff, but can also hold for other applications and phenomena. We show...
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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.
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 surfa...
Non-reflecting boundary conditions and tensile instability in smooth particle hydrodynamics
Powell, Seimon
2012-01-01
This thesis aimed at the understanding and further development of smoothed particle hydrodynamics (SPH). The first part described the implementations of non-reflecting boundary conditions for elastic- waves in SPH. The second part contains a stability analysis of the semi-discrete SPH equations and a new method for stabilising basic SPH in tension.
Dynamic response of tube bundles with time-dependent boundary conditions
International Nuclear Information System (INIS)
Chaushioung Yeh; Ingtzer Hwang
1993-01-01
For the problems of dynamic response of tube bundles in incompressible fluid, the fluid-inertia loading must be included in the governing equations of coupled motion of array of tubes. This inertia loading (hydrodynamic force) can be formulated as an added mass matrix by using boundary element technique for whatever shapes of tubes in an arbitrary array. To deal with the vibration of tube bundles with time-dependent boundary conditions, a general method is established. The complete solution of this linear partial differential equation can be divided into two parts; quasi-static and dynamic solutions, each satisfies the non-homogeneous boundary conditions and homogeneous conditions, respectively. In this paper, a method based on Betti's law and developed by Yeh and Liaw is adopted to find the solution without pursuing the quasistatic solution explicitly. The effects of the time-dependent boundary conditions on the responses of tube bundles of different shapes and arrays are analyzed and discussed in this paper
Effects of physical boundary conditions on the transverse vibration of single-layer graphene sheets
Sadeghzadeh, S.; Khatibi, M. M.
2016-09-01
The effects of various approaches for a comprehensive application of boundary conditions on the molecular dynamics of graphene nanosheets were studied in this paper. Fixing more than two rows of carbon atoms was tested for satisfaction of clamped boundary condition in dynamics problems, and it was demonstrated that a completely different view should be taken for clamped boundary conditions. To do this, through the frequency domain decomposition approach, operational modal analysis has been developed to carry out the Laboratory of Nanometric Operational Modal Analysis on a molecular dynamics platform. The theory of the mentioned approach was introduced, and some comparisons were made with experimental works. The modeling results have shown that for graphene sheets with simply supported edges, fixing two or more rows leads to the same response as fixing one row. For clamped edges, the use of a flexible base as a substrate satisfies the boundary condition with the best possible. At the end, as an example, it has been demonstrated that the second and third natural vibration frequencies increase with the increase in aspect ratio, while the first frequency remains unchanged.
A laser Doppler system for the remote sensing of boundary layer winds in clear air conditions
Lawrence, T. R.; Krause, M. C.; Craven, C. E.; Morrison, L. K.; Thomson, J. A. L.; Cliff, W. C.; Huffaker, R. M.
1975-01-01
The system discussed uses a laser Doppler radar in combination with a velocity azimuth display mode of scanning to determine the three-dimensional wind field in the atmospheric boundary layer. An attractive feature of this CW monostatic system is that the ambient aerosol provides a 'sufficient' scattering target to permit operation under clear air conditions. Spatial resolution is achieved by focusing.
Inference and testing on the boundary in extended constant conditional correlation GARCH models
DEFF Research Database (Denmark)
Pedersen, Rasmus Søndergaard
2017-01-01
We consider inference and testing in extended constant conditional correlation GARCH models in the case where the true parameter vector is a boundary point of the parameter space. This is of particular importance when testing for volatility spillovers in the model. The large-sample properties of ...... for (no) volatility spillovers between foreign exchange rates....
International Nuclear Information System (INIS)
Zagrebnov, V.A.
1980-01-01
Using resolvents for Kirkwood-Zalburg, Kirkwood-Ruelle and Meier-Montroll operators, solutions of the finite-volume correlation equations for tempered boundary conditions are obtained explicity. The uniqueness theorem is proved. A connection of the correlation equations with the Dobrushin-Landford-Ruelle equations for the Gibbs probability measure is discussed
Conformal field theory of dipolar SLE with the Dirichlet boundary condition
Kang, Nam-Gyu; Tak, Hee-Joon
2013-12-01
We develop a version of dipolar conformal field theory based on the central charge modification of the Gaussian free field with the Dirichlet boundary condition and prove that correlators of certain family of fields in this theory are martingale-observables for dipolar SLE. We prove the restriction property of dipolar SLE(8/3) and Friedrich-Werner's formula in the dipolar case.
Traditionally, it is considered that, under boundary lubrication conditions, the reduction in friction and wear is mostly dependent on Extreme Pressure (EP) additives, rather than the basestock. However, several studies indicate that vegetable oils also contribute to the lubricity under this regime...
Partially solved differential systems with two-point non-linear boundary conditions
Czech Academy of Sciences Publication Activity Database
Rontó, András; Rontó, M.; Varga, I.
2017-01-01
Roč. 18, č. 2 (2017), s. 1001-1014 ISSN 1787-2405 Institutional support: RVO:67985840 Keywords : implicit differential systems * non-linear two-point boundary conditions * parametrization technique Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.388, year: 2016 http://mat76.mat.uni-miskolc.hu/mnotes/article/2491
The femur as a musculo-skeletal construct: a free boundary condition modelling approach.
Phillips, A T M
2009-07-01
Previous finite element studies of the femur have made simplifications to varying extents with regard to the boundary conditions used during analysis. Fixed boundary conditions are generally applied to the distal femur when examining the proximal behaviour at the hip joint, while the same can be said for the proximal femur when examining the distal behaviour at the knee joint. While fixed boundary condition analyses have been validated against in vitro experiments it remains a matter of debate as to whether the numerical and experimental models are indicative of the in vivo situation. This study presents a finite element model in which the femur is treated as a complete musculo-skeletal construct, spanning between the hip and knee joints. Linear and non-linear implementations of a free boundary condition modelling approach are applied to the bone through the explicit inclusion of muscles and ligaments spanning both the hip joint and the knee joint. A non-linear force regulated, muscle strain based activation strategy was found to result in lower observed principal strains in the cortex of the femur, compared to a linear activation strategy. The non-linear implementation of the model in particular, was found to produce hip and knee joint reaction forces consistent with in vivo data from instrumented implants.
Thermocouple Rakes for Measuring Boundary Layer Flows Extremely Close to Surface
Hwang, Danny P.; Fralick, Gustave C.; Martin, Lisa C.; Blaha, Charles A.
2001-01-01
Of vital interest to aerodynamic researchers is precise knowledge of the flow velocity profile next to the surface. This information is needed for turbulence model development and the calculation of viscous shear force. Though many instruments can determine the flow velocity profile near the surface, none of them can make measurements closer than approximately 0.01 in. from the surface. The thermocouple boundary-layer rake can measure much closer to the surface than conventional instruments can, such as a total pressure boundary layer rake, hot wire, or hot film. By embedding the sensors (thermocouples) in the region where the velocity is equivalent to the velocity ahead of a constant thickness strut, the boundary-layer flow profile can be obtained. The present device fabricated at the NASA Glenn Research Center microsystem clean room has a heater made of platinum and thermocouples made of platinum and gold. Equal numbers of thermocouples are placed both upstream and downstream of the heater, so that the voltage generated by each pair at the same distance from the surface is indicative of the difference in temperature between the upstream and downstream thermocouple locations. This voltage differential is a function of the flow velocity, and like the conventional total pressure rake, it can provide the velocity profile. In order to measure flow extremely close to the surface, the strut is made of fused quartz with extremely low heat conductivity. A large size thermocouple boundary layer rake is shown in the following photo. The latest medium size sensors already provide smooth velocity profiles well into the boundary layer, as close as 0.0025 in. from the surface. This is about 4 times closer to the surface than the previously used total pressure rakes. This device also has the advantage of providing the flow profile of separated flow and also it is possible to measure simultaneous turbulence levels within the boundary layer.
Single particle nonlocality, geometric phases and time-dependent boundary conditions
Matzkin, A.
2018-03-01
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.
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T. Tharammal
2013-03-01
Full Text Available To understand the validity of δ18O proxy records as indicators of past temperature change, a series of experiments was conducted using an atmospheric general circulation model fitted with water isotope tracers (Community Atmosphere Model version 3.0, IsoCAM. A pre-industrial simulation was performed as the control experiment, as well as a simulation with all the boundary conditions set to Last Glacial Maximum (LGM values. Results from the pre-industrial and LGM simulations were compared to experiments in which the influence of individual boundary conditions (greenhouse gases, ice sheet albedo and topography, sea surface temperature (SST, and orbital parameters were changed each at a time to assess their individual impact. The experiments were designed in order to analyze the spatial variations of the oxygen isotopic composition of precipitation (δ18Oprecip in response to individual climate factors. The change in topography (due to the change in land ice cover played a significant role in reducing the surface temperature and δ18Oprecip over North America. Exposed shelf areas and the ice sheet albedo reduced the Northern Hemisphere surface temperature and δ18Oprecip further. A global mean cooling of 4.1 °C was simulated with combined LGM boundary conditions compared to the control simulation, which was in agreement with previous experiments using the fully coupled Community Climate System Model (CCSM3. Large reductions in δ18Oprecip over the LGM ice sheets were strongly linked to the temperature decrease over them. The SST and ice sheet topography changes were responsible for most of the changes in the climate and hence the δ18Oprecip distribution among the simulations.
Segregation of sp-impurities at grain boundaries and surfaces: comparison of fcc cobalt and nickel
Czech Academy of Sciences Publication Activity Database
Všianská, Monika; Vémolová, H.; Šob, Mojmír
2017-01-01
Roč. 25, č. 8 (2017), č. článku 085004. ISSN 0965-0393 R&D Projects: GA ČR(CZ) GA16-24711S Institutional support: RVO:68081723 Keywords : local magnetic-moments * total-energy calculations * augmented-wave method * solute segregation * tilt boundaries * embrittling potency * alloying elements * hcp metals * basis-set * 1st-principles * grain boundary segregation * strengthening/embrittling energy * grain boundary magnetism * ab initio calculations * surface segregation Subject RIV: BM - Solid Matter Physics ; Magnetism OBOR OECD: Condensed matter physics (including formerly solid state physics, supercond.) Impact factor: 1.891, year: 2016
An Implementation of Hydrostatic Boundary Conditions for Variable Density Lattice Boltzmann Methods
Bardsley, K. J.; Thorne, D. T.; Lee, J. S.; Sukop, M. C.
