Exterior Boundary Research Articles

Hand segmentation pipeline from depth map: an integrated approach of histogram threshold selection and shallow CNN classification

ABSTRACTWe propose a new approach which is a three-stage pipeline to fast and accurate segment hand from a single depth image. Firstly, a depth frame is segmented into several regions by histogram-based thresholds selection algorithm and tracing the exterior boundaries of objects. We found that MINIMUM, MEAN and MEDIAN are effective ways to separate objects and the threshold in the valley between two maxima similar to MINIMUM algorithm with a minimum error. Then, each segmentation proposal is evaluated by a 3-layers shallow convolutional neural network (CNN) which is trained as a binary classification function to predict whether it is a partition of hand. Finally, all hand components are merged as our hand segmentation result. In our experiment, we use a set of real data containing more than 200,000 frames of depth images. Compared with the results achieved by approaches based on RDF and SegNet, results demonstrate that our approach achieves better performance in high-accuracy (88.34% mean IoU) within shorter processing time (8 ms).

Geometric coupling of helicoidal ramps and curvature-inducing proteins in organelle membranes.

Cellular membranes display an incredibly diverse range of shapes, both in the plasma membrane and at membrane bound organelles. These morphologies are intricately related to cellular functions, enabling and regulating fundamental membrane processes. However, the biophysical mechanisms at the origin of these complex geometries are not fully understood from the standpoint of membrane-protein coupling. In this study, we focused on a minimal model of helicoidal ramps representative of specialized endoplasmic reticulum compartments. Given a helicoidal membrane geometry, we asked what is the distribution of spontaneous curvature required to maintain this shape at mechanical equilibrium? Based on the Helfrich energy of elastic membranes with spontaneous curvature, we derived the shape equation for minimal surfaces, and applied it to helicoids. We showed the existence of switches in the sign of the spontaneous curvature associated with geometric variations of the membrane structures. Furthermore, for a prescribed gradient of spontaneous curvature along the exterior boundaries, we identified configurations of the helicoidal ramps that are confined between two infinitely large energy barriers. Overall our results suggest possible mechanisms for geometric control of helicoidal ramps in membrane organelles based on curvature-inducing proteins.

Twofold Domain Decomposition Method for the Analysis of Multiscale Composite Structures

A nonconformal twofold domain decomposition method (TDDM) based on the hybrid finite element method-boundary element method (FEM-BEM) is proposed for analyzing 3-D multiscale composite structures. The proposed TDDM starts by partitioning the composite object into a closed exterior boundary domain and an interior volume domain. The interior and exterior boundary value problems are coupled to each other through the Robin transmission conditions (RTCs). Both domains are then independently decomposed into subregions to facilitate computation. Specifically, FEM-DDM with the second order transmission conditions (SOTCs) is employed for the interior domain, and BEM-discontinuous Galerkin (BEM-DG) based on the combined field integral equation (CFIE) is applied for the exterior boundary domain. The proposed TDDM allows for nonconformal discretization between any touching subdomains. Without the introduction of a stabilization term that relies on a line integral over intersection of nonmatching meshes and relevant terms involving surface-line integrals, the proposed TDDM provides an effective domain decomposition (DD) preconditioner for the global system. Numerical examples are presented, and the comparisons of the simulation results with FEM-BEM confirm the validity and accuracy of TDDM. Moreover, its ability to model practical large-scale and multiscale targets is also demonstrated.

Contactless electrical impedance and ultrasonic tomography: correlation, comparison and complementarity study

Electrical tomography (ET) and ultrasonic tomography (UT) techniques are effective and promising super-sensing tools with uses in many industrial process applications. They can create internal mapping images of both electrical and mechanical properties from measurements at the exterior boundaries of domains of interests. There are several different types of ET methods and different modes of UT imaging. Here we focus on contactless ET and contactless UT imaging for liquid masses, enabling fully non-intrusive, integrated mechanical and electrical imaging because direct contact to the process material is often a major limiting factor. ET is sensitive to the distribution of dielectric parameters inside the region of interest, and the highest sensitivity often lies near the outer surface of the boundary. UT has very good responses to the intersections of different phases of materials and has the highest resolution in the central area. Capacitively coupled electrical impedance tomography (CCEIT) is proposed as a contactless ET technique. This work investigates CCEIT based on phase measurements of the electrical impedance between transmitting and receiving electrodes, and UT based on the transmission mode, measuring the time-of-flight between the transmitted signal and the first received signals. A combined sensor which comprises a 16-electrode CCEIT array and a 16-transducer UT array is developed. Experimental results show the performances of the two tomography systems and their dual modality combination. This work highlights various aspects of the correlation, comparison and complementarity between these two contactless imaging techniques. Inclusion material characterization and identification is demonstrated using this novel dual modality.

