Spherical Surface Model Research Articles

Micro-Scale Spherical and Cylindrical Surface Modeling via Metaheuristic Algorithms and Micro Laser Line Projection

With the increasing micro-scale manufacturing industry, the micro-scale spherical and cylindrical surface modeling has become an important factor in the manufacturing process. Thus, the micro-scale manufacturing processes require efficient micro-scale spherical and cylindrical models to achieve accurate assembly. Therefore, it is necessary to implement models to represent micro-scale spherical and cylindrical surfaces. This study addresses metaheuristic algorithms based on micro laser line projection to perform micro-scale spherical and cylindrical surface modeling. In this technique, the micro-scale surface is recovered by an optical microscope system, which computes the surface coordinates via micro laser line projection. From the surface coordinates, a genetic algorithm determines the parameters of the mathematical models to represent the spherical and cylindrical surfaces. The genetic algorithm performs exploration and exploitation in the search space to optimize the models’ mathematical parameters. The search space is constructed via surface data to provide the optimal parameters, which determine the spherical and cylindrical surface models. The proposed technique improves the fitting accuracy of the micro-scale spherical and cylindrical surface modeling performed via optical microscope systems. This contribution is elucidated by a discussion about the model fitting between the genetic algorithms based on micro laser line projection and the optical microscope systems.

Formation and evolution of fracture spacing on various geometric surfaces in layered materials

Fracture spacing as a widespread phenomenon in nature shows similar patterns on various geometric surfaces. To explore the similarities and differences between various geometric surfaces in the process of fracture spacing formation, numerical simulations are conducted on bi-layered three-dimensional models of three various geometric surfaces, including slab surface, cylindrical surface, and spherical surface by the finite element method (FEM). The fractures develop under a quasi-static loading condition with constant displacement increments. The progressive failure process from fracture initiation to saturation is researched, and the material heterogeneity is introduced by using a probability distribution, which acts as the main reason for failures generating randomly inception. An intuitive explanation is also provided for the phenomenon of fracture saturation. Then, as the loading condition varies, fracture patterns in both slab surface models and cylindrical surface models show a transition from parallel fractures, step-like fractures to regular polygonal fractures. However, in spherical surface models, only uniform polygonal fractures emerge under the condition of radial expansion. Furthermore, through quantitative analysis by statistical means, we find that, except for the fractured layer thickness, curvature also has a significant impact on the crack density.

Study of the tool path generation method for an ultra-precision spherical complex surface based on a five-axis machine tool

The improvement of ultra-precision machining technology has significantly boosted the demand for the surface quality and surface accuracy of the workpieces to be machined. However, the geometric shapes of workpiece surfaces cannot be adequately manufactured with simple plane, cylindrical, or spherical surfaces because of their different applications in various fields. In this research, a method was proposed to generate tool paths for the machining of complex spherical surfaces based on an ultra-precise five-axis turning and milling machine with a C-Y-Z-X-B structure. Through the proposed tool path generation method, ultra-precise complex spherical surface machining was achieved. First, the complex spherical surface model was modeled and calculated, and then it was combined with the designed model to generate the tool path. Then the tool paths were generated with a numerically controlled (NC) program. Based on an ultra-precision three-coordinate measuring instrument and a white light interferometer, the machining accuracy of a workpiece surface was characterized, and the effectiveness of the tool path generation method was verified. The surface roughness of the machined workpiece was less than 90 nm. Furthermore, the surface roughness within the spherical region appeared to be less than 30 nm. The presented tool path generation method in this research produced ultra-precision spherical complex surfaces. The method could be applied to complex spherical surfaces with other characteristics.

Microscopic Eilenberger theory of Fulde-Ferrell-Larkin-Ovchinnikov states in the presence of vortices

We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entropy, and the zero-energy density of states are calculated. Those quantities are shown to start quickly growing upon entering the LO state. We also evaluate the wave length of the LO modulation, the flux line lattice form factors for small angle neutron scattering, and the NMR spectra to facilitate the identification of the LO state. Two cases of strong and intermediate Pauli paramagnetic effect are studied comparatively. The possibility of the LO phase in Sr$_2$RuO$_4$, CeCoIn$_5$, CeCu$_2$Si$_2$, and the organic superconductors is critically examined and crucial experiments to identify it are proposed.

