Spatial Boundary Conditions Research Articles

Climate-responsive design: A framework for an energy concept design-decision support tool for architects using principles of climate-responsive design

Climate-responsive design: A framework for an energy concept design-decision support tool for architects using principles of climate-responsive design

Nonlinear Rupture of Thin Micropolar Liquid Film Under a Magnetic Field

AbstractThis paper investigates the rupture problem of a thin micropolar liquid film under a magnetic field on a horizontal plate, using long-wave perturbation to resolve nonlinear evolution equations with a free film interface. The governing equation is resolved using a finite difference method as part of an initial value problem for spatial periodic boundary conditions. The effect of a micropolar liquid under a magnetic field on the nonlinear rupture mechanism is studied in terms of the micropolar parameter, R, the Hartmann constant, m and the initial disturbance amplitude, H0. Modeling results indicate that the R, m and H0 parameters strongly affect the film flow. Enhancing the micropolar and magnetic effects is found to delay the rupture time. In addition, the results show that the film rupture time increases as the values of initial disturbance magnitude decrease. The micropolar and magnetic parameters indeed play a significant role in the film flow on a horizontal plate. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Architectural Spatial Design Strategies for Summer Microclimate Control in Buildings: A Comparative Case Study of Chinese Vernacular and Modern Houses

The objective of this paper is to clarify the spatial design strategies used to control the microclimate of a Chinese vernacular house in summer by comparing the building with modern Chinese rural houses and presenting ideas for contemporary architectural design practice. For this goal the spatial configuration, the spatial boundary conditions, the vegetation in the space and the human activity in the space were analyzed for the vernacular house and for modern rural houses. Also, field measurements were conducted to evaluate the summer thermal environment in the vernacular and a modern house. The results show that the vernacular house has a diverse spatial design and a better building microclimate, making it easier to obtain thermal comfort than the modern houses. Therefore, spatial design strategies of Chinese vernacular houses are still of great value to modern house design, especially when the free-running thermal comfort theory is applied.

Large volumes and spectroscopy of walking theories

A detailed investigation of finite size effects is performed for SU(2) gauge theory with two fermions in the adjoint representation, which previous lattice studies have shown to be inside the conformal window. The system is investigated with different spatial and temporal boundary conditions on lattices of various spatial and temporal extensions, for two values of the bare fermion mass representing a {\em heavy} and {\em light} fermion regime. Our study shows that the infinite volume limit of masses and decay constants in the mesonic sector is reached only when the mass of the pseudoscalar particle $M_\mathrm{PS}$ and the spatial lattice size $L$ satisfy the relation $L M_\mathrm{PS} \ge 15$. This bound, which is at least a factor of three higher than what observed in QCD, is a likely consequence of the different spectral signatures of the two theories, with the scalar isosinglet ($0^{++}$ glueball) being the lightest particle in our model. In addition to stressing the importance of simulating large lattice sizes, our analysis emphasises the need to understand quantitatively the {\em full} spectrum of the theory rather than just the spectrum in the mesonic isotriplet sector. While for the lightest fermion measuring masses from gluonic operators proves to be still challenging, reliable results for glueball states are obtained at the largest fermion mass and, in the mesonic sector, for both fermion masses. As a byproduct of our investigation, we perform a finite size scaling of the pseudoscalar mass and decay constant. The data presented in this work support the conformal behaviour of this theory with an anomalous dimension $\gamma_* \simeq 0.37$.

Existence and Uniqueness Theorems for the Two-Dimensional Ericksen–Leslie System

In this paper we study the two dimensional Ericksen–Leslie equations for the nematodynamics of liquid crystals if the moment of inertia of the molecules does not vanish. We prove short time existence and uniqueness of strong solutions for the initial value problem in two situations: the space-periodic problem and the case of a bounded domain with spatial Dirichlet boundary conditions on the Eulerian velocity and the cross product of the director field with its time derivative. We also show that the speed of propagation of the director field is finite and give an upper bound for it.

