Real Contours Research Articles

Unstable instantons in A-model localization

We apply localization techniques to A-twisted N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = (2) theories of vector multiplets on S2. We derive formulae for A-model partition functions and correlators as integrals along a real contour, as opposed to a complex one. Using the correlator formula, we successfully recover the unstable instanton partition function of pure two-dimensional Yang-Mills theory from the vacuum expectation value of an A-model operator.

A landscape pattern gradient analysis method coupling wavelet algorithm for balancing development and protection activities of the coastal zone: A case study

Due to the economic importance and ecological vulnerability of coastal areas, the optimization of spatial patterns is important for the sustainable development of coastal zones. In this study, a new landscape pattern index gradient analysis method coupled with wavelet algorithm (GA-WA) was explored to balance the development and protection activities in the coastal zone. First, based on the classification results of remote sensing images, the gradient detection of the coastal zone was carried out using the cumulative moving window method, and the calculation of the landscape pattern index was carried out using Fragstats software to obtain the gradient change curve of the landscape pattern index. Secondly, the wavelet algorithm was applied to micro-analyze the above gradient change curves, and the results of multiscale analysis of the landscape pattern index in the study area were obtained. Finally, it is demonstrated how this method can help in practical decision making. It was found that:(1) The landscape pattern index gradient analysis method coupled with wavelet algorithms offers a new approach to balance the development and protection of coastal zones. This approach presents an innovative method for optimizing the ecological pattern of coastal zone landscapes from the perspective of macro–micro combination, which is not only applicable to coastal zones but also can be extended to other strip corridor landscapes.(2) The gradient analysis of the coastal zone landscape pattern index provides results at multiple spatial scales, which is superior to the analysis at a single spatial scale. The results of the gradient analysis method are finer and more stable, which solves the uncertainty problem of traditional landscape pattern index analysis. There is a significant difference between the landscape indices of the overall landscape and the gradient landscape, in which the AREA_MN index of the ecological land has the largest difference, reaching 110.18%.(3) Wavelet coefficient variance diagrams, real component contour diagrams, and modulus squared diagrams reveal the characteristics, cycles, and patterns of landscape dynamics changes, as well as the distribution at different gradient window scales. These tools help to identify the driving factors and development trends of landscape dynamics changes and solve problems of functional positioning in undeveloped areas, as well as the transformation of microscopic small parcels within developed areas. By analyzing regular cycles of landscape index changes, it is possible to determine the functional positioning of land and to position human intervention through peaks to guard against risky gradient windows.

A study on the correlation of cyclical fluctuations in vegetable commodity sales based on wavelet analysis modeling

As the sales volume and time of vegetable commodities tend to have a certain correlation, in order to explore the distribution law of the sales volume of each category and single product of vegetables, this paper firstly handles the data to get the monthly sales volume of each vegetable category and single product of time series data, then uses Matlab's Wavelet Toolbox to carry out wavelet analysis,drawing wavelet variance diagrams, the main cycle trend graph to judge the cyclical pattern of each vegetable category and single product,and then use Origin to make wavelet coefficients real part contour graph to verify the law, and finally get the distribution law. This study can help superstores better grasp the sales situation and development trend of each vegetable category and single product.

Unsupervised corneal contour extraction algorithm with shared model for dynamic deformation videos: improving accuracy and noise resistance

BackgroundIn this study, an automatic corneal contour extraction algorithm with a shared model is developed to extract contours from dynamic corneal videos containing noise, which improves the accuracy of corneal biomechanical evaluation and clinical diagnoses. The algorithm does not require manual labeling and completes the unsupervised semantic segmentation of each frame in corneal dynamic deformation videos based on a fully convolutional deep-learning network using corneal geometry and texture information.ResultsWe included 1027 corneal videos at Tianjin Eye Hospital (Nankai University Affiliated Eye Hospital) from May 2020 to November 2021. The videos were obtained by the ultra-high-speed Scheimpflug camera, and then we used the shared model mechanism to accelerate the segmentation of corneal regions in videos, effectively resist noise, determine corneal regions based on shape factors, and finally achieve automatic and accurate extraction of corneal region contours. The Intersection over Union (IoU) of the extracted and real corneal contours using this algorithm reached 95%, and the average overlap error was 0.05, implying that the extracted corneal contour overlapped almost completely with the real contour.ConclusionsCompared to other algorithms, the method introduced in this study does not require manual annotation of corneal contour data in advance and can still extract accurate corneal contours from noisy corneal videos with good repeatability.