Large radius of curvature measurement based on the evaluation of interferogram-quality metric in non-null interferometry

Non-null interferometry could use to measure the radius of curvature (ROC), we have presented a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method for large ROC measurement (Yang et al., 2016). In this paper, we propose a large ROC measurement method based on the evaluation of the interferogram-quality metric by the non-null interferometer. With the multi-configuration model of the non-null interferometric system in ZEMAX, the retrace errors and the phase introduced by the test surface are reconstructed. The interferogram-quality metric is obtained by the normalized phase-shifted testing Newton rings with the spherical surface model in the non-null interferometric system. The radius curvature of the test spherical surface can be obtained until the minimum of the interferogram-quality metric is found. Simulations and experimental results are verified the feasibility of our proposed method. For a spherical mirror with a ROC of 41,400 mm, the measurement accuracy is better than 0.13%.

Spherical cap surface model: A novel method for predicting renal function after partial nephrectomy.

To estimate the percent functional volume preservation from preoperative images using a novel method, the spherical cap surface model, and to investigate whether this model can preoperatively predict renal function after partial nephrectomy. A total of 233 patients with renal cell carcinoma who underwent open or laparoscopic partial nephrectomy between January 2011 and December 2013 were included in the present study. The spherical cap surface model was used to calculate the estimated percent functional volume preservation on preoperative computed tomography, and the estimated percent functional volume preservation was multiplied by the preoperative estimated glomerular filtration rate to predict the postoperative estimated glomerular filtration rate. The occurrence of acute kidney injury also served as an outcome. Univariate and multivariate linear regression, and receiver operating characteristic curve analysis were used to test the model. The estimated percent functional volume preservation calculated by the novel model was significantly associated with both nadir percent estimated glomerular filtration rate preservation and late percent estimated glomerular filtration rate preservation in the multivariate analysis (the P-values were 0.021 and 0.043, respectively). Receiver operating characteristic curve analysis for predicting acute kidney injury after partial nephrectomy showed that volume preservation (P<0.001) and warm ischemia time (P=0.040) were both significant. Regarding the ability to predict a significant decrease in late renal function after partial nephrectomy, only volume preservation (P=0.044) was significant. Preservation of functional volume is the primary determinant of functional outcomes after partial nephrectomy. The spherical cap surface model seems to represent a promising tool to predict nadir and late postoperative renal function in patients undergoing partial nephrectomy.

Subnuclei atrophy in the amygdala in patients with persistent insomnia and its relation with insomnia progression and depression