Three-dimensional spherical spatial boundary conditions differentially regulate osteogenic differentiation of mesenchymal stromal cells.

The spatial boundary condition (SBC) arising from the surrounding microenvironment imposes specific geometry and spatial constraints that affect organogenesis and tissue homeostasis. Mesenchymal stromal cells (MSCs) sensitively respond to alterations of mechanical cues generated from the SBC. However, mechanical cues provided by a three-dimensional (3D) environment are deprived in a reductionist 2D culture system. This study investigates how SBC affects osteogenic differentiation of MSCs using 3D scaffolds with monodispersed pores and homogenous spherical geometries. MSCs cultured under SBCs with diameters of 100 and 150 μm possessed the greatest capability of osteogenic differentiation. This phenomenon was strongly correlated with MSC morphology, organization of actin cytoskeleton, and distribution of focal adhesion involving α2 and α5 integrins. Further silencing either α2 or α5 integrin significantly reduced the above mentioned mechanosensitivity, indicating that the α2 and α5 integrins as mechano-sensitive molecules mediate MSCs’ ability to provide enhanced osteogenic differentiation in response to different spherical SBCs. Taken together, the findings provide new insights regarding how MSCs respond to mechanical cues from the surrounding microenvironment in a spherical SBC, and such biophysical stimuli should be taken into consideration in tissue engineering and regenerative medicine in conjunction with biochemical cues.

Layer methods for stochastic Navier–Stokes equations using simplest characteristics

We propose and study a layer method for stochastic Navier–Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploiting ideas of the weak sense numerical integration of stochastic differential equations. We prove some convergence results for the proposed method including its first mean-square order. Results of numerical experiments on two model problems are presented.

Group-specific analysis of commuting in the most disadvantaged areas of Hungary

The study aims to examine the commuting opportunities of the most disadvantaged job seeker groups living in Hungary's most disadvantaged regions, as well as Hungary’s spatial and group-specific boundary conditions. The study also aims to develop and present an indexation process (fMFA model), allowing the measurement of the mobility degree of different territorial units (in this case, the municipalities) and effects of certain factors determining commuting (transport subsidies, individual choices and options). The index measures the degree of mobility by considering individual and several types of public transport, expenses and expected time of commuting. The present document defines mobility for territorial units, separating its objective and subjective types. The group-specific analysis of boundary conditions is implemented through a questionnaire survey and logical models, the aim of which is twofold. On one hand, the model specifies the maximum commuting distance, which would be accepted rationally for the most disadvantaged job seekers. On the other hand, it presents a decision-making dilemma, namely the choice between commuting to work and local employment. Thus, the study provides insights into the specific features of labour market mobility of the target group. The Average Mobility Level Model and the Adjusted Mobility Index also evaluate the regional structure of the group-specific features of commuting. Through all these, the present study may promote a more efficient spatial allocation of employment policy measures. Strengthening of local employment in areas where group-specific mobility degrees are lower and support to improve commuting opportunities and employment centres where the mobility degrees are appropriate can contribute to the decrease of unemployment.

Decentralized string-stability analysis for heterogeneous cascades subject to load-matching requirements

A heterogeneous cascade of stable linear time-invariant subsystems is studied in terms of the spatial and temporal propagation of boundary conditions. The particular context requires constant spatial boundary conditions to be asymptotically matched by the interconnection signals along the string (e.g., to match supply to demand in steady state). Furthermore, the transient response associated with a step change in the spatial boundary condition must remain bounded across space in a string-length independent fashion. With this in mind, an infinite cascade abstraction is considered. A corresponding decentralized string-stability certificate for the desired behaviour is established in terms of the subsystem $$H_\infty $$H? norms, via Lyapunov-type analysis of a two-dimensional model in Roesser form. Verification of the certificate implies uniformly bounded interconnection signals in response to the following system inputs: (i) a square-summable (across space) sequence of initial conditions; and (ii) a uniformly-bounded (across time) finite-energy input applied as the spatial boundary condition (e.g., finite duration on-off pulse). The decentralized nature of the certificate facilitates subsystem-by-subsystem design of local controllers that achieve string-stable behaviour overall. This application of the analysis is explored within the context of a scalable approach to the design of distributed distant-downstream controllers for the sections of an automated irrigation channel.