2006-12-01
Lattice Boltzmann Methods (LBMs) have been under development for the last two decades and have become another capable numerical method for simulating fluid flow. Recent advances in lattice Boltzmann applications involve simulation of density-dependent fluid flow in closed (Dixit and Babu, 2006; D'Orazio et al., 2004) or periodic (Guo and Zhao, 2005) domains. However, standard pressure boundary conditions (BCs) are incompatible with concentration-dependent density flow simulations that use a body force for gravity. An implementation of hydrostatic BCs for use under these conditions is proposed here. The basis of this new implementation is an additional term in the pressure BC. It is derived to account for the incorporation of gravity as a body force and the effect of varying concentration in the fluid. The hydrostatic BC expands the potential of density-dependent LBM to simulate domains with boundaries other than the closed or periodic boundaries that have appeared in previous literature on LBM simulations. With this new implementation, LBM will be able to simulate complex concentration-dependent density flows, such as salt water intrusion in the classic Henry and Henry-Hilleke problems. This is demonstrated using various examples, beginning with a closed box system, and ending with a system containing two solid walls, one velocity boundary and one pressure boundary, as in the Henry problem. References Dixit, H. N., V. Babu, (2006), Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, 727-739. D'Orazio, A., M. Corcione, G.P. Celata, (2004), Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions, Int. J. Thermal Sci., 43, 575-586. Gou, Z., T.S. Zhao, (2005), Lattice Boltzmann simulation of natural convection with temperature-dependant viscosity in a porous cavity, Numerical Heat Transfer, Part B
Solvability of second-order boundary-value problems at resonance involving integral conditions
Directory of Open Access Journals (Sweden)
Yujun Cui
2012-03-01
Full Text Available This article concerns the second-order differential equation with integral boundary conditions $$displaylines{ x''(t=f(t,x(t,x'(t,quad tin (0,1,cr x(0=int_0^1x(sdalpha(s,quad x(1=int_0^1x(sdeta(s. }$$ Under the resonance conditions, we construct a projector and then applying coincidence degree theory to establish the existence of solutions.
Convective and global stability analysis of a Mach 5.8 boundary layer grazing a compliant surface
Dettenrieder, Fabian; Bodony, Daniel
2016-11-01
Boundary layer transition on high-speed vehicles is expected to be affected by unsteady surface compliance. The stability properties of a Mach 5.8 zero-pressure-gradient laminar boundary layer grazing a nominally-flat thermo-mechanically compliant panel is considered. The linearized compressible Navier-Stokes equations describe small amplitude disturbances in the fluid while the panel deformations are described by the Kirchhoff-Love plate equation and its thermal state by the transient heat equation. Compatibility conditions that couple disturbances in the fluid to those in the solid yield simple algebraic and robin boundary conditions for the velocity and thermal states, respectively. A local convective stability analysis shows that the panel can modify both the first and second Mack modes when, for metallic-like panels, the panel thickness exceeds the lengthscale δ99 Rex- 0 . 5 . A global stability analysis, which permits finite panel lengths with clamped-clamped boundary conditions, shows a rich eigenvalue spectrum with several branches. Unstable modes are found with streamwise-growing panel deformations leading to Mach wave-type radiation. Stable global modes are also found and have distinctly different panel modes but similar radiation patterns. Air Force Office of Scientific Research.
Wilson, Jack; Paxson, Daniel E.
2002-01-01
In one-dimensional calculations of pulsed detonation engine (PDE) performance, the exit boundary condition is frequently taken to be a constant static pressure. In reality, for an isolated detonation tube, after the detonation wave arrives at the exit plane, there will be a region of high pressure, which will gradually return to ambient pressure as an almost spherical shock wave expands away from the exit, and weakens. Initially, the flow is supersonic, unaffected by external pressure, but later becomes subsonic. Previous authors have accounted for this situation either by assuming the subsonic pressure decay to be a relaxation phenomenon, or by running a two-dimensional calculation first, including a domain external to the detonation tube, and using the resulting exit pressure temporal distribution as the boundary condition for one-dimensional calculations. These calculations show that the increased pressure does affect the PDE performance. In the present work, a simple model of the exit process is used to estimate the pressure decay time. The planar shock wave emerging from the tube is assumed to transform into a spherical shock wave. The initial strength of the spherical shock wave is determined from comparison with experimental results. Its subsequent propagation, and resulting pressure at the tube exit, is given by a numerical blast wave calculation. The model agrees reasonably well with other, limited, results. Finally, the model was used as the exit boundary condition for a one-dimensional calculation of PDE performance to obtain the thrust wall pressure for a hydrogen-air detonation in tubes of length to diameter ratio (L/D) of 4, and 10, as well as for the original, constant pressure boundary condition. The modified boundary condition had no performance impact for values of L/D > 10, and moderate impact for L/D = 4.
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
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.
Sullivan, Peter P.; McWilliams, James C.; Melville, W. Kendall
The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.
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Anzhou Cao
2013-01-01
Full Text Available Based on the theory of inverse problem, the optimization of open boundary conditions (OBCs in a 3D internal tidal model is investigated with the adjoint method. Fourier coefficients of M2 internal tide on four open boundaries, which are regarded as OBCs, are inverted simultaneously. During the optimization, the steepest descent method is used to minimize cost function. The reasonability and feasibility of the model are tested by twin experiments (TEs. In TE1, OBCs on four open boundaries are successfully inverted by using independent point (IP strategy, suggesting that IP strategy is useful in parameter estimation. Results of TE2 indicate that the model is effective even by assimilating inaccurate “observations.” Based on conclusions of TEs, the M2 internal tide around Hawaii is simulated by assimilating T/P data in practical experiment. The simulated cochart shows good agreement with that obtained from the Oregon State University tidal model and T/P observations. Careful inspection shows that the major difference between simulated results and OSU model results is short-scale fluctuations superposed on coamplitude lines, which can be treated as the surface manifestation modulated by the internal tide. The computed surface manifestation along T/P tracks is comparable to the estimation in previous work.
Directory of Open Access Journals (Sweden)
Oluwole Daniel Makinde
2011-01-01
Full Text Available Steady laminar natural convection flow over a semi-infinite moving vertical plate in the presence of internal heat generation and a convective surface boundary condition is examined in this paper. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. The governing non-linear partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge-Kutta integration scheme. The effects of physical parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Finally, numerical values of physical quantities, such as the local skin-friction coefficient and the local Nusselt number are presented in tabular form.
Verschaeve, Joris C G
2011-06-13
By means of the continuity equation of the incompressible Navier-Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.
Dynamic stability analysis of fluid-filled cylindrical shells with top end-fixed boundary condition
International Nuclear Information System (INIS)
Xu, Y.H.; Tsukimori, K.
1995-01-01
This study is aimed at understanding the dynamic instability mechanism of fluid-filled cylindrical shells with top end-fixed boundary condition under seismic excitation. The fluid-structure interaction problem is formulated using the concept of added mass. The contribution of each individual fluid pressure components are identified. A Galerkin/Finite Element discretization is applied to obtain the governing matrix equations. The model coupling among the various combinations of axial and circumferential modes are identified. For dynamic stability analysis, the matrix equations are cast into a set of coupled Hill's equations by employing an orthogonality transformation. The application of this method and the discussion on dynamic buckling behaviors of different boundary conditions are presented. The following comments are found: (1) Strong effect of added mass to the first beam mode frequency is observed in the top end-fixed case and the effect depends on the level of filled fluid and the ratio of shall radius to height; (2) The static and dynamic pressure acting on the bottom plate increase the axial frequency for n=2... N and the critical instability parameter ε cr in the top end-fixed case, respectively; (3) Strong effect of shell top boundary, open or closed, to axial frequencies for mode (i,n) (n=2... N) and instability behaviors is observed for fluid-filled tanks with bottom-fixed boundary condition. (author)
Sprofera, Joseph D.; Clark, Robert L.; Gibbs, Gary P.; Cabell, Randolph H.
2003-10-01
The study of control strategies aimed at the reduction of turbulent boundary layer noise transmission into the fuselage of an aircraft has been a topic of academic and industrial research for several years. In this work we focus on an approach that will attempt to address a practical application issue: the impact of uncertainty in boundary conditions on the choice of actuator and sensor locations for structural acoustic control. The selection of an optimized set of transducers and the creation of a suitably adjustable test system is used to demonstrate that robustness to bounded variations in boundary conditions of a plate is achievable in active structural acoustic control. This robustness is achieved through the optimization of transducer placement with respect to maximizing control of structural acoustic radiation over the desired range of boundary conditions. This project incorporates energy based modeling of the structure, electromechanical piezo coupling, radiation filter modeling, and control analysis through the use of Hankel Singular Value (HSV) estimates and optimization based upon the genetic algorithm. Testing in a transmission loss facility will be used to validate the selected transducer placements and demonstrate a reduction in radiated sound power. [Work supported by NASA.
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.
MHD boundary layer flow of a power-law nanofluid with new mass flux condition
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Masood Khan
2016-02-01
Full Text Available An analysis is carried out to study the magnetohydrodynamic MHD boundary layer flow of power-law nanofluid over a non-linear stretching sheet. In the presence of a transverse magnetic field, the flow is generated due to non-linear stretching sheet. By using similarity transformations, the governing boundary layer equations are reduced into a system of ordinary differential equations. A recently proposed boundary condition requiring zero nanoparticle mass flux is employed in the flow analysis of power-law fluid. The reduced coupled differential equations are then solved numerically by the shooting method. The variations of dimensionless temperature and nanoparticle concentration with various parameters are graphed and discussed in detail. Numerical values of physical quantities such as the skin-friction coefficient and the reduced local Nusselt number are computed in tabular form.