Despite high comorbidity rates of insomnia and depression, the pathways in which insomnia and depression are linked are still unclear. The high comorbidity and heightened level of arousal in both neuropsychiatric conditions calls for a study of the amygdala, which plays a crucial role in the neurobiological mechanisms underlying emotional disorders. We thus studied MR local volumentry of the amygdala in insomnia patients and controls with a longitudinal study design. Sixty patients presenting persistent insomnia at three time points spaced two years apart (PI, age = 51.13¡‘3/48.06, males = 60%) and 44 good sleepers (GS, age = 48.09¡‘3/46.47, males = 56.8%) were randomly selected from a larger population-based study. All participants underwent 1.5 Tesla MRI at endpoint. Vertex-wise volumetry was performed using spherical harmonic-based surface models extracted from manual delineation of the amygdala. We performed vertex-wise t -tests for group comparisons between PI and GS. Participants also completed the Pittsburgh Sleep Quality Index (PSQI) and Beck Depression Inventory (BDI) at each visitation. We defined longitudinal change of PSQI scores as ¡‘®PSQI at the 3rd PSQI at 1st time point¡‘ ¯ to measure insomnia progression. Linear regression analysis was then conducted to predict amygdalar volume, with insomnia progression and insomnia groups as independent variables. All statistical tests included age and sex, and depression as covariates. Multiple comparisons were corrected using the False Discovery Rate. PI presented atrophy in the laterobasal subnuclei of the amygdala (LBA) relative to GS ( p < 0.05 corrected). Progressive worsening of sleep quality was significantly associated with LBA atrophy ( r < −.47, p < 0.001). Further interaction analyses demonstrated that the association in the PI group was stronger than the GS group ( F = 3.2, p < 0.001). The BDI in PI correlated negatively with volumes located in the centromedial amygdala (CMA). This pioneer neuroimaging study reveals the presence of LBA atrophy in patients with PI, which increases in relation to progressively worsening insomnia. Extracellular recordings suggest that the neuronal activity pattern in LBA is deeply related to the sleep-wake cycle, whereas an MRI study observes that volume changes in CMA are associated with anxiety. Our findings may facilitate further clarification of the bidirectional relationship between insomnia and depression. This study was performed at the Korea University Hospital, Ansan, Republic of Korea. This study was supported by grants from the Korean Center for Disease Control, Prevention and the Korean Ministry for Health and Welfare, and the National Research Foundation of Korea Grant funded by the Korean Government. [Grant 2005-E71001-00, Grant 2006-E71005-00, Grant 2007-E71001-00, Grant 2008-E71001-00, Grant 2009-E71002-00, Grant 2010-E71001-00, Grant 2011-E71004-0, NRF-2012-S1A5BA01].

Three-Dimensional Surface Profile Measurement of Microlenses Using the Shack–Hartmann Wavefront Sensor

We present a 3-D surface profiling method for microlenses that utilizes a Shack-Hartmann wavefront sensor. This method applies to both solid microlenses and liquid-liquid interfaces in liquid microlenses. The wavefront at the aperture stop of a microlens is measured by a Shack-Hartmann wavefront sensor and is then used to calculate the 3-D surface profile of the microlens. Three types of microlenses-a photoresist microlens, a hydrogel-driven tunable liquid lens, and an electrowetting-driven tunable liquid lens-were fabricated and measured. The variable-focus liquid lenses were tested within a wide focal length range. The obtained surface profiles were fitted to spherical and conical surface models to study their geometrical properties. The photoresist microlens was found to be approximately spherical. For the hydrogel-driven microlens, the profile was smooth and nearly spherical at the center but became steep and linear at the aperture edges. The electrowetting-driven liquid lens was also fitted better with the conical model, and its conic constant was determined. The obtained surface profiles were used to estimate the optical properties of microlenses in an optical analysis software package. The comparison between the simulation and experiment results indicated that the accuracy of the estimation is rough and the error could be due to the wavefront measurement and surface fitting approximation.

Shape Transformations of Triangulated Spherical Surfaces in Parallel Plates

We numerically study a spherical surface model and find that the model undergoes a shape transformation between the pancake phase and the concave phase. A constraint potential included in the Hamiltonian confines the surface inside a couple of parallel plates. The Hamiltonian including the Gaussian bond potential and the extrinsic curvature energy is discretized on fixed-connectivity triangulated surfaces, which are allowed to self-intersect. The shape transformation between the pancake phase and the concave phase occurs at relatively large bending rigidity b, where the surface is quite smooth and hence self-avoiding. This transformation is considered to be a phase transition because the size fluctuation follows to a scaling relation typical to the continuous transition, although the curvature energy remains almost constant against b at the transition region.

An Alternative Isovelocity Surface Model for Quantitation of Effective Regurgitant Orifice Area in Mitral Regurgitation With an Elongated Orifice: Application to Functional Mitral Regurgitation