WE-AB-BRA-02: Development of Biomechanical Models to Describe Dose-Volume Response to Liver Stereotactic Body Radiation Therapy (SBRT) Patients

Purpose: Previous studies have shown that radiotherapy treatment for liver metastases causes marked liver hypertrophy in areas receiving low dose and atrophy/fibrosis in areas receiving high dose. The purpose of this work is to develop and evaluate a biomechanical model-based dose-response model to describe these liver responses to SBRT. Methods: In this retrospective study, a biomechanical model-based deformable registration algorithm, Morfeus, was expanded to include dose-based boundary conditions. Liver and tumor volumes were contoured on the planning images and CT/MR images three months post-RT and converted to finite element models. A thermal expansion-based relationship correlating the delivered dose and volume response was generated from 22 patients previously treated. This coefficient, combined with the planned dose, was applied as an additional boundary condition to describe the volumetric response of the liver of an additional cohort of metastatic liver patients treated with SBRT. The accuracy of the model was evaluated based on overall volumetric liver comparisons and the target registration error (TRE) using the average deviations in positions of identified vascular bifurcations on each set of registered images, with a target accuracy of the 2.5mm isotropic dose grid (vector dimension 4.3mm). Results: The thermal expansion coefficient models the volumetric change of the liver to within 3%. The accuracy of Morfeus with dose-expansion boundary conditions a TRE of 5.7±2.8mm compared to 11.2±3.7mm using rigid registration and 8.9±0.28mm using Morfeus with only spatial boundary conditions. Conclusion: A biomechanical model has been developed to describe the volumetric and spatial response of the liver to SBRT. This work will enable the improvement of correlating functional imaging with delivered dose, the mapping of the delivered dose from one treatment onto the planning images for a subsequent treatment, and will further provide information to assist with the biological characterization of patients’ response to radiation.

Global-in-time existence of weak solutions to Kolmogorov's two-equation model of turbulence

We consider Kolmogorov's model for the turbulent motion of an incompressible fluid in R3. This model consists in a Navier–Stokes-type system for the mean flow u and two further partial differential equations: an equation for the frequency ω and for the kinetic energy k each. We investigate this system of partial differential equations in a cylinder Ω×]0,T[ (Ω⊂R3 cube, 0<T<+∞) under spatial periodic boundary conditions on ∂Ω×]0,T[ and initial conditions in Ω×{0}. We present an existence result for a weak solution {u,ω,k} to the problem under consideration, with ω, k obeying the inequalities c1+t≤1ω≤t+c2 and k1/2ω≥c3t1/2 (c1,c2,c3=const>0).

Estimating Permeability Using the Parameter Estimation Method in a High-permeability Area of the Kurobe River Alluvial Fan, Japan

The parameter estimation (PEST) method was used to estimate the spatial distribution of permeability coefficients in a high-permeability area of the Kurobe River alluvial fan in Toyama Prefecture, Japan. We considered spatial resolution, estimated period, soil structure, recharge source, and boundary conditions in the model. Numerical experiments produced estimated permeability coefficients that were consistent with the observed data and those of previous studies under all conditions. However, the estimated groundwater levels were lower than those of previous studies. Spatial resolution and the number of foundation layers did not have a large effect on estimates of the vertical permeability coefficient (kz). However, recharge source and boundary conditions were important for estimating permeability coefficients. Finally, the estimates of specific storage (Ss) and specific yield (Sy) were similar to the observed data under all conditions.

