Comment on Coleman-DeLuccia instantons

We complete an old argument that causal diamonds in the crunching region of the Lorentzian continuation of a Coleman-Deluccia instanton for transitions out of de Sitter space have finite area, and provide quantum models consistent with the principle of detailed balance, which can mimic the instanton transition probabilities for the cases where this diamond is larger or smaller than the causal patch of de Sitter space. We review arguments that potentials which do not have a positive energy theorem when the lowest de Sitter minimum is shifted to zero, may not correspond to real models of quantum gravity.

Universal non-Hermitian skin effect in two and higher dimensions

Skin effect, experimentally discovered in one dimension, describes the physical phenomenon that on an open chain, an extensive number of eigenstates of a non-Hermitian hamiltonian are localized at the end(s) of the chain. Here in two and higher dimensions, we establish a theorem that the skin effect exists, if and only if periodic-boundary spectrum of the hamiltonian covers a finite area on the complex plane. This theorem establishes the universality of the effect, because the above condition is satisfied in almost every generic non-Hermitian hamiltonian, and, unlike in one dimension, is compatible with all spatial symmetries. We propose two new types of skin effect in two and higher dimensions: the corner-skin effect where all eigenstates are localized at one corner of the system, and the geometry-dependent-skin effect where skin modes disappear for systems of a particular shape, but appear on generic polygons. An immediate corollary of our theorem is that any non-Hermitian system having exceptional points (lines) in two (three) dimensions exhibits skin effect, making this phenomenon accessible to experiments in photonic crystals, Weyl semimetals, and Kondo insulators.

FPGA Design of Enhanced Scale-Invariant Feature Transform with Finite-Area Parallel Feature Matching for Stereo Vision

In this paper, we propose an FPGA-based enhanced-SIFT with feature matching for stereo vision. Gaussian blur and difference of Gaussian pyramids are realized in parallel to accelerate the processing time required for multiple convolutions. As for the feature descriptor, a simple triangular identification approach with a look-up table is proposed to efficiently determine the direction and gradient of the feature points. Thus, the dimension of the feature descriptor in this paper is reduced by half compared to conventional approaches. As far as feature detection is concerned, the condition for high-contrast detection is simplified by moderately changing a threshold value, which also benefits the reduction of the resulting hardware in realization. The proposed enhanced-SIFT not only accelerates the operational speed but also reduces the hardware cost. The experiment results show that the proposed enhanced-SIFT reaches a frame rate of 205 fps for 640 × 480 images. Integrated with two enhanced-SIFT, a finite-area parallel checking is also proposed without the aid of external memory to improve the efficiency of feature matching. The resulting frame rate by the proposed stereo vision matching can be as high as 181 fps with good matching accuracy as demonstrated in the experimental results.

Multi-Physics Modeling of Electrochemical Deposition

Electrochemical deposition (ECD) is a common method used in the field of microelectronics to grow metallic coatings on an electrode. The deposition process occurs in an electrolyte bath where dissolved ions of the depositing material are suspended in an acid while an electric current is applied to the electrodes. The proposed computational model uses the finite volume method and the finite area method to predict copper growth on the plating surface without the use of a level set method or deforming mesh because the amount of copper layer growth is not expected to impact the fluid motion. The finite area method enables the solver to track the growth of the copper layer and uses the current density as a forcing function for an electric potential field on the plating surface. The current density at the electrolyte-plating surface interface is converged within each PISO (Pressure Implicit with Splitting Operator) loop iteration and incorporates the variance of the electrical resistance that occurs via the growth of the copper layer. This paper demonstrates the application of the finite area method for an ECD problem and additionally incorporates coupling between fluid mechanics, ionic diffusion, and electrochemistry.

Uniform bounds on harmonic Beltrami differentials and Weil–Petersson curvatures

In this article we show that for every finite area hyperbolic surface X of type {(g,n)} and any harmonic Beltrami differential μ on X, then the magnitude of μ at any point of small injectivity radius is uniform bounded from above by the ratio of the Weil–Petersson norm of μ over the square root of the systole of X up to a uniform positive constant multiplication. We apply the uniform bound above to show that the Weil–Petersson Ricci curvature, restricted at any hyperbolic surface of short systole in the moduli space, is uniformly bounded from below by the negative reciprocal of the systole up to a uniform positive constant multiplication. As an application, we show that the average total Weil–Petersson scalar curvature over the moduli space is uniformly comparable to {-g} as the genus g goes to infinity.