Higher-order Potentials Research Articles

ASYMPTOTIC SOLUTIONS OF HYDRODYNAMIC INTERFACIAL INSTABILITIES IN CYLINDRICAL FLOW

We present a high-order potential flow model for the motion of hydrodynamic unstable interfaces in cylindrical geometry. The asymptotic solutions of the bubbles in the gravity-induced instability and the shock-induced instability are obtained from the high-order model. We show that the model gives significant high-order corrections for the solution of the bubble.

Feature Correlation Hypergraph: Exploiting High-order Potentials for Multimodal Recognition

In computer vision and multimedia analysis, it is common to use multiple features (or multimodal features) to represent an object. For example, to well characterize a natural scene image, we typically extract a set of visual features to represent its color, texture, and shape. However, it is challenging to integrate multimodal features optimally. Since they are usually high-order correlated, e.g., the histogram of gradient (HOG), bag of scale invariant feature transform descriptors, and wavelets are closely related because they collaboratively reflect the image texture. Nevertheless, the existing algorithms fail to capture the high-order correlation among multimodal features. To solve this problem, we present a new multimodal feature integration framework. Particularly, we first define a new measure to capture the high-order correlation among the multimodal features, which can be deemed as a direct extension of the previous binary correlation. Therefore, we construct a feature correlation hypergraph (FCH) to model the high-order relations among multimodal features. Finally, a clustering algorithm is performed on FCH to group the original multimodal features into a set of partitions. Moreover, a multiclass boosting strategy is developed to obtain a strong classifier by combining the weak classifiers learned from each partition. The experimental results on seven popular datasets show the effectiveness of our approach.

Optical solitons in gas-filled, hollow-core photonic crystal fibers with inter-modal dispersion and self-steepening

The optical solitons in a gas-filled, hollow-core photonic crystal fiber with higher-order dispersion, inter-modal dispersion, Raman effect, self-steepening, detuning, external potential, and dissipation have been studied theoretically by employing the Bäcklund transformation and Hirota’s direct method. The bilinear forms and exact optical one-soliton solutions to the nonlinear optical transmission equation are obtained under the constraint conditions. The influence of correlation coefficients on the width, amplitude, and phase of optical solitons are analyzed. These results have important application features in optical soliton control in gas-filled, hollow-core photonic crystal fibers.

A Semisupervised Context-Sensitive Change Detection Technique via Gaussian Process

In this letter, we propose a semisupervised context-sensitive technique for change detection in high-resolution multitemporal remote sensing images. This is achieved by analyzing the posterior probability of probabilistic Gaussian process (GP) classifier within a Markov random field (MRF) model. In particular, the method consists of two steps: 1) A semisupervised initialization exploits both labeled and unlabeled data based on a probabilistic GP classifier, and 2) an MRF regularization aims at refining the posterior probability by employing the spatial context information. In particular, both edge information and high-order potential are utilized in MRF energy function formulation. Experimental results obtained on real remote sensing multitemporal imagery data sets confirm the effectiveness of the proposed approach.

Semantic Segmentation with Same Topic Constraints

A popular approach to semantic segmentation problems is to construct a pair wise Conditional Markov Random Field (CRF) over image pixels where the pair wise term encodes a preference for smoothness within pixel neighborhoods. Recently, researchers have considered higher-order models that encode local region or soft non-local constraints (e.g., label consistency or co-occurrence statistics). These new models with higher-order terms have significantly pushed the state-of-the-art for semantic segmentation problems. In this study, we consider a novel non- local constraint that enforces consistent pixel labels among those image regions having the same topic. These topics are discovered by Probabilistic Latent Semantic Analysis model (PLSA). We encode this constraint as a robust Pn higher-order potential among all the image regions of the same topic in a unified CRF model. We experimentally demonstrate quantitative and qualitative improvements over a refined baseline unary and pair wise CRF models.

HIGH-ORDER POTENTIAL FLOW MODELS FOR HYDRODYNAMIC UNSTABLE INTERFACE

We present two high-order potential flow models for the evolution of the interface in the Rayleigh-Taylor instability in two dimensions. One is the source-flow model and the other is the Layzer-type model which is based on an analytic potential. The late-time asymptotic solution of the source-flow model for arbitrary density jump is obtained. The asymptotic bubble curvature is found to be independent to the density jump of the fluids. We also give the time- evolution solutions of the two models by integrating equations numerically. We show that the two high-order models give more accurate solutions for the bubble evolution than their low- order models, but the solution of the source-flow model agrees much better with the numerical solution than the Layzer model.