The purpose of this study was to develop and test a simple, clinically practical alternative isovelocity surface (ISVS) model for calculating effective regurgitant orifice area (EROA) in mitral regurgitation (MR) when the regurgitant orifice is elongated, such as in functional MR. Clinical experience and 3-dimensional imaging suggest that the traditional hemispheric ISVS model used in the conventional proximal isovelocity surface area (PISA) calculation is invalid in certain MR cases and can cause erroneous EROA values. Our ISVS model consisted of 3 sections of equal radius (R): a cylindrical midsection of length (L) positioned between 2 hemispheroidal end sections. Total ISVS area (T(S)) is equal to 2πR(2) + πLR and EROA is equal to (V(N/)V(CW))T(S), where V(N) is the flow velocity crossing perpendicular to the ISVS, and V(CW) is the peak MR jet velocity by continuous-wave Doppler. This EROA was corrected for any obtuse angle, θ formed by tented leaflets, by multiplying T(S) by a planar factor, (θ/180) or a combination of this planar factor for the cylindrical midsection and the solid-angle factor, 1-cos(θ/2), for the 2 spheroidal end sections. In 24 cases of severe or 3+ functional MR, we calculated EROA using 3 traditional hemispheric surfaces and 3 alternative ISVS models that differed in the leaflet angle correction applied. Results were compared with continuity-based EROA using the standard mitral valve - aortic valve stroke volume method and with predictions based upon theoretical geometric considerations. The mean differences between continuity EROA and ISVS area-based EROA for no angle correction, planar correction, or combined angle correction were, respectively, 0.38, 0.32, and 0.28 cm(2) for the 3 spherical surface models and 0.17, 0.018, and -0.012 cm(2) for the 3 alternative 3-section ISVS models. The empiric EROA results with both the traditional spherical and alternative ISVS models agreed well with theoretical geometric predictions. The traditional spherical PISA model underestimates EROA in functional MR. For elongated MR orifices, an ISVS model that mirrors orifice shape yields more accurate EROA values. Correction to the ISVS area for obtuse leaflet angulation improves accuracy of EROA estimation.

A source location algorithm of lightning detection networks in China

Abstract. Fast and accurate retrieval of lightning sources is crucial to the early warning and quick repairs of lightning disaster. An algorithm for computing the location and onset time of cloud-to-ground lightning using the time-of-arrival (TOA) and azimuth-of-arrival (AOA) data is introduced in this paper. The algorithm can iteratively calculate the least-squares solution of a lightning source on an oblate spheroidal Earth. It contains a set of unique formulas to compute the geodesic distance and azimuth and an explicit method to compute the initial position using TOA data of only three sensors. Since the method accounts for the effects of the oblateness of the Earth, it would provide a more accurate solution than algorithms based on planar or spherical surface models. Numerical simulations are presented to test this algorithm and evaluate the performance of a lightning detection network in the Hubei province of China. Since 1990s, the proposed algorithm has been used in many regional lightning detection networks installed by the electric power system in China. It is expected that the proposed algorithm be used in more lightning detection networks and other location systems.

Flat Histogram Monte Carlo Simulations of Triangulated Fixed-Connectivity Surface Models

Using the Wang-Landau flat histogram Monte Carlo (FHMC) simulation technique, we were able to study two types of triangulated spherical surface models in which the two-dimensional extrinsic curvature energy is assumed in the Hamiltonian. The Gaussian bond potential is also included in the Hamiltonian of the first model, but it is replaced by a hard-wall potential in the second model. The results presented in this paper are in good agreement with the results previously reported by our group. The transition of surface fluctuations and collapsing transition were studied using the canonical Metropolis Monte Carlo simulation technique and were found to be of the first-order. The results obtained in this paper also show that the FHMC technique can be successfully applied to triangulated surface models. It is non-trivial whether the technique is applicable or not to surface models because the simulations are performed on relatively large surfaces.

Spherical Surface Models with Directors

A triangulated spherical surface model is numerically studied, and it is shown that the model undergoes phase transitions between the smooth phase and the collapsed phase. The model is defined by using a director field, which is assumed to have an interaction with a normal of the surface. The interaction between the directors and the surface maintains the surface shape. The director field is not defined within the two-dimensional differential geometry, and this is in sharp contrast to the conventional surface models, where the surface shape is maintained only by the curvature energies. We also show that the interaction makes the Nambu-Goto model well-defined, where the bond potential is given by the area of triangles; the Nambu-Goto model is well-known as an ill-defined one even when the conventional two-dimensional bending energy is included in the Hamiltonian.