Angoshtari, Arzhang; Yavari, Arash
2015-12-01
We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first Piola-Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work done by the prescribed boundary displacements. This condition is very similar to the classical compatibility equations for the linear strain. Since these compatibility equations for linear and nonlinear strains involve infinite-dimensional spaces and consequently are not easy to use in practice, we derive alternative compatibility equations, which are written in terms of some finite-dimensional spaces and are more useful in practice. Using these new compatibility equations, we present some non-trivial examples that show that compatible strains may become incompatible in the presence of prescribed boundary displacements.
Directory of Open Access Journals (Sweden)
Florencio Rusty Punzalan
Full Text Available Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs. Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code
Time-dependent density functional theory with twist-averaged boundary conditions
Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.
2016-05-01
Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be
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.
Surface color from boundaries: a new 'watercolor' illusion.
Pinna, B; Brelstaff, G; Spillmann, L
2001-09-01
A colored line flanking a darker border will appear to assimilate its color onto the enclosed white area over distances of up to 45 deg (the Watercolor Effect). This coloration is uniform and complete within 100 ms. We found that thin (6 arcmin), winding inducing lines with different contrasts to the ground are generally more effective than thick, straight, and equiluminant lines. Blue and red lines induce the strongest effects, but watercolor spreading may also be seen with green and yellow. On a white background, color spreading is stronger than on chromatic, gray or black backgrounds. Little or no color is perceived when a narrow white zone (gap) is inserted in between the two inducing lines. However, chains of colored dots instead of continuous lines suffice to produce spreading. Edge-induced color is also observed when the two colored lines are presented dichoptically, suggesting a cortical origin. The Watercolor Effect described here may serve to enhance figure-ground segregation by imparting surface color onto the enclosed area, and to promote grouping between distant stimulus elements. As a grouping factor, watercolor coloration wins over proximity. Assimilative color spreading may arise in two steps: First, weakening of the contour by lateral inhibition between differentially activated edge cells (local diffusion); and second, unbarriered flow of color onto the enclosed area (global diffusion).
Free surface simulation of a two-layer fluid by boundary element method
Directory of Open Access Journals (Sweden)
Weoncheol Koo
2010-09-01
Full Text Available A two-layer fluid with free surface is simulated in the time domain by a two-dimensional potential-based Numerical Wave Tank (NWT. The developed NWT is based on the boundary element method and a leap-frog time integration scheme. A whole domain scheme including interaction terms between two layers is applied to solve the boundary integral equation. The time histories of surface elevations on both fluid layers in the respective wave modes are verified with analytic results. The amplitude ratios of upper to lower elevation for various density ratios and water depths are also compared.
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...
Influence of the Outer Boundary Condition on models of AGB stars
Wagstaff, G.; Weiss, A.
2018-04-01
Current implementations of the stellar atmosphere typically derive boundary conditions for the interior model from either grey plane-parallel atmospheres or scaled solar atmospheres, neither of which can be considered to have appropriate underlying assumptions for the Thermally Pulsing Asymptotic Giant Branch (TP-AGB). This paper discusses the treatment and influence of the outer boundary condition within stellar evolution codes, and the resulting effects on the AGB evolution. The complex interaction of processes, such as the third dredge up and mass loss, governing the TP-AGB can be affected by varying the treatment of this boundary condition. Presented here are the results from altering the geometry, opacities and the implementation of a grid of MARCS/COMARCS model atmospheres in order to improve this treatment. Although there are changes in the TP-AGB evolution, observable quantities, such as the final core mass, are not significantly altered as a result of the change of atmospheric treatment. During the course of the investigation, a previously unseen phenomena in the AGB models was observed and further investigated. This is believed to be physical, although arising from specific conditions which make its presence unlikely. If it were present in stars, this phenomenon would increase the carbon-star lifetime above 10Myr and increase the final core mass by ˜0.1M⊙ in the narrow initial-mass range where it was observed (˜2 - 2.3M⊙).
Directory of Open Access Journals (Sweden)
Kyncl Martin
2017-01-01
Full Text Available 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
Friction behaviors of rough chromium surfaces under starving lubrication conditions
Liu, Derong; Yan, Bo; Shen, Bin; Liu, Lei; Hu, Wenbin
2018-01-01
Surface texturing has become an effective method for improving the tribological properties of mechanical components under the oil lubrication. In this study, a rough surface, with the bumps arranged in a random array, was prepared by means of electrodeposition. A post-grinding and polishing processing was employed to fabricate flat areas for tribological tests under conformal contact. Compared with the smooth surfaces, the rough surface improves the load capacity of coatings at high loads. The effects of rough surfaces on friction reduction become more pronounced at higher speeds and lower normal loads due to the transition of lubricant regime from the boundary to mixed lubrication.
Motion of particles in solar and galactic systems by using Neumann boundary condition
Shenavar, Hossein
2016-12-01
A new equation of motion, which is derived previously by imposing Neumann boundary condition on cosmological perturbation equations (Shenavar in Astrophys. Space Sci., 2016a, doi: 10.1007/s10509-016-2676-5), is investigated. By studying the precession of perihelion, it is shown that the new equation of motion suggests a small, though detectable, correction in orbits of solar system objects. Then a system of particles is surveyed to have a better understanding of galactic structures. Also the general form of the force law is introduced by which the rotation curve and mass discrepancy of axisymmetric disks of stars are derived. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near a constant acceleration 2c1a0 where c1 is the Neumann constant and a0 = 6.59 ×10^{-10} m/s2 is a fundamental acceleration. Furthermore, it is shown that a critical surface density equal to σ0=a0/G, in which G is the Newton gravitational constant, has a significant role in rotation curve and mass discrepancy plots. Also, the specific form of NFW mass density profile at small radii, ρ∝1/r, is explained too. Finally, the present model will be tested by using a sample of 39 LSB galaxies for which we will show that the rotation curve fittings are generally acceptable. The derived mass to light ratios too are found within the plausible bound except for the galaxy F571-8.
Boundary lubrication by brushed salivary conditioning films and their degree of glycosylation.
Veeregowda, Deepak H; van der Mei, Henny C; de Vries, Joop; Rutland, Mark W; Valle-Delgado, Juan J; Sharma, Prashant K; Busscher, Henk J
2012-10-01
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 lubrication of SCFs after different modes of brushing and to explain their lubrication on the basis of their roughness, dehydrated layer thickness, and degree of glycosylation. A pilot study was performed to relate in vitro lubrication with mouthfeel in human volunteers. Coefficient of friction (COF) on 16-h-old SCFs after manual, rotary-oscillatory, and sonically driven brushing was measured using colloidal probe atomic force microscopy (AFM). AFM was also used to assess the roughness of SCFs prior to and after brushing. Dehydrated layer thicknesses and glycosylation of the SCFs were determined using X-ray photoelectron spectroscopy. Mouthfeel after manual and both modes of powered brushing were evaluated employing a split-mouth design. Compared with unbrushed and manually or sonically driven brushed SCFs, powered rotary-oscillatory brushing leads to deglycosylation of the SCF, loss of thickness, and a rougher film. Concurrently, the COF of a powered rotary-oscillatory brushed SCF increased. Volunteers reported a slightly preferred mouthfeel after sonic brushing as compared to powered rotating-oscillating brushing. Deglycosylation and roughness increase the COF on SCFs. Powered rotary-oscillatory brushing can deglycosylate a SCF, leading to a rougher film surface as compared with manual and sonic brushing, decreasing the lubricative function of the SCF. This is consistent with clinical mouthfeel evaluation after different modes of brushing.
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.
Air Entrainment and Surface Ripples in a Turbulent Ship Hull Boundary Layer
Masnadi, Naeem; Erinin, Martin; Duncan, James H.
2017-11-01
The air entrainment and free-surface fluctuations caused by the interaction of a free surface and the turbulent boundary layer of a vertical surface-piercing plate is studied experimentally. In this experiment, a meter-wide stainless steel belt travels horizontally in a loop around two rollers with vertically oriented axes. This belt device is mounted inside a large water tank with the water level set just below the top edge of the belt. The belt, rollers, and supporting frame are contained within a sheet metal box to keep the device dry except for one 6-meter-long straight test section. The belt is accelerated suddenly from rest until reaching constant speed in order to create a temporally evolving boundary layer analogous to the spatially evolving boundary layer that would exist along a surface-piercing towed flat plate. Surface ripples are measured using a cinematic laser-induced fluorescence technique with the laser sheet oriented parallel or normal to the belt surface. Air entrainment events and bubble motions are recorded from underneath the water surface using a stereo imaging system. Measurements of small bubbles, that tend to stay submerged for a longer time, are planned via a high-speed digital in-line holographic system. The support of the Office of Naval Research is gratefully acknowledged.
Influence of Contact Angle Boundary Condition on CFD Simulation of T-Junction
Arias, S.; Montlaur, A.
2018-03-01
In this work, we study the influence of the contact angle boundary condition on 3D CFD simulations of the bubble generation process occurring in a capillary T-junction. Numerical simulations have been performed with the commercial Computational Fluid Dynamics solver ANSYS Fluent v15.0.7. Experimental results serve as a reference to validate numerical results for four independent parameters: the bubble generation frequency, volume, velocity and length. CFD simulations accurately reproduce experimental results both from qualitative and quantitative points of view. Numerical results are very sensitive to the gas-liquid-wall contact angle boundary conditions, confirming that this is a fundamental parameter to obtain accurate CFD results for simulations of this kind of problems.
Directory of Open Access Journals (Sweden)
Samira Hosseini
Full Text Available Abstract One of the main drawbacks of Element Free Galerkin (EFG method is its dependence on moving least square shape functions which don’t satisfy the Kronecker Delta property, so in this method it’s not possible to apply Dirichlet boundary conditions directly. The aim of the present paper is to discuss different aspects of three widely used methods of applying Dirichlet boundary conditions in EFG method, called Lagrange multipliers, penalty method, and coupling with finite element method. Numerical simulations are presented to compare the results of these methods form the perspective of accuracy, convergence and computational expense. These methods have been implemented in an object oriented programing environment, called INSANE, and the results are presented and compared with the analytical solutions.