Perception of illusory contours in children and adults: An eye-tracking study.

The eye-tracking study investigated the perception of subjective Kanizsa and Ehrenstein figures in adults and in children aged 3-4, 5-6, 7-8, and 9-11 years of age. More specifically, the distribution of looking at the inner stimulus part versus the inducing elements was measured for illusory figures, figures with real contours, and control displays. It was hypothesized that longer looking at the inner area of the illusory figures indicates global contour interpolation, whereas longer looking at the inducing elements indicates a local processing mode. According to the results, participants of all ages looked longer at the illusory Kanizsa and Ehrenstein contours than at the figures' inducing elements. However, performance was lowest in the children aged 3-4 years and increased during the preschool period. Moreover, the illusory contour displays elicited comparable visual responses as did the real contour displays. The use of the control displays that contained no contour information ensured that the participants' looking behavior was not driven by a spontaneous tendency to attend to the inner stimulus parts. The study confirms the view that sensitivity to illusory contours emerges very early in life.

BallastGAN: Random generation of ballast particle contour based on generative adversarial networks

Railway ballast particles exhibit unique variations in shape, and this diversity significantly impacts the mechanical performance of ballast beds. An intuitive approach involves defining corresponding morphological parameters through morphological analysis of particle contours to randomly generate ballast particle contours. This involves deriving the probability distribution of these parameters based on mathematical statistics of ballast particle samples. However, due to the empirical nature and underlying assumptions of these morphological parameters, the accuracy of the generated particle contours is often compromised. To generate highly realistic ballast particle images, we propose a novel model named BallastGAN for random ballast particle contour generation. This model employs fractal dimension regularization and optimizes the loss function of the discriminator within the framework of StyleGAN3. This optimization effectively controls the roughness characteristics of generated ballast particle images. Mutual transformation and style blending between different ballast particle contours are achieved by decoupling the latent space. The ballast particle image dataset (BPID) is curated to train the model. Experimental results demonstrate that the proposed model's randomly generated ballast particle contours exhibit a remarkably high degree of consistency with real contours. This indicates that the generated contours can be directly applied to numerical simulations in mechanics.

Feasibility of Using a Single Planning MRI for Two-Insertion Intracavitary Brachytherapy for Cervical Cancer

MRI is an essential tool in treatment planning for cervical cancer patients undergoing definitive chemoradiation involving brachytherapy. However, due access to MRI for many patients may be limited. We sought to examine the feasibility and quality of treatment planning for organs at risk (OAR) and target volumes of a single treatment planning MRI for a planned two-insertion HDR intracavitary cervical brachytherapy. Eighteen patients with cervical cancer who underwent MRI-based treatment planning for intracavitary brachytherapy were selected for analysis. Patients underwent two intracavitary applicator insertions using a tandem and ring applicator (TnR_1 and TnR_2) with both CT (for digitization only) and MRI following each insertion and two fractions delivered with each insertion (total 7 Gy x 4fx). MRI-based TnR_2 plans were retrospectively replanned with the following procedure: 1) register MRI from TnR_1 to TnR_2 CT, 2) transfer cervix contour (Cx_simul) and plan from TnR_1 to TnR_2 CT, simulating blinding from TnR_2 MRI, 3) crop Cx_simul from TnR_2 OARs, 4) adjust plan only to meet OAR constraints or clinical doses if clinical plan (TnR_2 original MRI plan summed with TnR_1 and EBRT doses) violates constraints. Coverage changes (∆_D90%) in actual MRI defined TnR_2 cervix (Cx_real) was compared to clinical plans and evaluated against our clinical target goal: >85 Gy EQD2 (EBRT+BT). Differences between Cx_simul and Cx_real contours were evaluated with Dice Similarity Coefficient (DSC). Changes in bladder, rectum, rectosigmoid, and bowel D2cc was evaluated. Procedure time was recorded to determine time added by MRI (time between CT and final MRI timestamps; n = 29). Plan modification to meet OAR constraints was required for 5/18 plans. Cx_real target coverage from clinical to simulated plans decreased in 7/18 plans (∆_D90% = 1.7±6%). Composite EQD2 was <85 Gy in 2/18 cases, with ∆_D90% of -1.3% (clinical EQD2<85 Gy for this case also) and -7.3%, which was due to inconsistent cervix shape between insertions 1 and 2. Cervix DSC values between Cx_simul and Cx_real ranged from 0.68-0.88 (mean = 0.78 ± 0.06). Bladder, rectum, rectosigmoid, and bowel D2cc increased on average 4 ± 12%, 3 ± 9%, 5 ± 10%, and 5 ± 17%, respectively. Including planning MRI increased procedure time by 41.8 ± 10.4 min. The proposed method of utilizing TnR_1 MRI contours for TnR_2 CT planning reduces procedure time and provides reasonable target coverage for most cases. OAR assessment varies between imaging modality which likely represents variability in OAR position rather than treatment planning modality. Next steps are to increase patients studied, and implement this technique prospectively while waiting for TnR_2 MRI completion and compare the clinical TnR_2 MRI plan with the TnR_2 CT plan created with Cx_simul. This will provide further confidence in validity of the approach and ensure plan quality is maintained prior to full implementation.