Non-trivial effect of the in-plane shear elasticity on the phase transitions of fixed-connectivity meshwork models

We numerically study the phase structure of two types of triangulated spherical surface models, which includes an in-plane shear energy in the Hamiltonian, and we found that the phase structure of the models is considerably influenced by the presence of the in-plane shear elasticity. The models undergo a first-order collapsing transition and a first-order (or second-order) transition of surface fluctuations; the latter transition was reported to be of second-order in the first model without the in-plane shear energy. This leads us to conclude that the in-plane elasticity strengthens the transition of surface fluctuations. We also found that the in-plane elasticity decreases the variety of phases in the second model without the in-plane energy. The Hamiltonian of the first model is given by a linear combination of the Gaussian bond potential, a one-dimensional bending energy, and the in-plane shear energy. The second model is obtained from the first model by replacing the Gaussian bond potential with the Nambu-Goto potential, which is defined by the summation over the area of triangles.

Possible effects of tilt order on phase transitions of a fixed connectivity surface model

We study the phase structure of a phantom tethered surface model shedding light on the internal degrees of freedom (IDOF), which correspond to the three-dimensional rodlike structure of the lipid molecules. The so-called tilt order is assumed as IDOF on the surface model. The model is defined by combining the conventional spherical surface model and the XY model, which describes not only the interaction between lipids but also the interaction between the lipids and the surface. The interaction strength between IDOF and the surface varies depending on the interaction strength between the variables of IDOF. We know that the model without IDOF undergoes a first-order transition of surface fluctuations and a first order collapsing transition. We observe in this paper that the order of the surface fluctuation transition changes from first order to second order and to higher order with increasing strength of the interaction between IDOF variables. On the contrary, the order of collapsing transition remains first order and is not influenced by the presence of IDOF.

405 2重膜構造をもつ面積エネルギー膜モデルの相転移(計算力学と数値シミュレーション,オーガナイズドセッション)

405 2重膜構造をもつ面積エネルギー膜モデルの相転移(計算力学と数値シミュレーション,オーガナイズドセッション)

Phase structure of a spherical surface model on fixed connectivity meshes

An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The shape of surfaces is maintained by a one-dimensional bending energy, which is defined on the mesh, and no two-dimensional bending energy is included in the Hamiltonian.

Phase Transition of Triangulated Spherical Surfaces with Elastic Skeletons

A first-order transition is numerically found in a spherical surface model with skeletons, which are linked to each other at junctions. The shape of the triangulated surfaces is maintained by skeletons, which have a one-dimensional bending elasticity characterized by the bending rigidity $b$, and the surfaces have no two-dimensional bending elasticity except at the junctions. The surfaces swell and become spherical at large $b$ and collapse and crumple at small $b$. These two phases are separated from each other by the first-order transition. Although both of the surfaces and the skeleton are allowed to self-intersect and, hence, phantom, our results indicate a possible phase transition in biological or artificial membranes whose shape is maintained by cytoskeletons.

Electron-electron interactions and the electrical resistivity of lithium at low temperatures

The electron-electron interactions in lithium metal have been examined keeping in view the recent developments. The contribution of the electron-electron Umklapp scattering processes in the electrical resistivity of lithium at low temperatures has been evaluated using a simplified spherical Fermi surface model with isotropic transition probability. Our values of the electrical resistivity so obtained compare fairly well with the experimental results for lithium.

Phase structure of intrinsic curvature models on dynamically triangulated disk with fixed boundary length

A first-order phase transition is found in two types of intrinsic curvature models defined on dynamically triangulated surfaces of disk topology. The intrinsic curvature energy is included in the Hamiltonian. The smooth phase is separated from a non-smooth phase by the transition. The crumpled phase, which is different from the non-smooth phase, also appears at sufficiently small curvature coefficient $\alpha$. The phase structure of the model on the disk is identical to that of the spherical surface model, which was investigated by us and reported previously. Thus, we found that the phase structure of the fluid surface model with intrinsic curvature is independent of whether the surface is closed or open.