New method for solving the bending problem of rectangular plates with mixed boundary conditions
Directory of Open Access Journals (Sweden)
Liu Xin Min
2016-01-01
Full Text Available A new method is used to solve the rectangular plate bending problem with mixed boundary conditions. The method overcomes the complicated derivation of the classical solution by Fourth-order differential problem into integrating question. Under uniform loading rectangular plate bending problem with one side fixed the opposite side half simply supported half fixed the other two sides free rectangular plate, one side simply supported the opposite side half simply supported half fixed the other two sides free rectangular plate is systematically solved. According to the actual boundary conditions of the rectangular plate, the corresponding characteristic equation can easily be set up. It is presented deflection curve equation and the numerical calculation. By compared the results of the equation to the finite element program, we are able to demonstrate the correctness of the method. So the method not only has certain theoretical value, but also can be directly applied to engineering practice.
Du, Kui
2011-07-01
We consider electromagnetic scattering from two-dimensional (2D) overfilled cavities embedded in an infinite ground plane. The unbounded computational domain is truncated to a bounded one by using a transparent boundary condition (TBC) proposed on a semi-ellipse. For overfilled rectangular cavities with homogeneous media, another TBC is introduced on the cavity apertures, which produces a smaller computational domain. The existence and uniqueness of the solutions of the variational formulations for the transverse magnetic and transverse electric polarizations are established. In the exterior domain, the 2D scattering problem is solved in the elliptic coordinate system using the Mathieu functions. In the interior domain, the problem is solved by a finite element method. Numerical experiments show the efficiency and accuracy of the new boundary conditions.
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....
On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
Hagendorf, Christian; Liénardy, Jean
2018-03-01
The square-lattice eight-vertex model with vertex weights a, b, c, d obeying the relation (a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab) and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for L = 2n + 1 vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly degenerate eigenvalue \\Thetan = (a+b){\\hspace{0pt}}2n+1 . This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to \\Thetan are shown to be the ground states of the spin-chain Hamiltonian. Moreover, for positive vertex weights \\Thetan is the largest eigenvalue of the transfer matrix.
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.
Confinement dynamics and boundary condition studies in the Reversed Field Pinch
International Nuclear Information System (INIS)
Schoenberg, K.F.; Ingraham, J.C.; Moses, R.W. Jr.
1988-01-01
The study of confinement dynamics, including investigation of the boundary conditions required for plasma sustainment, are central to the development of the Reversed Field Pinch (RFP) concept. Recently, several insights into confinement have emerged from a detailed investigation RFP electron and ion dynamics. These insights derive from the recognition that both magnetohydrodynamic (MHD) and electron kinetic effects play an important and coupled role in RFP stability, sustainment, and confinement. In this paper, we summarize the results of confinement studies on the ZT-40M experiment, and boundary condition studies on the Wisconsin non-circular RFP experiment. A brief description of the newly commissioned Madison Symmetric Torus (MST) is also presented. 28 refs., 3 figs
Artificial Boundary Conditions for Finite Element Model Update and Damage Detection
2017-03-01
Combining (2.15) and (2.16) results in the stiffness element matrix: 2 2 2 2 12 6 12 6 6 64 2 12 6 12 6 6 62 4 e L L L L L LEI K L L L L L L L...structural damage detection using artificial boundary conditions,” M.S. thesis, MEC , NPS, Monterey, CA, 2007. [20] R. L. Fox and M. P. Kapoor, “Rate
Numerical solution of the right boundary condition inverse problem for the Black-Scholes equation
Georgiev, Slavi G.; Vulkov, Lubin G.
2017-12-01
In this work we report the development of an algorithm to solve inverse problems of determining the right boundary condition according to a measurement inside a truncated domain for the Black-Scholes equation. The difference schemes for the direct and inverse problems are derived on non-uniform Tavella-Randall grids. We propose and discuss results of computational experiments for several European options.
Source-to-Sink: An Earth/Mars Comparison of Boundary Conditions for Eolian Dune Systems
Kocurek, Gary; Ewing, Ryan C.
2012-01-01
Eolian dune fields on Earth and Mars evolve as complex systems within a set of boundary conditions. A source-to-sink comparison indicates that although differences exist in sediment production and transport, the systems largely converge at the dune-flow and pattern-development levels, but again differ in modes of accumulation and preservation. On Earth, where winds frequently exceed threshold speeds, dune fields are sourced primarily through deflation of subaqueous deposits as these sediments...
Czech Academy of Sciences Publication Activity Database
Mácha, Václav; Tichý, J.
2014-01-01
Roč. 16, č. 4 (2014), s. 823-845 ISSN 1422-6928 R&D Projects: GA ČR GA201/09/0917 Institutional support: RVO:67985840 Keywords : generalized Stokes system * perfect slip boundary conditions * Lq theory Subject RIV: BA - General Math ematics Impact factor: 1.186, year: 2014 http://link.springer.com/article/10.1007%2Fs00021-014-0190-5
Discrete maximum principle for Poisson equation with mixed boundary conditions solved by hp-FEM
Czech Academy of Sciences Publication Activity Database
Vejchodský, Tomáš; Šolín, P.
2009-01-01
Roč. 1, č. 2 (2009), s. 201-214 ISSN 2070-0733 R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496; GA ČR GA102/05/0629 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete maximum principle * hp-FEM * Poisson equation * mixed boundary conditions Subject RIV: BA - General Mathematics
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....
Energy Technology Data Exchange (ETDEWEB)
Viswanathan, K. K.; Aziz, Z. A.; Javed, Saira; Yaacob, Y. [Universiti Teknologi Malaysia, Johor Bahru (Malaysia); Pullepu, Babuji [S R M University, Chennai (India)
2015-05-15
Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters. The governing equations of motion for truncated conical shell are obtained in terms of displacement functions. The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem. The parametric studies have been made and discussed.
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 OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517716222
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Slavov, S.I.
1989-01-01
Vector nonlinear Schroedinger equations (VS3) is investigated under quasi-constant boundary conditions. New two-soliton solutions are obtained with such non-trivial dynamics that they may be called the breather solutions. A version of the basic Novikov-Dubrovin-Krichever algebro-geometrical approach is applied to obtain breather like solutions existing for all types of internal symmetry is specified are formulated in terms of the soliton velocity expressed via the parameters of the problem. 4 refs
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-03-01
Full Text Available This paper investigates the existence of solutions for higher order fractional differential inclusions with fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. Our study includes the cases when the right-hand side of the inclusion has convex as well non-convex values. Some standard fixed point theorems for multivalued maps are applied to establish the main results. An illustrative example is also presented.
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 OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http:// journals .sagepub.com/doi/abs/10.1177/1081286517716222
Open-ocean boundary conditions from interior data: Local and remote forcing of Massachusetts Bay
Bogden, P.S.; Malanotte-Rizzoli, P.; Signell, R.
1996-01-01
Massachusetts and Cape Cod Bays form a semienclosed coastal basin that opens onto the much larger Gulf of Maine. Subtidal circulation in the bay is driven by local winds and remotely driven flows from the gulf. The local-wind forced flow is estimated with a regional shallow water model driven by wind measurements. The model uses a gravity wave radiation condition along the open-ocean boundary. Results compare reasonably well with observed currents near the coast. In some offshore regions however, modeled flows are an order of magnitude less energetic than the data. Strong flows are observed even during periods of weak local wind forcing. Poor model-data comparisons are attributable, at least in part, to open-ocean boundary conditions that neglect the effects of remote forcing. Velocity measurements from within Massachusetts Bay are used to estimate the remotely forced component of the flow. The data are combined with shallow water dynamics in an inverse-model formulation that follows the theory of Bennett and McIntosh [1982], who considered tides. We extend their analysis to consider the subtidal response to transient forcing. The inverse model adjusts the a priori open-ocean boundary condition, thereby minimizing a combined measure of model-data misfit and boundary condition adjustment. A "consistency criterion" determines the optimal trade-off between the two. The criterion is based on a measure of plausibility for the inverse solution. The "consistent" inverse solution reproduces 56% of the average squared variation in the data. The local-wind-driven flow alone accounts for half of the model skill. The other half is attributable to remotely forced flows from the Gulf of Maine. The unexplained 44% comes from measurement errors and model errors that are not accounted for in the analysis.
Vibrational spectra of four-coordinated random networks with periodic boundary conditions
International Nuclear Information System (INIS)
Guttman, L.
1976-01-01
Examples of perfectly four-coordinated networks satisfying periodic boundary conditions are constructed by a pseudo-random process, starting from a crystalline region. The unphysical features (high density, large deviations from the tetrahedral bond-angle) are removed by systematic modification of the bonding scheme. The vibrational spectra are calculated, using a valence-force potential, and the neutron scattering is computed by a phonon-expansion approximation
Vibration analysis of multi-span beam system under arbitrary boundary and coupling conditions
Directory of Open Access Journals (Sweden)
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.
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.
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.
Templeton, Jeremy; Jones, Reese
2012-11-01
Molecular dynamics (MD) is a useful technique for scientific investigations of nanofluidic processes as it explicitly represents the dynamics of every atom in a system. In order to model systems of interest, e.g. nanochannels, it is necessary to constrain atomic motions to conform to conditions corresponding to large-scale information, e.g. thermodynamic variables. However, many engineered configurations involve complex interactions between the system and its environment, and take place in non-trivial geometries. To accurately simulate these phenomena, methods to apply boundary conditions to MD systems are required that simultaneously regulate the temperature (i.e., energy) and momentum of the atoms in a local manner. This work uses an atomistic-to-continuum formulation to generate boundary conditions by using finite elements (FE) and their associated shape functions to define ``boundaries'' for a particle system. By projecting onto the FE basis, coarse-scale observables are identified for regulation based on separating the mean and fluctuating velocity components defining the momentum and temperature. Regulating the MD system is achieved by applying constraints posed on the coarse-grained variables. The method is illustrated by application to several nanofluidic systems. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE.
Assessment of a PML Boundary Condition for Simulating an MRI Radio Frequency Coil
Directory of Open Access Journals (Sweden)
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.