Forced vibrations of orthotropic shells when there is viscous resistance

Forced vibrations of orthotropic shells when there is viscous resistance are considered, when two versions of the spatial boundary conditions are given on the upper face of the shell, and the displacement vector is given on the lower face. The solution of the corresponding dynamic equations of the three-dimensional problem of elasticity theory is obtained by an asymptotic method. The amplitudes of the forced vibrations are determined and it is established that the viscous resistance causes the amplitudes of the forced vibrations to increase in the range of values of natural vibrations, but they remain finite. Boundary-layer type functions are obtained, and characteristic equations for determining the rate of decay of boundary vibrations in the direction from the side surface into the shell are established.

Schrödinger functional boundary conditions and improvement for N &gt;3

The standard method to calculate non-perturbatively the evolution of the running coupling of a SU(N) gauge theory is based on the Schr\"odinger 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 O(a) improvement coefficients for N>3 needed to remove boundary cutoff effects from the gauge action. After this, residual cutoff effects on the step scaling function are shown to be very small even when considering non-fundamental representations. We also calculate the ratio of Lambda parameters between the MS-bar and SF schemes.

Methodology for implementing patient-specific spatial boundary condition during a cardiac cycle from phase-contrast MRI for hemodynamic assessment.

Pulmonary insufficiency (PI) can render the right ventricle dysfunctional due to volume overloading and hypertrophy. The treatment requires a pulmonary valve replacement surgery. However, determining the right time for the valve replacement surgery has been difficult with currently employed clinical techniques such as, echocardiography and cardiac MRI. Therefore, there is a clinical need to improve the diagnosis of PI by using patient-specific (PS) hemodynamic endpoints. While there are many reported studies on the use of PS geometry with time varying boundary conditions (BC) for hemodynamic computation, few use spatially varying PS velocity measurement at each time point of the cardiac cycle. In other words, the gap is that, there are limited number of studies which implement both spatially- and time-varying physiologic BC directly with patient specific geometry. The uniqueness of this research is in the incorporation of spatially varying PS velocity data obtained from phase-contrast MRI (PC-MRI) at each time point of the cardiac cycle with PS geometry obtained from angiographic MRI. This methodology was applied to model the complex developing flow in human pulmonary artery (PA) distal to pulmonary valve, in a normal and a subject with PI. To validate the methodology, the flow rates from the proposed method were compared with those obtained using QFlow software, which is a standard of care clinical technique. For the normal subject, the computed time average flow rates from this study differed from those obtained using the standard of care technique (QFlow) by 0.8 ml/s (0.9%) at the main PA, by 2 ml/s (3.4%) at the left PA and by 1.4 ml/s (3.8%) at the right PA. For the subject with PI, the difference was 7 ml/s (12.4%) at the main PA, 5.5 ml/s (22.6%) at the left PA and 4.9 ml/s (18.0%) at the right PA. The higher percentage differences for the subject with PI, was the result of overall lower values of the forward mean flow rate caused by excessive flow regurgitation. This methodology is expected to provide improved computational results when PS geometry from angiographic MRI is used in conjunction with PS PC-MRI data for solving the flow field.

A Discontinuous Galerkin Time Domain Framework for Periodic Structures Subject to Oblique Excitation

A nodal Discontinuous Galerkin (DG) method is derived for the analysis of time-domain (TD) scattering from doubly periodic PEC/dielectric structures under oblique interrogation. Field transformations are employed to elaborate a formalism that is free from any issues with causality that are common when applying spatial periodic boundary conditions simultaneously with incident fields at arbitrary angles of incidence. An upwind numerical flux is derived for the transformed variables, which retains the same form as it does in the original Maxwell problem for domains without explicitly imposed periodicity. This, in conjunction with the amenability of the DG framework to non-conformal meshes, provides a natural means of accurately solving the first order TD Maxwell equations for a number of periodic systems of engineering interest. Results are presented that substantiate the accuracy and utility of our method.