Occlusion-Aware Instance Segmentation Via BiLayer Network Architectures.

Segmenting highly-overlapping image objects is challenging, because there is typically no distinction between real object contours and occlusion boundaries on images. Unlike previous instance segmentation methods, we model image formation as a composition of two overlapping layers, and propose Bilayer Convolutional Network (BCNet), where the top layer detects occluding objects (occluders) and the bottom layer infers partially occluded instances (occludees). The explicit modeling of occlusion relationship with bilayer structure naturally decouples the boundaries of both the occluding and occluded instances, and considers the interaction between them during mask regression. We investigate the efficacy of bilayer structure using two popular convolutional network designs, namely, Fully Convolutional Network (FCN) and Graph Convolutional Network (GCN). Further, we formulate bilayer decoupling using the vision transformer (ViT), by representing instances in the image as separate learnable occluder and occludee queries. Large and consistent improvements using one/two-stage and query-based object detectors with various backbones and network layer choices validate the generalization ability of bilayer decoupling, as shown by extensive experiments on image instance segmentation benchmarks (COCO, KINS, COCOA) and video instance segmentation benchmarks (YTVIS, OVIS, BDD100 K MOTS), especially for heavy occlusion cases.

Dosimetric and workflow impact of synthetic-MRI use in prostate high-dose-rate brachytherapy

Target and organ delineation during prostate high-dose-rate (HDR) brachytherapy treatment planning can be improved by acquiring both a postimplant CT and MRI. However, this leads to a longer treatment delivery workflow and may introduce uncertainties due to anatomical motion between scans. We investigated the dosimetric and workflow impact of MRI synthesized from CT for prostate HDR brachytherapy. Seventy-eight CT and T2-weighted MRI datasets from patients treated with prostate HDR brachytherapy at our institution were retrospectively collected to train and validate our deep-learning-based image-synthesis method. Synthetic MRI was assessed against real MRI using the dice similarity coefficient (DSC) between prostate contours drawn using both image sets. The DSC between the same observer's synthetic and real MRI prostate contours was compared with the DSC between two different observers' real MRI prostate contours. New treatment plans were generated targeting the synthetic MRI-defined prostate and compared with the clinically delivered plans using target coverage and dose to critical organs. Variability between the same observer's prostate contours from synthetic and real MRI was not significantly different from the variability between different observer's prostate contours on real MRI. Synthetic MRI-planned target coverage was not significantly different from that of the clinically delivered plans. There were no increases above organ institutional dose constraints in the synthetic MRI plans. We developed and validated a method for synthesizing MRI from CT for prostate HDR brachytherapy treatment planning. Synthetic MRI use may lead to a workflow advantage and removal of CT-to-MRI registration uncertainty without loss of information needed for target delineation and treatment planning.