Inlet and outlet boundary conditions for the discrete velocity direction model
Zhang, Zhenyu; Zhao, Wei; Zhao, Qingjun; Lu, Guojing; Xu, Jianzhong
2018-02-01
The discrete velocity direction model is an approximate method to the Boltzmann equation, which is an optional kinetic method to microgas flow and heat transfer. In this paper, the treatment of the inlet and outlet boundary conditions for the model is proposed. In the computation strategy, the microscopic molecular speed distribution functions at inlet and outlet are indirectly determined by the macroscopic gas pressure, mass flux and temperature, which are all measurable parameters in microgas flow and heat transfer. The discrete velocity direction model with the pressure correction boundary conditions was applied into the plane Poiseuille flow in microscales and the calculations cover all flow regimes. The numerical results agree well with the data of the NS equation near the continuum regime and the date of linearized Boltzmann equation and the DSMC method in the transition regime and free molecular flow. The Knudsen paradox and the nonlinear pressure distributions have been accurately captured by the discrete velocity direction model with the present boundary conditions.
Effect of boundary conditions on downstream vorticity from counter-rotating swirlers
Directory of Open Access Journals (Sweden)
Weiye Huo
2015-02-01
Full Text Available Particle image velocimetry (PIV is utilized to measure the non-reacting flow field in a reflow combustor with multiple and single swirlers. The velocity field, vortex structure and total vorticity levels are experimentally obtained using two different boundary conditions, representing a single confined swirler and multiple swirlers in an annular combustor. The influence of the boundary conditions on the flow field at several locations downstream of the swirlers is experimentally investigated, showing that the central vortex in the multi-swirler case is more concentrated than in the single-swirler case. The vorticity of the central vortex and average cross-sectional vorticity are relatively low at the swirler outlet in both cases. Both of these statistics gradually increase to the maximum values near 20 mm downstream of the swirler outlet, and subsequently decrease. It is also found that the central vortex in the multi-swirler case is consistently greater than the single-swirler case. These results demonstrate the critical influence of boundary conditions on flow characteristic of swirling flow, providing insight into the difference of the experiments on test-bed combustor and the full-scale annular combustors.
Effect of boundary conditions, impact loading and hydraulic stiffening on femoral fracture strength.
Haider, Ifaz T; Speirs, Andrew D; Frei, Hanspeter
2013-09-03
Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading. Copyright © 2013 Elsevier Ltd. All rights reserved.
Surface roughness and grain boundary scattering effects on the electrical conductivity of thin films
Palasantzas, George
1998-01-01
In this work, we investigate surface/interface roughness and grain boundary scattering effects on the electrical conductivity of polycrystalline thin films in the Born approximation. We assume for simplicity a random Gaussian roughness convoluted with a domain size distribution ~e^-πr^2/ζ^2 to
Impact of Bay-Breeze Circulations on Surface Air Quality and Boundary Layer Export
Loughner, Christopher P.; Tzortziou, Maria; Follette-Cook, Melanie; Pickering, Kenneth E.; Goldberg, Daniel; Satam, Chinmay; Weinheimer, Andrew; Crawford, James H.; Knapp, David J.; Montzka, Denise D.;
2014-01-01
Meteorological and air-quality model simulations are analyzed alongside observations to investigate the role of the Chesapeake Bay breeze on surface air quality, pollutant transport, and boundary layer venting. A case study was conducted to understand why a particular day was the only one during an 11-day ship-based field campaign on which surface ozone was not elevated in concentration over the Chesapeake Bay relative to the closest upwind site and why high ozone concentrations were observed aloft by in situ aircraft observations. Results show that southerly winds during the overnight and early-morning hours prevented the advection of air pollutants from the Washington, D.C., and Baltimore, Maryland, metropolitan areas over the surface waters of the bay. A strong and prolonged bay breeze developed during the late morning and early afternoon along the western coastline of the bay. The strength and duration of the bay breeze allowed pollutants to converge, resulting in high concentrations locally near the bay-breeze front within the Baltimore metropolitan area, where they were then lofted to the top of the planetary boundary layer (PBL). Near the top of the PBL, these pollutants were horizontally advected to a region with lower PBL heights, resulting in pollution transport out of the boundary layer and into the free troposphere. This elevated layer of air pollution aloft was transported downwind into New England by early the following morning where it likely mixed down to the surface, affecting air quality as the boundary layer grew.
Debye potentials, electromagnetic reciprocity and impedance boundary conditions for efficient analytic approximation of coupling impedances in complex heterogeneous accelerator pipes
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)
Tidriri, M.
2004-01-01
In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via $BV_{loc}$ theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to $L^1\\cap L^\\infty$ with the additional regularity assumptions that the initial data are in $BV_{loc}$. We also extend our hydrodynamic analysis...
Yousefzadeh, Behrooz; Hodgson, Murray
2012-09-01
A beam-tracing model was used to study the acoustical responses of three empty, rectangular rooms with different boundary conditions. The model is wave-based (accounting for sound phase) and can be applied to rooms with extended-reaction surfaces that are made of multiple layers of solid, fluid, or poroelastic materials-the acoustical properties of these surfaces are calculated using Biot theory. Three room-acoustical parameters were studied in various room configurations: sound strength, reverberation time, and RApid Speech Transmission Index. The main objective was to investigate the effects of modeling surfaces as either local or extended reaction on predicted values of these three parameters. Moreover, the significance of modeling interference effects was investigated, including the study of sound phase-change on surface reflection. Modeling surfaces as of local or extended reaction was found to be significant for surfaces consisting of multiple layers, specifically when one of the layers is air. For multilayers of solid materials with an air-cavity, this was most significant around their mass-air-mass resonance frequencies. Accounting for interference effects made significant changes in the predicted values of all parameters. Modeling phase change on reflection, on the other hand, was found to be relatively much less significant.
International Nuclear Information System (INIS)
Takagi, T.; Miki, K.; Chen, B.C.J.; Sha, W.T.
1985-01-01
A new method is presented for numerically generating boundary-fitted coordinate systems for arbitrarily curved surfaces. The three-dimensional surface has been expressed by functions of two parameters using the geometrical modeling techniques in computer graphics. This leads to new quasi-one- and two-dimensional elliptic partial differential equations for coordinate transformation. Since the equations involve the derivatives of the surface expressions, the grids geneated by the equations distribute on the surface depending on its slope and curvature. A computer program GRID-CS based on the method was developed and applied to a surface of the second order, a torus and a surface of a primary containment vessel for a nuclear reactor. These applications confirm that GRID-CS is a convenient and efficient tool for grid generation on arbitrarily curved surfaces
Numerical model simulations of boundary-layer dynamics during winter conditions
DEFF Research Database (Denmark)
Melas, D.; Persson, T.; Bruin, H. de
2001-01-01
forcing. Model results are evaluated against in-situ measurements performed during the WINTEX field campaign held in Sodankyla, Northern Finland in March 1997. The results show that the land-surface parameterization employed in the mesoscale model is not able to reproduce the magnitude of the daytime......A mesoscale numerical model, incorporating a land-surface scheme based on Deardorffs' approach, is used to study the diurnal variation of the boundary layer structure and surface fluxes during four consecutive days with air temperatures well below zero, snow covered ground and changing synoptic...... sensible heat fluxes and especially the pronounced maximum observed in the afternoon. Additional model simulations indicate that this drawback is to a large extent removed by the implementation of a shading factor in the original Deardorff scheme. The shading factor, as discussed in Gryning et al. (2001...
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.
Directory of Open Access Journals (Sweden)
Cheng-yong Li
2015-01-01
Full Text Available The bottom-hole pressure response which can reflect the gas flow characteristics is important to study. A mathematical model for description of gas from porous coalbed methane (CBM reservoirs with complex boundary conditions flowing into horizontal wells has been developed. Meanwhile, basic solution of boundary elements has been acquired by combination of Lord Kelvin point source solution, the integral of Bessel function, and Poisson superimpose formula for CBM horizontal wells with complex boundary conditions. Using this model, type curves of dimensionless pressure and pressure derivative are obtained, and flow characteristics of horizontal wells in complex boundary reservoirs and relevant factors are accordingly analyzed.
Directory of Open Access Journals (Sweden)
Lizal Frantisek
2016-01-01
Full Text Available Correct definition of boundary conditions is crucial for the appropriate simulation of a flow. It is a common practice that simulation of sufficiently long upstream entrance section is performed instead of experimental investigation of the actual conditions at the boundary of the examined area, in the case that the measurement is either impossible or extremely demanding. We focused on the case of a benchmark channel with ventilation outlet, which models a regular automotive ventilation system. At first, measurements of air velocity and turbulence intensity were performed at the boundary of the examined area, i.e. in the rectangular channel 272.5 mm upstream the ventilation outlet. Then, the experimentally acquired results were compared with results obtained by numerical simulation of further upstream entrance section defined according to generally approved theoretical suggestions. The comparison showed that despite the simple geometry and general agreement of average axial velocity, certain difference was found in the shape of the velocity profile. The difference was attributed to the simplifications of the numerical model and the isotropic turbulence assumption of the used turbulence model. The appropriate recommendations were stated for the future work.
Directory of Open Access Journals (Sweden)
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.
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.
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.
International Nuclear Information System (INIS)
Teles, V.; Mouche, E.; Maugis, P.; Huhle, M.; Brulhetz, J.; Vigneron, G.; Wendlingz, J.