A Method for Solving an Exterior Boundary Value Problem for the Laplace Equation by Overlapping Domain Decomposition

We propose a numerical method for solving an exterior three-dimensional boundary value problem for the Laplace equation based on the overlapping decomposition of the computational domain. The initial boundary value problem is reduced to solving an operator equation for the sought values of the function on an auxiliary sphere enclosing the interior boundary. This equation is approximated by a system of linear algebraic equations which is solved by iterative methods in the Krylov subspaces. A series of numerical experiments for model problems with known solutions demonstrates not only the convergence of the method and the attained accuracy of the calculations but also a sufficiently short runtime.

Fast and accurate algorithm for cavities reconstruction in an elasticity problem

The aim of this work is to reconstruct the location and geometry of a cavity embedded in a linear isotropic material Ω via an exterior boundary measurement of the displacement field. The considered problem is governed by the linear elasticity system. This inverse problem of geometry reconstruction (ie, location and shape) is formulated as a topology optimization one and solved by minimizing a Kohn‐Vogelius type functional with the help of the topological sensitivity method. Some numerical results are presented using a noniterative geometric algorithm.

Rational Solutions of the Painlev\xe9-III Equation: Large Parameter Asymptotics

The Painlevé-III equation with parameters Theta _0=n+m and Theta _infty =m-n+1 has a unique rational solution u(x)=u_n(x;m) with u_n(infty ;m)=1 whenever nin mathbb {Z}. Using a Riemann–Hilbert representation proposed in Bothner et al. (Stud Appl Math 141:626–679, 2018), we study the asymptotic behavior of u_n(x;m) in the limit nrightarrow +infty with min mathbb {C} held fixed. We isolate an eye-shaped domain E in the y=n^{-1}x plane that asymptotically confines the poles and zeros of u_n(x;m) for all values of the second parameter m. We then show that unless m is a half-integer, the interior of E is filled with a locally uniform lattice of poles and zeros, and the density of the poles and zeros is small near the boundary of E but blows up near the origin, which is the only fixed singularity of the Painlevé-III equation. In both the interior and exterior domains we provide accurate asymptotic formulæ for u_n(x;m) that we compare with u_n(x;m) itself for finite values of n to illustrate their accuracy. We also consider the exceptional cases where m is a half-integer, showing that the poles and zeros of u_n(x;m) now accumulate along only one or the other of two “eyebrows,” i.e., exterior boundary arcs of E.

Existence of surface acoustic waves in one-dimensional piezoelectric phononic crystals of general anisotropy

The paper is concerned with the surface acoustic waves propagating in half-infinite one-dimensional piezoelectric phononic crystals of general anisotropy. The phononic crystal is formed of periodically repeated perfectly bonded layers, and its exterior boundary is one of the layer boundaries. The surface waves occurring in the so-called full stop bands are considered. It appears that the number of surface waves existing within a full stop band for a given layered structure is interrelated with their number in the same stop band for the phononic crystal different from the given one only due to the reversed ordering of layers within a period. A series of statements is proved on the maximum possible number of surface waves per full stop band for both these structures in total, i.e., embracing surface-wave occurrences in either one or the other structure. The analysis is performed for the electrically closed, electrically open, and electrically free types of boundary conditions on the mechanically free crystal surface, in which cases it admits a correspondingly different number of surface waves. A subsidiary instance of mechanically clamped surface is addressed as well. It is observed that the piezoelectric coupling can create new surface waves which disappear when piezoelectric coefficients turn to zero. Besides the general case of arbitrary anisotropy, we also consider two specific situations where the crystallographic symmetry allows the existence of sagittally polarized piezoactive surface waves and of shear horizontally polarized piezoactive surface waves. Numerical examples of surface-wave branches under various boundary conditions are provided.