Small UAV Design Using an Integrated Design Tool

A numerical design tool was developed that greatly facilitates the design process of small UAVs. The integrated approach of the method makes it highly suitable for the aerodynamic needs of such small aircraft. Traditional design tools and methodologies are typically tailored for the design of larger aircraft, such as for general aviation, whose aerodynamics generally exhibit more linear behaviors. Building on this motivation, a user friendly integrated design tool was developed and validated in order to provide a more tailored approach to designing low Reynolds number aircraft. At the heart of the tool is a performance prediction that relies on a higher-order free wake potential flow aerodynamic code that employs viscous drag corrections. Subsequently, the method provides accurate characteristics for a wide range of Reynolds numbers and aspect ratio wings. In a validation process, the flight performance results of the method are compared with the results of other prediction methods as well as with several experimental flight test results. In general good agreement exists. The utility of the integrated design tool is demonstrated with the design application of a small UAV for a heavy lift competition. The design tool greatly streamlined the design process, limiting it to two weeks rather than the typical several months.

Uniformly Reweighted Belief Propagation for Estimation and Detection in Wireless Networks

In this paper, we propose a new inference algorithm, suitable for distributed processing over wireless networks. The algorithm, called uniformly reweighted belief propagation (URW-BP), combines the local nature of belief propagation with the improved performance of tree-reweighted belief propagation (TRW-BP) in graphs with cycles. It reduces the degrees of freedom in the latter algorithm to a single scalar variable, the uniform edge appearance probability ρ. We provide a variational interpretation of URW-BP, give insights into good choices of ρ, develop an extension to higher-order potentials, and complement our work with numerical performance results on three inference problems in wireless communication systems: spectrum sensing in cognitive radio, cooperative positioning, and decoding of a low-density parity-check (LDPC) code.

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N2 scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.

3D segmentation of SBFSEM images of neuropil by a graphical model over supervoxel boundaries

The segmentation of large volume images of neuropil acquired by serial sectioning electron microscopy is an important step toward the 3D reconstruction of neural circuits. The only cue provided by the data at hand is boundaries between otherwise indistinguishable objects. This indistinguishability, combined with the boundaries becoming very thin or faint in places, makes the large body of work on region-based segmentation methods inapplicable. On the other hand, boundary-based methods that exploit purely local evidence do not reach the extremely high accuracy required by the application domain that cannot tolerate the global topological errors arising from false local decisions. As a consequence, we propose a supervoxel merging method that arrives at its decisions in a non-local fashion, by posing and approximately solving a joint combinatorial optimization problem over all faces between supervoxels. The use of supervoxels allows the extraction of expressive geometric features. These are used by the higher-order potentials in a graphical model that assimilate knowledge about the geometry of neural surfaces by automated training on a gold standard. The scope of this improvement is demonstrated on the benchmark dataset E1088 (Helmstaedter et al., 2011) of 7.5billionvoxels from the inner plexiform layer of rabbit retina. We provide C++ source code for annotation, geometry extraction, training and inference.

A hybrid approach for MRF optimization problems: Combination of stochastic sampling and deterministic algorithms

In computer vision, many applications have been formulated as Markov Random Field (MRF) optimization or energy minimization problems. To solve them effectively, numerous algorithms have been developed, including the deterministic and stochastic sampling algorithms. The deterministic algorithms include Graph Cuts, Belief Propagation, and Tree-Reweighted Message Passing while the stochastic sampling algorithms include Simulated Annealing, Markov Chain Monte Carlo (MCMC), and Population-based Markov Chain Monte Carlo (Pop-MCMC). Although many of them produce good results for relatively easy problems, they are still unsatisfactory when it comes to more difficult MRF problems such as non-submodular energy functions, strongly coupled MRFs, and high-order clique potentials. In this paper, we propose a new hybrid algorithm which successfully combines the stochastic sampling and deterministic algorithms to solve such challenging MRF problems. By combining those two different approaches in a unified framework, we can utilize the advantages from both approaches. For example, the deterministic algorithms guide the solution to rapidly move into lower energy state of the solution space. The stochastic sampling algorithms help the solution not to be stuck in local minima and explore larger area. Consequently, the proposed algorithm substantially increases the quality of the solutions. We present a thorough analysis of the algorithm in synthetic MRF problems by controlling the hardness of the problems. We also demonstrate the effectiveness of the proposed algorithm by the experiments on real applications including photomontage and inpainting.