2005-01-01
The geomorphologic evolution in the Eastern part of the Paris Basin has been important during the last three hundred thousand years. The landscape evolution has been characterized mainly by outcrop retreat linked to valley incisions. The outcropping limestones have been affected by karst development. The hydrographic network has evolved through a stepped process due to river piracies. In the Meuse/Haute Marne region, the Meuse River tributaries have been captured progressively by rivers of the Seine basin. Specifically, on the Bure area, the Saulx and Ornain Rivers became tributaries of the Marne River since circa 200 ky B.P. Based on mapping and dating results, Andra has quantified the geomorphological evolution of the Meuse/Haute-Marne site for several hundred thousand years in the past and has estimated the future evolution over 1 million years. The Callovo-Oxfordian boundary conditions depend on the hydraulic heads in the two surrounding aquifers, the Oxfordian limestone on top and the Dogger one below. Both aquifer outcrops are modified over the next million years. For the present study, the geomorphologic evolution is considered independently of other processes and translated in the hydrogeological model in terms of changes in the hydraulic boundary conditions at the surface. The hydrodynamic simulations have been performed with the code CASTEM2000 (implemented by CEA (Atomic Energy Commissariat)) using a mixed hybrid finite-element formulation. For these groundwater flow simulations, three modelled stages are presented: the present, 500,000 years (500 Ky) and 10 6 years (I Ma) in the future. The landscape evolution is merely considered through the use of three different topographies on which the boundary conditions are applied. According to Andra predictions, at the Meuse/Haute-Marne site, the valley incisions on the Bure plateau will locally reach the Oxfordian limestone. Thus, the Oxfordian aquifer exhibits more changes due to topographic evolution than
Campbell, Charles H.; Berger, Karen; Anderson, Brian
2012-01-01
Hypersonic entry flight testing motivated by efforts seeking to characterize boundary layer transition on the Space Shuttle Orbiters have identified challenges in our ability to acquire high quality quantitative surface temperature measurements versus time. Five missions near the end of the Space Shuttle Program implemented a tile surface protuberance as a boundary layer trip together with tile surface thermocouples to capture temperature measurements during entry. Similar engineering implementations of these measurements on Discovery and Endeavor demonstrated unexpected measurement voltage response during the high heating portion of the entry trajectory. An assessment has been performed to characterize possible causes of the issues experienced during STS-119, STS-128, STS-131, STS-133 and STS-134 as well as similar issues encountered during other orbiter entries.
Strong influence of periodic boundary conditions on lateral diffusion in lipid bilayer membranes
Energy Technology Data Exchange (ETDEWEB)
Camley, Brian A. [Center for Theoretical Biological Physics and Department of Physics, University of California, San Diego, California 92093 (United States); Department of Physics, University of California, Santa Barbara, California 93106 (United States); Lerner, Michael G. [Department of Physics and Astronomy, Earlham College, Richmond, Indiana 47374 (United States); Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892 (United States); Pastor, Richard W. [Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892 (United States); Brown, Frank L. H. [Department of Physics, University of California, Santa Barbara, California 93106 (United States); Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106 (United States)
2015-12-28
The Saffman-Delbrück hydrodynamic model for lipid-bilayer membranes is modified to account for the periodic boundary conditions commonly imposed in molecular simulations. Predicted lateral diffusion coefficients for membrane-embedded solid bodies are sensitive to box shape and converge slowly to the limit of infinite box size, raising serious doubts for the prospects of using detailed simulations to accurately predict membrane-protein diffusivities and related transport properties. Estimates for the relative error associated with periodic boundary artifacts are 50% and higher for fully atomistic models in currently feasible simulation boxes. MARTINI simulations of LacY membrane protein diffusion and LacY dimer diffusion in DPPC membranes and lipid diffusion in pure DPPC bilayers support the underlying hydrodynamic model.
International Nuclear Information System (INIS)
Adesanya, S.O.; Oluwadare, E.O.; Falade, J.A.; Makinde, O.D.
2015-01-01
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. - Highlights: • The influence of magnetic field on the free convective fluid flow is considered. • The coupled equations are solved by using Adomian decomposition method. • The Adomian series solution agreed with previously obtained result. • Magnetic field decreases the velocity maximum but enhances temperature field
DEFF Research Database (Denmark)
Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin
2017-01-01
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....
Electron Conditioning of Technical Aluminium Surfaces
Energy Technology Data Exchange (ETDEWEB)
Le Pimpec, F
2004-09-02
The effect of electron conditioning on commercially aluminium alloys 1100 and 6063 were investigated. Contrary to the assumption that electron conditioning, if performed long enough, can reduce and stabilize the SEY to low values (= 1.3, value of many pure elements [1]), the SEY of aluminium did not go lower than 1.8. In fact, it reincreases with continued electron exposure dose.
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.
Directory of Open Access Journals (Sweden)
Yazid Bindar
2009-11-01
Full Text Available The present study is an attempt to introduce the method for optimizing the geometry of the unit process. The comprehensive unit process performances are generated by a CFD engine. The CFD engine can simulate the unit process performances at what ever conditions. Both design geometry and operating variables weree used on the CFD simulation. The burden on a simplified process was taken out from CFD simulation. A complex geometry of a unit process is represented by a secondary reformer. A secondary reformer has a conical volume as a space to undergo the combustion reaction before entering the catalyst bed. This complexity is added by the boundary of the porous solid surface as the top surface of catalyst bed. The spread angle affect the flow pattern in side the conical volume having a porous solid surface as a base. The spread angle above 65o results the disappearing of the recirculation flow. The inlet distance from the porous solid surface also can exhibit different characteristics of recirculation flow. The closer the distance to the porous solid surface, the stronger the recirculation is. The inlet velocity values have no significant effect on the flow pattern. The introduction of a solid volume inside the geometry creates the distortion of the flow pattern. In the application, the inserted solid volume is equivalent to a burner. It means that the use of the burner inherently produces some problems of the flow distribution
Physical Modeling of Shear Behavior of Infilled Rock Joints Under CNL and CNS Boundary Conditions
Shrivastava, Amit Kumar; Rao, K. Seshagiri
2018-01-01
Despite their frequent natural occurrence, filled discontinuities under constant normal stiffness (CNS) boundary conditions have been studied much less systematically, perhaps because of the difficulties arising from the increased number of variable parameters. Because of the lack of reliable and realistic theoretical or empirical relations and the difficulties in obtaining and testing representative samples, engineers rely on judgment and often consider the shear strength of the infilled material itself as shear strength of rock joints. This assumption leads to uneconomical and also sometimes the unsafe design of underground structures, slopes, rock-socketed piles and foundations. To study the effect of infill on the shear behavior of rock joints, tests were performed on the modeled infilled rock joint having different joint roughness under constant normal load (CNL) and CNS boundary conditions at various initial normal stress and varying thickness of the infilled material. The test results indicate that shear strength decreases with an increase in t/ a ratio for both CNL and CNS conditions, but the reduction in shear strength is more for CNL than for CNS condition for a given initial normal stress. The detailed account of the effect of thickness of infilled material on shear and deformation behavior of infilled rock joint is discussed in this paper, and a model is proposed to predict shear strength of infilled rock joint.
Free surface flows under compensated gravity conditions
Dreyer, Miachel E
2007-01-01
This book considers the behavior of fluids in a low-gravity environment with special emphasis on application in PMD (propellant management device) systems . In the compensated gravity environment of a spacecraft, the hydrostatic pressure decreases to very low values depending on the residual acceleration, and surface tension forces become dominant. Consequently, surface tension can be used to transport and position liquids if the residual acceleration and the resulting hydrostatic pressure are small compared to the capillary pressure. One prominent application is the use of PMDs in surface-tension satellite tanks. PMDs must ensure that the tank outlet is covered with liquid whenever outflow is demanded. Furthermore, PMDs are used to ensure expulsion and refilling of tanks for liquids and gases for life support, reactants, and experiment supplies. Since most of the PMD designs are not testable on ground and thus rely on analytical or numerical concepts, this book treats three different flow problems with analy...
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
Belmiloudi , Aziz; Mahé , Fabrice
2014-01-01
International audience; The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical si...
Energy Technology Data Exchange (ETDEWEB)
May, Peter T.; Long, Charles N.; Protat, Alain
2012-08-01
The diurnal variation of convection and associated cloud and radiative properties remains a significant issue in global NWP and climate models. This study analyzes observed diurnal variability of convection in a coastal monsoonal environment examining the interaction of convective rain clouds, their associated cloud properties, and the impact on the surface radiation and corresponding boundary layer structure during periods where convection is suppressed or active on the large scale. The analysis uses data from the Tropical Warm Pool International Cloud Experiment (TWP-ICE) as well as routine measurements from the Australian Bureau of Meteorology and the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) program. Both active monsoonal and large-scale suppressed (buildup and break) conditions are examined and demonstrate that the diurnal variation of rainfall is much larger during the break periods and the spatial distribution of rainfall is very different between the monsoon and break regimes. During the active monsoon the total net radiative input to the surface is decreased by more than 3 times the amount than during the break regime - this total radiative cloud forcing is found to be dominated by the shortwave (SW) cloud effects because of the much larger optical thicknesses and persistence of long-lasting anvils and cirrus cloud decks associated with the monsoon regime. These differences in monsoon versus break surface radiative energy contribute to low-level air temperature differences in the boundary layer over the land surfaces.
International Nuclear Information System (INIS)
Valentín, D; Presas, A; Egusquiza, E; Valero, C
2014-01-01
The dynamic response of submerged and confined disk-like structures is of interest in the flied of hydraulic machinery, especially in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because the fact of the added mass and damping effects. Moreover, the effect of the shaft coupling is also important for certain mode-shapes of the structure. In the present study, the influence of the added mass effect and boundary conditions on the dynamic behavior of a submerged disk attached to a shaft is evaluated through experimental tests and structural- acoustic coupling numerical simulations. For the experimentation, a test rig has been developed. It consists of a confined disk attached to a shaft inside a cylindrical container full of water. The disk can be fixed at different axial positions along the shaft. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. For each configuration tested, the natural frequencies of the disk and the shaft are studied. Numerical results have been compared with experimental results
International Nuclear Information System (INIS)
Nunes, Carlos Eduardo de Araujo
2011-01-01
As neutron fission events do not take place in the non-multiplying regions of nuclear reactors, e.g., moderator, reflector, and structural core, these regions do not generate power and the computational efficiency of nuclear reactor global calculations can hence be improved by eliminating the explicit numerical calculations within the non-multiplying regions around the active domain. Discussed here is the computational efficiency of approximate discrete ordinates (SN) albedo boundary conditions for two-energy group eigenvalue problems in X, Y geometry. Albedo, the Latin word for w hiteness , was originally defined as the fraction of incident light reflected diffusely by a surface. This Latin word has remained the usual scientific term in astronomy and in this dissertation this concept is extended for the reflection of neutrons. The non-standard SN albedo substitutes approximately the reflector region around the active domain, as we neglect the transverse leakage terms within the non-multiplying reflector. Should the problem have no transverse leakage terms, i.e., one dimensional slab geometry, then the offered albedo boundary conditions are exact. By computational efficiency we mean analyzing the accuracy of the numerical results versus the CPU execution time of each run for a given model problem. Numerical results to two 1/4 symmetric test problems are shown to illustrate this efficiency analysis. (author)
Jansen, I G H; Schneiders, J J; Potters, W V; van Ooij, P; van den Berg, R; van Bavel, E; Marquering, H A; Majoie, C B L M
2014-08-01
Attempts have been made to associate intracranial aneurysmal hemodynamics with aneurysm growth and rupture status. Hemodynamics in aneurysms is traditionally determined with computational fluid dynamics by using generalized inflow boundary conditions in a parent artery. Recently, patient-specific inflow boundary conditions are being implemented more frequently. Our purpose was to compare intracranial aneurysm hemodynamics based on generalized versus patient-specific inflow boundary conditions. For 36 patients, geometric models of aneurysms were determined by using 3D rotational angiography. 2D phase-contrast MR imaging velocity measurements of the parent artery were performed. Computational fluid dynamics simulations were performed twice: once by using patient-specific phase-contrast MR imaging velocity profiles and once by using generalized Womersley profiles as inflow boundary conditions. Resulting mean and maximum wall shear stress and oscillatory shear index values were analyzed, and hemodynamic characteristics were qualitatively compared. Quantitative analysis showed statistically significant differences for mean and maximum wall shear stress values between both inflow boundary conditions (P computational fluid dynamics results in different wall shear stress magnitudes and hemodynamic characteristics. Generalized inflow boundary conditions result in more vortices and inflow jet instabilities. This study emphasizes the necessity of patient-specific inflow boundary conditions for calculation of hemodynamics in cerebral aneurysms by using computational fluid dynamics techniques. © 2014 by American Journal of Neuroradiology.