Early warning and basin stability in a stochastic vegetation-water dynamical system

The dynamical evolution of a vegetation-water system subjected to Gaussian noise disturbance is explored. With regard to the regime shift of the stationary response of the system, the early warning signal can be detected by the maximum of the stationary probability density function. And for the transient response of the bistable system, the basin stability is investigated by two different deterministic quantities, the first escape probability and the mean first exit time. Firstly, the stochastic system with two variable is translated into the Itô stochastic differential equation to derive the analytical expression of the first escape probability and the mean first exit time with different Balayage-Dirichlet exterior boundary condition. Then, the two indexes are calculated by the finite difference method, respectively. The results, compared with the ones through Monte Carlo simulations, shows that the proposed method works very well. It turns out that the increase of noise intensity induces advance of the early warning and decreases basin stability of the vegetation-water system.

Reconstruction of a volumetric source domain

Inverse and ill-posed problems which consist of reconstructing the unknown support of a three-dimensional volumetric source from a single pair of exterior boundary Cauchy data are investigated. The underlying dependent variable may satisfy the Laplace, Poisson, Helmholtz or modified Helmholtz equations. In the case of constant physical properties, the solutions of these elliptic PDEs are sought as linear combinations of fundamental solutions, as in the method of fundamental solutions (MFS). The unknown source domain is parametrized by the radial coordinate, as a function of the spherical angles. The resulting least-squares functional estimating the gap between the measured and the computed data is regularized and minimized using the lsqnonlin toolbox routine in Matlab. Numerical results are presented and discussed for both exact and noisy data, confirming the accuracy and stability of reconstruction.

Inverse transmission scattering problem via a Dirichlet-to-Neumann map

In this paper, we consider an inverse scattering problem of a time-harmonic wave from a penetrable obstacle. A Dirichlet-to-Neumann map is defined to convert this problem into an exterior boundary value problem with an impedance-like boundary condition. The problem is then solved without the need of solving an interior problem which is inevitable in the usual way. This process reduces the size of the problem and thus enables an efficient treatment of this inverse scattering problem.

A method for solving an exterior boundary value problem for the Laplace equation by overlapping domain decomposition

A method for solving an exterior boundary value problem for the Laplace equation by overlapping domain decomposition

A Semi-Analytical Method for Modeling Two-Phase Flow Behavior in Fractured Carbonate Oil Reservoirs

It is quite common for oil/gas two-phase flow in developing fractured carbonate oil reservoirs. Many analytical models proposed for black oil wells in fractured carbonate reservoirs are limited to single-phase flow cases and conventional methods have been the use of numerical simulations for this problem. In this approach, a novel semi-analytical method is proposed to integrate the complexities of phase change, pressure-dependent pressure-volume-temperature (PVT) properties, two-phase flow behavior, and stress-dependent fracture permeability characteristics. A dual-porosity, black oil model considering the phase change and two-phase flow is applied to model the fractured carbonate reservoirs. To linearize the model, only flow equations of oil phase are used to develop the mathematical model. Nonlinear parameters and producing gas–oil ratio (GOR) are updated with coupled flowing material balance equations, followed by a novel proposed procedure for history matching of field production data and making forecasts. The semi-analytical method is validated with a commercial simulator Eclipse. The results show that both of the production rate curves of oil and gas phase using the proposed model coincide with the numerical simulator. The results also show that the effects of pressure-dependent fracture permeability, fracture porosity, and exterior boundary on production rate are significant. Stress sensitivity influences production rate during the whole process, reducing the cumulative production. Fracture porosity influences production rate during the intermediate flow periods. The exterior boundary affects production rate mainly in the early and intermediate production periods. Finally, a field example from the eastern Pre-Caspian basin is used to demonstrate the practicability of the method. Acceptable history match is achieved and the interpreted parameters are all reasonable.

Freeze-thaw risk in solid masonry: are moisture reference years able to represent real climate conditions?

Today, there is no consensus on the selection method of representative exterior boundary conditions when performing HAM (Heat Air Moisture) simulations on building envelopes. Many existing methods to select moisture reference years (MRY) fail to provide an acceptable validation in terms of quantified risk assessment. Although new methods have been suggested during the past few years, the influence of several parameters on the selection of “critical years” in long-term datasets still needs to be assessed. The objective of this paper is to validate the application of MRY’s to evaluate freeze-thaw risk in retrofitted solid masonry. Furthermore, the influence of the chosen wall assembly, damage criterion, preconditioning and start date of the evaluation period on the ranking of critical years is assessed, using a 31-year meteorological dataset of Brussels. Results indicate that for a given wall assembly and freeze-thaw criterion, as well as a smart start date of the evaluated period, single year simulations entail a similar ranking of critical years as the corresponding year in the 31-year simulation. The number of critical freeze-thaw cycles only varies between 0 - 2 cycles (0 - 2.9%). However, changing the wall assembly and damage criterion, alters the top 5 ranking of critical years substantially.

