The conventional bulk-boundary correspondence directly connects the number of topological edge states in a finite system with the topological invariant in the bulk band structure with periodic boundary condition (PBC). However, recent studies show that this principle fails in certain non-Hermitian systems with broken reciprocity, which stems from the non-Hermitian skin effect (NHSE) in the finite system where most of the eigenstates decay exponentially from the system boundary. In this work, we experimentally demonstrate a 1D non-Hermitian topological circuit with broken reciprocity by utilizing the unidirectional coupling feature of the voltage follower module. The topological edge state is observed at the boundary of an open circuit through an impedance spectra measurement between adjacent circuit nodes. We confirm the inapplicability of the conventional bulk-boundary correspondence by comparing the circuit Laplacian between the periodic boundary condition (PBC) and open boundary condition (OBC). Instead, a recently proposed non-Bloch bulk-boundary condition based on a non-Bloch winding number faithfully predicts the number of topological edge states.

Turbulence initiated by Richtmyer-Meshkov ͑RM͒ instability provides an important environment for studying three-dimensional, high-speed, compressible, and variable-density flow physics. The active baroclinic term in the vorticity evolution equation complicates the vortex dynamics and challenges existing vortex identification schemes. In this paper, we examine the insufficiency of existing vortex identification schemes when applied to a simulated RM flow ͓Zhang et al., J. Turbul. 6, 1 ͑2005͔͒. We propose a new scheme, eigen helicity density ͑H e ͒, based on the eigen analysis of the velocity gradient tensor. This Galilean invariant scheme successfully identifies vortex tubes in the same simulation.The physical phenomena associated with RayleighTaylor ͑RT͒ and Richtmyer-Meshkov ͑RM͒ instabilities are commonly seen in nature, from supernova explosions in outer space to internal combustion in gas turbines. 1 The most distinguishable physics in this flow environment is the active baroclinic term in the vorticity evolution equation, ͑١ ϫ ١p͒ / 2 . In traditional configurations, ١p is imposed by shocks ͑RM case͒ or gravity ͑RT case͒. More recent works 2,13 show that the baroclinic process may exist whenever materials inhomogeneities ͑source of ١͒ exist and interact with vortices ͑source of ١p͒.As vortex dynamics play an extremely important role in this flow at late time when turbulent mixing dominates, 3 automatic identification and tracking of vortical and material flow features provide additional means of flow visualization and quantification. In Zhang et al., 4 a statistical analysis of flow features has stimulated an understanding of the correlation of the momentum and mass diffusivity, indicated respectively by the spatial distribution and temporal evolution of the vortices and gas bubbles extracted from the raw simulation data. An accurate vortex identification scheme becomes the first challenge in extending this work to three dimensions.Although there are a number of studies devoted to vortex identification, the question of "what is a vortex" remains open even in incompressible, single-fluid flows. In the following, we categorize and review existing works.From a flow physics standpoint, variants of low-pressure ͑p scheme hereafter͒ and high-vorticity magnitude ͉͉͑ scheme hereafter͒ regions are still used to identify vortices, despite the failure cases pointed out by many studies; for example, Jeong and Hussian. 5 These schemes are numerically simple and physically straightforward. There are two main schemes advanced along these lines.Rather than simply balancing pressure and centrifugal forces in a swirling flow, as assumed in the p scheme, Jeong and Hussian 5 subtracted unsteady and viscous straining terms from the pressure Hessian, and derived the widely used 2 scheme ͑ 2 ഛ 0 regions identify vortices͒. 2 is the second largest eigenvalue of the symmetric tensor ⍀ 2 + S 2 . Here, ⍀ and S are the vorticity and strain-rate tensors-the antisymmetric and symmetric parts of the velocity gradient tensor ١u, respective...

Today there are still many challenges in the quantitative interpretation of downhole distributed temperature measurements to diagnose multistage fracture treatments in horizontal wells. These challenges include handling enormous amount of data measured by the sensors continuously in time and space domain, a readily-to-be-used fast but robust forward model to simulate temperature behavior, and an efficient algorithm to inverse the parameters that are of interest. Because multistage fracturing involves many uncertain parameters; ranging from reservoir properties to treatment design, to fracture geometries and conductivity; the problem is extremely complex when inverse the measured temperature to a downhole flow profile. This study presents an approach to combine forward and inversion models to interpret downhole temperature data. The goal is to improve computational efficiency. Examples use the field data from a gas well in Marcellus shale formation to illustrate the feasibility of quantitative interpretation of temperature measurement for fracture diagnosis. The forward model uses the fast marching method. The forward simulation is order-of-magnitude faster than even the semi-analytical model, which is the essential contribution to apply the method in the field case successfully. The inversion procedure starts with a sensitivity study to select the inversion parameters among various parameters such as fracture half-length, fracture conductivity, and determine the impact of their uncertainty on inversion. The inversion model uses the initial analysis on temperature gradient to identify the zones with significant temperature changes for interpretation and eliminates the rest of the data from interpretation. Thus, we obtain a prior estimation of the selected inversion parameters, which will be used as an initial guess of the inversion process. This prior estimation saves significant computation. The inversion is performed fracture by fracture either using parallel computing or sequential computing based on the sensor locations. We first show a synthetic example with multiple fractures to illustrate the approach, test the procedure accuracy and computation speed. The primary inversion parameter is flow rate, and either fracture length or fracture conductivity, with all other parameters as an additional constraint. With an adequate initial guess, the inverted parameters match the reference "true value" properly. The inversion process converges with limited iterations for each fracture. The operation time highlights the advantages of the inversion model. The guided initial guess ensures the gradient inversion method converge and avoid local minimization. Finally, a field application is performed using this inversion model and shows encouraging results. The results of the paper illustrate the feasibility and procedure of using temperature date to diagnose multistage fracture treatment. The proposed inversion model is fast and reliable which provides a promising tool that can be used to interpret downhole temperature data quantitatively.

The computation of model matrix in the iterative imaging reconstruction process is crucial for the quantitative photoacoustic tomography (PAT). However, it is challenging to establish an outstanding model matrix to improve the overall imaging quality in PAT due to the noisy signal acquisition and inevitable artifacts. In this work, we present a novel method, named as the curve-driven-based model-matrix inversion (CDMMI), to calculate the model matrix for tomographic reconstruction in photoacoustic imaging. It eliminated the use of interpolation techniques, and thus avoided all interpolation related errors. The conventional interpolated-matrix-model inversion (IMMI) method was applied to evaluate its performance in numerical simulation, tissue-mimicking phantom and in vivo small animal studies. Results demonstrated that CDMMI achieved better reconstruction accuracy until IMMI kept increasing discrete points to 10000. Furthermore, the proposed method can suppress the negative influence of noise and artifacts effectively, which benefited the overall imaging quality of photoacoustic tomography.