Large Scale Skill in Regional Climate Modeling and the Lateral Boundary Condition Scheme
Veljović, K.; Rajković, B.; Mesinger, F.
2009-04-01
Several points are made concerning the somewhat controversial issue of regional climate modeling: should a regional climate model (RCM) be expected to maintain the large scale skill of the driver global model that is supplying its lateral boundary condition (LBC)? Given that this is normally desired, is it able to do so without help via the fairly popular large scale nudging? Specifically, without such nudging, will the RCM kinetic energy necessarily decrease with time compared to that of the driver model or analysis data as suggested by a study using the Regional Atmospheric Modeling System (RAMS)? Finally, can the lateral boundary condition scheme make a difference: is the almost universally used but somewhat costly relaxation scheme necessary for a desirable RCM performance? Experiments are made to explore these questions running the Eta model in two versions differing in the lateral boundary scheme used. One of these schemes is the traditional relaxation scheme, and the other the Eta model scheme in which information is used at the outermost boundary only, and not all variables are prescribed at the outflow boundary. Forecast lateral boundary conditions are used, and results are verified against the analyses. Thus, skill of the two RCM forecasts can be and is compared not only against each other but also against that of the driver global forecast. A novel verification method is used in the manner of customary precipitation verification in that forecast spatial wind speed distribution is verified against analyses by calculating bias adjusted equitable threat scores and bias scores for wind speeds greater than chosen wind speed thresholds. In this way, focusing on a high wind speed value in the upper troposphere, verification of large scale features we suggest can be done in a manner that may be more physically meaningful than verifications via spectral decomposition that are a standard RCM verification method. The results we have at this point are somewhat
Gunn, A.; Jerolmack, D. J.; Edmonds, D. A.; Ewing, R. C.; Wanker, M.; David, S. R.
2017-12-01
Aolian sand dunes grow to 100s or 1000s of meters in wavelength by sand saltation, which also produces dust plumes that feed cloud formation and may spread around the world. The relations among sediment transport, landscape dynamics and wind are typically observed at the limiting ends of the relevant range: highly resolved and localized ground observations of turbulence and relevant fluxes; or regional and synoptic-scale meteorology and satellite imagery. Between the geostrophic winds aloft and shearing stress on the Earth's surface is the boundary layer, whose stability and structure determines how momentum is transferred and ultimately entrains sediment. Although the literature on atmospheric boundary layer flows is mature, this understanding is rarely applied to aeolian landscape dynamics. Moreover, there are few vertically and time-resolved datasets of atmospheric boundary layer flows in desert sand seas, where buoyancy effects are most pronounced. Here we employ a ground-based upward-looking doppler lidar to examine atmospheric boundary layer flow at the upwind margin of the White Sands (New Mexico) dune field, providing continuous 3D wind velocity data from the surface to 300-m aloft over 70 days of the characteristically windy spring season. Data show highly resolved daily cyles of convective instabilty due to daytime heating and stable stratification due to nightime cooling which act to enhance or depress, respectively, the surface wind stresses for a given free-stream velocity. Our data implicate convective instability in driving strong saltation and dust emission, because enhanced mixing flattens the vertical velocity profile (raising surface wind speed) while upward advection helps to deliver dust to the high atmosphere. We also find evidence for Ekman spiralling, with a magnitude that depends on atmospheric stability. This spiralling gives rise to a deflection in the direction between geostrophic and surface winds, that is significant for the
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.
Eigenvalue problem in two dimensions for an irregular boundary: Neumann condition
Panda, S.; Chakraborty, S.; Khastgir, S. P.
2011-07-01
We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (∇2 + k 2) ψ = 0 in two dimensions when the normal derivative of ψ vanishes on an irregular closed curve. The unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.
Finite-size effects for anisotropic 2D Ising model with various boundary conditions
Izmailian, N. Sh
2012-12-01
We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
International Nuclear Information System (INIS)
Pratt, L.R.; Haan, S.W.
1981-01-01
An exact formal theory for the effects of periodic boundary conditions on the equilibrium properties of computer simulated classical many-body systems is developed. This is done by observing that use of the usual periodic conditions is equivalent to the study of a certain supermolecular liquid, in which a supermolecule is a polyatomic molecule of infinite extent composed of one of the physical particles in the system plus all its periodic images. For this supermolecular system in the grand ensemble, all the cluster expansion techniques used in the study of real molecular liquids are directly applicable. As expected, particle correlations are translationally uniform, but explicitly anisotropic. When the intermolecular potential energy functions are of short enough range, or cut off, so that the minimum image method is used, evaluation of the cluster integrals is dramatically simplified. In this circumstance, a large and important class of cluster expansion contributions can be summed exactly, and expressed in terms of the correlation functions which result when the system size is allowed to increase without bound. This result yields a simple and useful approximation to the corrections to the particle correlations due to the use of periodic boundary conditions with finite systems. Numerical application of these results are reported in the following paper
Finite temperature LGT in a finite box with BPS monopole boundary conditions
International Nuclear Information System (INIS)
Ilgenfritz, E.-M.; Molodtsov, S.V.; Mueller-Preussker, M.; Veselov, A.I.
1999-01-01
Finite temperature SU(2) lattice gauge theory is investigated in a 3D cubic box with fixed boundary conditions (b.c.) provided by a discretized, static BPS monopole solution with varying core scale μ. For discrete μ-values we find stable classical solutions either of electro-magnetic ('dyon') or of purely magnetic type inside the box. Near the deconfinement transition we study the influence of the b.c. on the quantized fields inside the box. In contrast to the purely magnetic background field case, for the dyon case we observe confinement for temperatures above the usual critical one
Sheng, Yin; Zeng, Zhigang
2017-09-01
In this paper, synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and unbounded discrete time-varying delays is investigated. By virtue of theories of partial differential equations, inequality methods, and stochastic analysis techniques, pth moment exponential synchronization and almost sure exponential synchronization of the underlying neural networks are developed. The obtained results in this study enhance and generalize some earlier ones. The effectiveness and merits of the theoretical criteria are substantiated by two numerical simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Chang, Se Myong [Kunsan National Univ., Kunsan (Korea, Republic of); Kim, Hyoung Tae [KAERI, Daejeon (Korea, Republic of)
2012-10-15
Inside the Calandria tubes in the moderator system of a heavy water reactor, there are pressure tubes undergoing high pressure and temperature. If the cooling water dries out due to the local film boiling at the outer tube boundary, the excessive heat flux can deform the pressure tube to even contact with outer Calandria tube. To limit the subcooling for the avoidance of dryout condition in a CANDU reactor, a suitable experiment should be proposed such as Ref.. In this study, we simulated this experiment in 2 D with COMSOL Multi physics.
Effects from magnetic boundary conditions in superconducting-magnetic proximity systems
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
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.
Directory of Open Access Journals (Sweden)
Ishfaq Ahmad Ganaie
2014-01-01
Full Text Available Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.
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....
Energy Technology Data Exchange (ETDEWEB)
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)
Influence of the boundary conditions on heat and mass transfer in spacer-filled channels
Ciofalo, M.; La Cerva, M. F.; Di Liberto, M.; Tamburini, A.
2017-11-01
The purpose of this study is to discuss some problems which arise in heat or mass transfer in complex channels, with special reference to the spacer-filled channels adopted in membrane processes. Among the issues addressed are the consistent definition of local and mean heat or mass transfer coefficients; the influence of the wall boundary conditions; the influence of one-side versus two-side heat/mass transfer. Most of the results discussed were obtained by finite volume CFD simulations concerning heat transfer in Membrane Distillation or mass transfer in Electrodialysis and Reverse Electrodialysis, but many of the conclusions apply also to different processes involving geometrically complex channels
Semiconductor quantum wells with BenDaniel–Duke boundary conditions: approximate analytical results
International Nuclear Information System (INIS)
Barsan, Victor; Ciornei, Mihaela-Cristina
2017-01-01
The Schrödinger equation for a particle moving in a square well potential with BenDaniel–Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states energy are transformed into tractable, algebraic equations. For the ground state and the first excited state, they are cubic equations; we obtain simple formulas for their physically interesting roots. The case of higher excited states is also analysed. Our results have direct applications in the physics of type I and type II semiconductor heterostructures. (paper)
Semiconductor quantum wells with BenDaniel-Duke boundary conditions: approximate analytical results
Barsan, Victor; Ciornei, Mihaela-Cristina
2017-01-01
The Schrödinger equation for a particle moving in a square well potential with BenDaniel-Duke boundary conditions is solved. Using algebraic approximations for trigonometric functions, the transcendental equations of the bound states energy are transformed into tractable, algebraic equations. For the ground state and the first excited state, they are cubic equations; we obtain simple formulas for their physically interesting roots. The case of higher excited states is also analysed. Our results have direct applications in the physics of type I and type II semiconductor heterostructures.