Effectiveness and legitimacy of forest carbon standards in the OTC voluntary carbon market

BackgroundIn recent years, the voluntary over-the-counter (OTC) carbon market has reached a significant market volume. It is particularly interesting for forest mitigation projects which are either ineligible in compliance markets or confronted with a plethora of technical and financial hurdles and lacking market demand. As the OTC market is not regulated, voluntary standards have been created to secure the social and environmental integrity of the traded mitigation projects and thus to ensure the quality of the resulting carbon credits. Building on a theoretical efficiency-legitimacy framework, this study aims to identify and analyse the characteristics and indicators that determine the efficiency and organisational legitimacy of standards for afforestation/reforestation carbon projects.ResultsAll interviewed market actors consider third-party certification and standards as a crucial component of market functionality, which provide quality assurance mechanisms that reduce information asymmetries and moral hazard between the actors regarding the quality of carbon credits, and thus reduce transaction costs. Despite this development, the recent evolution of many new and differing standards is seen as a major obstacle that renders it difficult for project developers and buyers to select an appropriate standard. According to the interviewed experts the most important legitimating factors of standards are assurance of a sufficient level of quality of carbon credits, scientifically substantiated methodological accounting and independent third-party verification, independence of standard bodies, transparency, wide market acceptance, back-up of the wider community including experts and NGOs, rigorous procedures, and the resemblance to the Afforestation/Reforestation (A/R) CDM due to its international policy endorsements. In addition, standards must provide evidence that projects contribute to a positive social and environmental development, do no harm as a minimum requirement and build a strong track record of successful projects. Project developers require clear, easily and practically applicable standards at lowest possible costs with a high potential in order to achieve good carbon prices, while buyers require that standards are legitimate, credible and that no public criticism arises when carbon credits are purchased from projects certified by a certain standard.ConclusionsDespite the fragmented and immature state of the OTC market, standards act as 'market-making' intermediaries and contribute to the quality and transparency of the OTC market. However, the variety of different standards imposes new hurdles for their efficiency and often creates confusion instead of confidence among potential buyers. Despite the lacking legitimacy of the standards, pressures from the institutional environment on standards ensure a minimum quality of carbon credits (including positive social and environmental impacts of carbon credits) that serves as an insurance mechanism for the integrity of standards. Its unregulated nature and the pressure from an increasingly competitive environment provides innovative space to deliver efficient certification procedures without imposing unreasonably high transaction costs on market actors. Furthermore, voluntary standards imply a more innovative certification approach, as one legal authority could do, because standards have to compete for adopters backed by civil society organisations. Thereby, the forest sector in OTC voluntary market bears great opportunities to provide the forest sector with crucial lessons for international climate policy and governmental institutions when designing regulation for forest regulation such as international and national REDDplus schemes.

Five-brane superpotentials, blow-up geometries and SU(3) structure manifolds

We investigate the dynamics of space-time filling five-branes wrapped on curves in heterotic and orientifold Calabi-Yau compactifications. We first study the leading N=1 scalar potential on the infinite deformation space of the brane-curve around a supersymmetric configuration. The higher order potential is also determined by a brane superpotential which we compute for a subset of light deformations. We argue that these deformations map to new complex structure deformations of a non-Calabi-Yau manifold which is obtained by blowing up the brane-curve into a four-cycle and by replacing the brane by background fluxes. This translates the original brane-bulk system into a unifying geometrical formulation. Using this blow-up geometry we compute the complete set of open-closed Picard-Fuchs differential equations and identify the brane superpotential at special points in the field space for five-branes in toric Calabi-Yau hypersurfaces. This has an interpretation in open mirror symmetry and enables us to list compact disk instanton invariants. As a first step towards promoting the blow-up geometry to a supersymmetric heterotic background we propose a non-Kaehler SU(3) structure and an identification of the three-form flux.

Perveance and ion bunch structure from a “compact, high-pressure” laser ion source

The Dublin City University (DCU) laser ion source (LIS) is a “compact high-pressure” laser ion source utilizing a table top Q-switched laser. The DCU-LIS combines high laser fluence (F>4 kJ cm−2), high laser intensity (I>1011 W cm−2) with a short field free region (L=48 mm) and high source potential (Vext>40 kV) in order to offset recombination losses within the plasma and maximize the proportion of highly charged ions which are extracted from the plasma plume. Such a configuration also provides high peak currents (Ip>3 mA), high current densities (J>5 mA cm−2), and high charge states (Cu6+) in the extracted ion-bunch train. However, to obtain and utilize these parameter values in a high pressure LIS requires characterization and control of a number of processes related to ion dynamics and space charge effects on the extracted ions at the plasma plume-anode-extraction gap interface. Relevant issues include electric field distortion, Debye shielding, beam divergence, overfocusing, and perveance (P) in addition to current density profiles for the extracted ion beam. In this paper we focus on these issues and their impact on charge particle extraction and acceleration with a view to elucidating the parameter regimes within which the DCU-LIS performance envelope is optimal.