Direction change of plant root growth by the impenetrable boundary

Spatial boundary conditions must be considered when utilizing mathematical modeling of plant root growth in the container or along with the imbedding solid obstacle. Using basic root growth principles and the geometry of the boundary surface, a mathematical model can be designed to keep all root elements inside the container or outside the obstacle without passing through the boundary after the minimum deflection of growth direction, and it is based on the minimum friction between root tips and soil and energy saving principles. Such a mathematical method is used to simulate the spatial distribution of root growth and the morphological architecture of the root system near the boundary. The validity of this model is supported by experimental observations that confirm some typical characteristics predicted by the simulations. This model can be widely used in resolving boundary condition complications where water and nutrients are consumed by plants in a spatially limited or heterogeneous resource field.

A fast non-Fourier method for Landau-fluid operators

An efficient and versatile non-Fourier method for the computation of Landau-fluid (LF) closure operators [Hammett and Perkins, Phys. Rev. Lett. 64, 3019 (1990)] is presented, based on an approximation by a sum of modified-Helmholtz-equation solves (SMHS) in configuration space. This method can yield fast-Fourier-like scaling of the computational time requirements and also provides a very compact data representation of these operators, even for plasmas with large spatial nonuniformity. As a result, the method can give significant savings compared with direct application of “delocalization kernels” [e.g., Schurtz et al., Phys. Plasmas 7, 4238 (2000)], both in terms of computational cost and memory requirements. The method is of interest for the implementation of Landau-fluid models in situations where the spatial nonuniformity, particular geometry, or boundary conditions render a Fourier implementation difficult or impossible. Systematic procedures have been developed to optimize the resulting operators for accuracy and computational cost. The four-moment Landau-fluid model of Hammett and Perkins has been implemented in the BOUT++ code using the SMHS method for LF closure. Excellent agreement has been obtained for the one-dimensional plasma density response function between driven initial-value calculations using this BOUT++ implementation and matrix eigenvalue calculations using both Fourier and SMHS non-Fourier implementations of the LF closures. The SMHS method also forms the basis for the implementation, which has been carried out in the BOUT++ code, of the parallel and toroidal drift-resonance LF closures. The method is a key enabling tool for the extension of gyro-Landau-fluid models [e.g., Beer and Hammett, Phys. Plasmas 3, 4046 (1996)] to codes that treat regions with strong profile variation, such as the tokamak edge and scrapeoff-layer.

Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms

This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. The solutions turn out to be, at the first order, the superposition of traveling waves, traveling in the opposite or the same directions. The proofs are based on the variational Lyapunov-Schmidt reduction and the linking theorem, while the bifurcation equations are solved by variational methods.

POMI: a model inter-comparison exercise over the Po Valley

The Po Valley (Italy) model inter-comparison exercise (POMI) has been carried out in order to explore the changes in air quality in response to changes in emissions. The starting point was the evaluation of the simulated particulate matter and ozone (O3) modelled concentrations against observations for the year 2005 of the six participating chemical transport models. As models were run with the same configuration in terms of spatial resolution, boundary condition, emissions and meteorology, the differences presented in the models’ results are only related to their formulation. As described in the paper, significant efforts have been made to improve the accuracy of the anthropogenic emissions and meteorological input data. Nevertheless, none of the models using the proposed meteorology succeeded to fulfil the quality performance criteria set in the 2008 Air Quality Directive and in the literature for particulate matter, while also for ozone the results are not very satisfying. Although the overall performances look better for O3 than for particulate matter with an aerodynamic diameter smaller than 10 μm (PM10), the models tend to exhibit a similar behaviour and show the largest model variability in locations where concentrations are the highest (urban areas for PM10 and suburbs and hilly areas for O3). While differences are significant in terms of standard deviation and bias, the correlation remains quite similar among models indicating that models generally capture well the main temporal variations, especially the seasonal ones. Possible explanations for this common behaviour and a discussion of the differences among models’ results are presented in this paper.