Directory of Open Access Journals (Sweden)
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.
Lam, Yun Fat; Cheung, Hung Ming; Fu, Joshua; Huang, Kan
2015-04-01
Applying Global Chemistry Model (GCM) for regional Boundary Conditions (BC) has become a common practice to account for long-range transport of air pollutants in the regional air quality modeling. The limited domain model such as CMAQ and CAMx requires a global BC to prescribe the real-time chemical flux at the boundary grids, in order to give a realistic estimate of boundary impacts. Several GCMs have become available recently for use in regional air quality studies. In this study, three GCM models (i.e., GEOS-chem, CHASER and IFS-CB05 MACC provided by Seoul National University, Nagoya University and ECWMF, respectively) for the year of 2010 were applied in CMAQ for the East Asia domain under the framework of Model Inter-comparison Study Asia Phase III (MISC-Asia III) and task force on Hemispheric Transport of Air Pollution (HTAP) jointed experiments. Model performance evaluations on vertical profile and spatial distribution of O3 and PM2.5 have been made on those three models to better understand the model uncertainties from the boundary conditions. Individual analyses on various mega-cities (i.e., Hong Kong, Guangzhou, Taipei, Chongqing, Shanghai, Beijing, Tianjin, Seoul and Tokyo) were also performed. Our analysis found that the monthly estimates of O3 for CHASER were a bit higher than GEOS-Chem and IFS-CB05 MACC, particularly in the northern part of China in the winter and spring, while the monthly averages of PM2.5 in GEOS-Chem were the lowest among the three models. The hourly maximum values of PM2.5 from those three models (GEOS-Chem, CHASER and IFS-CB05 MACC are 450, 321, 331 μg/m3, while the maximum O3 are 158, 212, 380 ppbv, respectively. Cross-comparison of CMAQ results from the 45 km resolution were also made to investigate the boundary impacts from the global GCMs. The results presented here provide insight on how global GCM selection influences the regional air quality simulation in East Asia.
Czech Academy of Sciences Publication Activity Database
Lanzendörfer, Martin; Stebel, Jan
2011-01-01
Roč. 56, č. 3 (2011), s. 265-285 ISSN 0862-7940 R&D Projects: GA MŠk LC06052 Grant - others:GA ČR(CZ) GA201/06/0352 Institutional research plan: CEZ:AV0Z10300504; CEZ:AV0Z10190503 Keywords : existence * weak solutions * incompressible fluids * non-Newtonian fluids * pressure dependent viscosity * shear dependent viscosity * inflow/outflow boundary conditions * pressure boundary conditions * filtration boundary conditions Subject RIV: BK - Fluid Dynamics Impact factor: 0.480, year: 2011 http://dml.cz/handle/10338.dmlcz/141486
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.
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Natural convection - radiation interaction in boundary layer flow over horizontal surfaces
International Nuclear Information System (INIS)
Ali, M.M.; Chen, T.S.; Armaly, B.F.
1982-01-01
A numerical model is developed for natural convection-radiation interaction in the boundary layer over a semi-infinite horizontal flat plate with one hot and one cold surface. The fluid is assumed to be gray, to emit, absorb, be nonscattering, and constant with a density variation in the vertical direction, which induces a buoyancy force. Two-dimensional, boundary-layer equations are defined, and the radiative heat flux is simplified using a Rosseland approximation. Conservation equations are transformed into a system of nonlinear ordinary differential equations which can be solved simultaneously with a Runge-Kutta integration scheme, along with the Newton-Raphson shooting technique. The thermal radiation is found to enhance the wall shear stress and the surface heat transfer rate on both the hot and cold sides
Impact of land surface conditions on 2004 North American monsoon in GCM experiments
Feng, X.; Bosilovich, M.; Houser, P.; Chern, J.-D.
2013-01-01
In this study, two sets of six-member ensemble simulations were performed for the boreal summer of 2004 using the Finite Volume General Circulation model to investigate the sensitivity of the North American monsoon (NAM) system to land surface conditions and further to identify the mechanisms by which land surface processes control the NAM precipitation. The control simulation uses a fully interactive land surface model, whereas the sensitivity experiment uses prescribed land surface fields from the Global Land Data Assimilation System.The response of the monsoon precipitation to land surface changes varies over different regions modulated by two different soil moisture-precipitation feedbacks. The vast northern NAM region, including most of Arizona and New Mexico, as well as the northwestern Mexico shows that soil moisture has a positive feedback with precipitation primarily due to local recycling mechanisms. The reduction of soil moisture decreases latent heat flux and increases sensible heat flux and consequently increases the Bowen ratio and surface temperature, leading to a deep (warm and dry) boundary layer, which suppresses convection and hence reduces precipitation. Over the west coast of Mexico near Sinaloa, a negative soil moisture-precipitation relationship is noted to be associated with a large-scale mechanism. The reduced soil moisture changes surface fluxes and hence boundary layer instability and ultimately low-level circulation. As a result, the changes in surface pressure and large scale wind field increase moisture flux convergence and consequently moisture content, leading to increased atmospheric instability and in turn enhancing convection and accordingly precipitation. These results further reinforce the important role of land surface conditions on surface process, boundary structure, atmospheric circulation, and rainfall during the NAM development.
The Interaction of a Turbulent Ship-Hull Boundary Layer and a Free Surface
Masnadi, N.; Washuta, N.; Wang, A.; Duncan, J. H.
2013-11-01
The free-surface deformation pattern caused by subsurface turbulent velocity fluctuations in the boundary layer at the mid-length of a naval ship is studied with a novel laboratory scale experimental technique. In this technique, the boundary layer is created in a large tank (13.4 m long, 1.3 m tall, and 2.4 m wide) with a surface-piercing meter-wide stainless steel belt that travels in a horizontal loop around two vertically oriented rollers whose axes are separated by 7.5 m. The device is enclosed in a dry box except for one of the two lengths between the rollers where a straight 6-meter-long section is exposed to the water and represents one side of the ship hull. The belt operates at full-scale ship speeds (up to 15 m/s) in order to match the Reynolds, Froude, and Weber numbers to those of naval ships, thus faithfully modeling the interaction of the turbulence with the free surface at laboratory scale. The water surface profile history midway between the rollers is recorded cinematically in a vertical plane normal to the belt using a Laser Induced Fluorescence (LIF) technique. This surface profile data is used to study the near-wall and far-field frequency content and propagation behavior of the surface ripples. The support of the Office of Naval Research is gratefully acknowledged.
Li, Longfei; Braun, R. J.; Maki, K. L.; Henshaw, W. D.; King-Smith, P. E.
2014-01-01
We study tear film dynamics with evaporation on a wettable eye-shaped ocular surface using a lubrication model. The mathematical model has a time-dependent flux boundary condition that models the cycles of tear fluid supply and drainage; it mimics blinks on a stationary eye-shaped domain. We generate computational grids and solve the nonlinear governing equations using the OVERTURE computational framework. In vivo experimental results using fluorescent imaging are used to visualize the influx and redistribution of tears for an open eye. Results from the numerical simulations are compared with the experiment. The model captures the flow around the meniscus and other dynamic features of human tear film observed in vivo. PMID:24926191
Directory of Open Access Journals (Sweden)
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
International Nuclear Information System (INIS)
Kupka, F.
1997-11-01
This thesis deals with the extension of sparse grid techniques to spectral methods for the solution of partial differential equations with periodic boundary conditions. A review on boundary and initial-boundary value problems and a discussion on numerical resolution is used to motivate this research. Spectral methods are introduced by projection techniques, and by three model problems: the stationary and the transient Helmholtz equations, and the linear advection equation. The approximation theory on the hyperbolic cross is reviewed and its close relation to sparse grids is demonstrated. This approach extends to non-periodic problems. Various Sobolev spaces with dominant mixed derivative are introduced to provide error estimates for Fourier approximation and interpolation on the hyperbolic cross and on sparse grids by means of Sobolev norms. The theorems are immediately applicable to the stability and convergence analysis of sparse grid spectral methods. This is explicitly demonstrated for the three model problems. A variant of the von Neumann condition is introduced to simplify the stability analysis of the time-dependent model problems. The discrete Fourier transformation on sparse grids is discussed together with its software implementation. Results on numerical experiments are used to illustrate the performance of the new method with respect to the smoothness properties of each example. The potential of the method in mathematical modelling is estimated and generalizations to other sparse grid methods are suggested. The appendix includes a complete Fortran90 program to solve the linear advection equation by the sparse grid Fourier collocation method and a third-order Runge-Kutta routine for integration in time. (author)
Spectroscopy of {sup 12}C within the boundary condition for three-body resonant states
Energy Technology Data Exchange (ETDEWEB)
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.
Sircar, A.; Paul, C.; Ferreyro, S.; Imren, A.; Haworth, D. C.; Roy, S.; Ge, W.; Modest, M. F.
2016-11-01
The lack of accurate submodels for in-cylinder radiation and heat transfer has been identified as a key shortcoming in developing truly predictive CFD models that can be used to develop combustion systems for advanced high-efficiency, low-emissions engines. Recent measurements of wall layers in engines show discrepancies of up to 100% with respect to standard CFD boundary-layer models. And recent analysis of in-cylinder radiation based on recent spectral property databases and high-fidelity radiative transfer equation (RTE) solvers has shown that at operating conditions typical of heavy-duty CI engines, radiative emission can be as high as 40% of the wall heat losses, that molecular gas radiation can be more important than soot radiation, and that a significant fraction of the emitted radiation can be reabsorbed before reaching the walls. That is, radiation changes the in-cylinder temperature distribution, which in turn affects combustion and emissions. The goal of this research is to develop models that explicitly account for the potentially strong coupling between radiative and turbulent boundary layer heat transfer. For example, for optically thick conditions, a simple diffusion model might be formulated in terms of an absorption-coefficient-dependent turbulent Prandtl number. NSF, DOE.