Evaluative Case Study in Lightweight Wooden Wall Research

This presented article deals with two newly designed experimental walls with different measuring sections (5 for each lightweight wooden wall). All fragments meet the standards required for zero and energy-plus buildings, which would be mandatory in Slovakia from the year 2020. The experimental walls are located in central Europe (town Zilina, Slovakia). Description of individual test sections, the measuring technology, data collection, interior technical equipment and outdoor boundary conditions monitoring are introduced. In the future, the experimental research should progressively combine theoretical calculations with real measurement and computer HAM simulation. In this paper, the focus is aimed to the temperature profiles in wall fragments during seven days chosen from the spring period in the year 2017. The results were graphically presented and evaluated from a point of view of continuous temperature measurement in the structure, exterior boundary conditions, wall orientation and surface character (material, color). Also further intensions of research are drawn.

Impact of radiation on hygrothermal behavior of ventilated cavity wall

This work deals with the performance of a high school building renovated with prefabricated ventilated façade elements through a field experimental study under oceanic climate. Temperature, relative humidity and heat flux were measured at different points of the renovated façade and are analyzed as function of the exterior boundary conditions. The measured data are compared to numerical results. For this purpose, two models are considered: an energy balance is made for the cladding, while a heat and moisture transfer model is solved within the insulation materials. In this study, particular attention is paid in the influence of the radiative exchanges in short and long wavelengths on the hygrothermal behavior of the retrofitted wall.

A novel method for estimating the distribution of convective heat flux in ducts: Gaussian filtered singular value decomposition

ABSTRACTA new regularization approach for the unconstrained linear least square problem is proposed and assessed. This approach improves the classical methods based on the singular value decomposition approach by employing the Gaussian filter, a kind of filter which has been proved to be effective in several applications related to noise suppression. In particular, as a benchmark, it is hereby considered the estimation of the heat flux density at the internal wall surface in a forced convection problem in ducts, by solving the inverse heat conduction problem in the solid wall only using temperature distribution available at the exterior boundary. Results on both synthetic and experimental data are reported with the aim of discussing the effectiveness of the proposed method in comparison to other similar solution approaches.

A New Non-Overlapping Domain Decomposition Method for a 3D Laplace Exterior Problem

We propose a method for solving three-dimensional boundary value problems for Laplace’s equation in an unbounded domain. It is based on non-overlapping decomposition of the exterior domain into two subdomains so that the initial problem is reduced to two subproblems, namely, exterior and interior boundary value problems on a sphere. To solve the exterior boundary value problem, we propose a singularity isolation method. To match the solutions on the interface between the subdomains (the sphere), we introduce a special operator equation approximated by a system of linear algebraic equations. This system is solved by iterative methods in Krylov subspaces. The performance of the method is illustrated by solving model problems.

New blow-up results for nonlinear boundary value problems in exterior domains

We consider exterior boundary value problems with nontrivial boundary conditions, including three types of semilinear equations: heat equation, wave equation and damped wave equation. Using a test function approach with a choice of a suitable family of test functions, we obtain the critical exponents in the sense of Fujita for the considered problems. Our obtained results close some open questions from the literature.

The size of the boundary in first-passage percolation

First-passage percolation is a random growth model defined using i.i.d. edge-weights $(t_{e})$ on the nearest-neighbor edges of $\mathbb{Z}^{d}$. An initial infection occupies the origin and spreads along the edges, taking time $t_{e}$ to cross the edge $e$. In this paper, we study the size of the boundary of the infected (“wet”) region at time $t$, $B(t)$. It is known that $B(t)$ grows linearly, so its boundary $\partial B(t)$ has size between $ct^{d-1}$ and $Ct^{d}$. Under a weak moment condition on the weights, we show that for most times, $\partial B(t)$ has size of order $t^{d-1}$ (smooth). On the other hand, for heavy-tailed distributions, $B(t)$ contains many small holes, and consequently we show that $\partial B(t)$ has size of order $t^{d-1+\alpha }$ for some $\alpha >0$ depending on the distribution. In all cases, we show that the exterior boundary of $B(t)$ [edges touching the unbounded component of the complement of $B(t)$] is smooth for most times. Under the unproven assumption of uniformly positive curvature on the limit shape for $B(t)$, we show the inequality $\#\partial B(t)\leq (\log t)^{C}t^{d-1}$ for all large $t$.