Phase-field simulations of nuclei and early stage solidification microstructures

To investigate the local properties of heterogeneous nuclei on substrates, a phase-fieldmodel is extended to incorporate volume constraints and a third order line tension in thegradient free energy density formulation. The new model is applied to sessile dropsimulations of Cu nuclei on Ni substrates to precisely analyse 3D equilibrium shapes anddiffusion processes across the phase boundaries. In particular, the formalism with higherorder potentials is used to investigate the length-scale dependent effect of theline tension on Young’s force balance at triple lines in 3D. The employment ofparallel and adaptive simulation techniques is essential for three-dimensionalnumerical computations. Early stage solidification microstructures of cubic Ni crystalsare simulated by scale-bridging molecular dynamics (MD) and phase-field (PF)simulations. The domain of the PF computations is initialized by transferringMD data of the atomic positions and of the shape of the nuclei. The combinedapproach can be used to study the responses of microstructures upon nucleation.

Vibration energy levels of the PH3, PH2D, and PHD2 molecules calculated from high order potential energy surface

Vibrational energy levels of the PH(3), PH(2)D, and PHD(2) molecules were calculated from the new extended potential energy surface (PES) determined in this work. The coupled-cluster approach with the perturbative inclusion of the connected triple excitations CCSD(T) and correlation consistent polarized valence basis set cc-pV5Z was employed in the ab initio calculations of electronic ground state energies. The contribution of relativistic effects to the overall electronic energy surface was computed using quasirelativistic mass-velocity-Darwin approach. These ab initio points were fitted by a parametrized function with one parameter empirically adjusted. The grid of 11,697 geometrical nuclear configurations covers a large domain of the six dimensional internal coordinate space and was designed to provide vibration energy levels of phosphine molecule up to 7000 cm(-1) above the zero point vibration energy with reasonable accuracy. The analytical representation of the PES was determined through the expansion in symmetry adapted products of nonlinear internal coordinates for various orders of analytical expansions up to the tenth order. The dependence of calculated vibration energy levels on the analytical representation of PES and on the coordinate choice was studied. Calculated vibration levels are in very good agreement with observations: The root mean squares deviation between theoretically calculated and observed band centers is 1.4 cm(-1) for PH(3), 0.4 cm(-1) for PH(2)D, and 0.6 cm(-1) for PHD(2).

The effect of scanning strategies on electron beam sintering

The electron beam technology offers a wide range of possibilities for the use with industrial production processes. In addition to welding applications the fast beam deflection with electromagnetic coils can be used within additive layer manufacturing to gain a higher scanning speed and to realize new deflection figures compared to laser based systems. Therefore, the electron beam sintering exhibits a high application potential in order to achieve higher build-up rates. After explaining the functional principle and the relating process steps the examination of different scanning strategies is presented. By means of part analysis and visual observation, determining effects could be identified. In the following, the analysis of temperature profiles by means of thermal simulation was carried out in order to optimize the sintering of one layer. Based on these results the adaptation of process parameters could be derived. It is shown that the scanning strategies have a significant influence on the process and the part quality respectively.

Higher-order Kato class potentials for Schrödinger operators

Higher-order Kato class potentials for Schrödinger operators

The Killing spinor equation with higher order potentials

Let ( M n , g ) be a Riemannian spin manifold. The basic equations in supergravity models of type IIa string theory with 4-form flux involve a 3-form T , a 4-form F , a spinorial covariant derivative ∇ depending on ∇ g , T , F , and a ∇ -parallel spinor field Ψ . We classify and construct many explicit families of solutions to this system of spinorial field equations by means of non-integrable special geometries. The latter include α -Sasakian structures in dimensions 5 and 7, almost Hermitian structures in dimension 6 and cocalibrated G 2 -structures in dimension 7. We show that there are several examples also satisfying an additional constraint for the energy-momentum tensor.

Surface solitons supported by Bessel optical potential

A simple but new model, an interface separated by 1-D Bessel optical potential with different modulation depth on the opposite side of the interface was proposed. We show this model can support stable surface solitons. Surface solitons form because diffraction and defocusing nonlinearity are balanced by the Bessel potential. We demonstrate numerically such solitons are stable in their entire existence domain even for higher-order Bessel potential.