Hierarchical Tensor Decomposition of Module Partition for the Mechanical Simulation

The mechanical simulation experiment can provide guidelines for the structural design of materials, but the module partition of mechanical simulation experiments is still in its infancy. A mechanical simulation contour, e.g., strain and stress contour, has hierarchical characteristics. By analyzing the contour at different layers, the physical properties of the structure material can be improved. Current state-of-the-art methods cannot distinguish between simulation strain contours, as well as sparsely distributed spots of strain (stress concentrations) from simulation strain contour images, resulting in simulation data that does not accurately reflect real strain contours. In this paper, a Hierarchical Tensor Decomposition (HTD) method is proposed to extract hierarchical contours and stress concentrations from the simulation strain contours and then improve the mechanical simulation. HTD decomposes a tensor into three classes of components: the multi-smooth layers, the sparse spots layer, and the noise layer. The number of multismooth layers is determined by the scree plot, which is the difference between the smooth layers and the sparse spots layer. The proposed method is validated by several numerical examples, which demonstrate its effectiveness and efficiency. A further benefit of the module partition is the improvement of the mechanical structural properties.

Ship Contour Extraction From SAR Images Based on Faster R-CNN and Chan–Vese Model

Compared with most ship detection methods for synthetic aperture radar (SAR) images, ship contour extraction can provide more of the detailed shape and edge information of an observed ship and play a significant role in sea surface monitoring and marine transportation. In this study, a joint ship contour extraction method (Faster R-CNN, FNLM, and Chan-Vese model; FFCV method) was proposed to obtain detailed ship information from SAR images, including ship detection in complex scenes and contour extraction in target slices. First, Faster R-CNN was employed to slice ships from large-scene SAR images. Then, Fast non-local mean (FNLM) filtering was applied to denoise and enhance the structural information of the target slices. Finally, an optimized Chan-Vese model was proposed in this paper, which can not only accurately extract the contour of the observed ship, but also reduce the computation time of the model. The SAR ship detection dataset (SSDD) was selected and finely relabeled to evaluate the contour extraction performance. An evaluation index <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_N</i> , including quantitative value and offset direction, was developed to evaluate the extraction accuracy of the target contour from the SAR images. Compared with the Mask R-CNN network, the average contour extraction accuracy index <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R_N</i> of the proposed FFCV method reached -0.002 on all the images in SSDD dataset, and its results were closer to the real ship contours while maintaining the applicability to complex scenes.

DEEP LEARNING APPROACHES FOR ANOMALIES DETECTION OF BLADDER CT CONTOURS IN PROSTATE CANCER PATIENTS

In radiation therapy, poor contour delineations of Region of Interests (ROI) may result in incorrect radiation dosing and increase the chance of radiation-induced toxicities. To better recognize these contours, we used a feature fusion-based 3-dimensional convolution neural network (3D-CNN), multi-view convolution neural network (MV-CNN), and 3D point cloud to retrospectively detect abnormal bladder contours among prostate cancer patients. We defined three patterns of abnormal bladder contours: (1) discontinuities: missing slices and disparate volumes, (2) surface aberrations: extended or contracted slices, (3) small volume: bladder volume [Formula: see text][Formula: see text]ml. We created virtual samples for discontinuities and surface aberrations by randomly adding pixel to one or more slices outside the original contours and randomly extending or shrinking one or more slices. For both 3D-CNN and MV-CNN methods, we utilized the Local Binary Pattern (LBP) and Canny operators for feature extraction and compared several feature fusion-based approaches, including Original image + LBP processed image, Original image + Canny processed image, Original image + LBP processed image + Canny processed image. For the 3D point cloud, we applied the 3D point cloud segmentation method (Rand LA-Net) and the 3D point cloud classifying method (DGCNN). We had 344 samples available (219 real contours and 125 virtual contours) altogether. All the algorithms were trained on 200 bladder contours, validated on 100 bladders, then tested on 44 real annotated contours. Among all the approaches, the “Original + LBP”-based MV-CNN model achieved the highest accuracy: 100% for predicting discontinuity and small volume, 91.3% for predicting normal contours, and 90.9% for predicting surface aberrations. MV-CNN performed more accurately and efficiently across all the feature fusion methods. In particular, “Original + LBP”-based MV-CNN achieved the highest test accuracy. Our tools can detect anomalies of bladder contours in clinical settings and may improve the process of contour quality assurance (QA).

Gravitational thermodynamics without the conformal factor problem: partition functions and Euclidean saddles from Lorentzian path integrals

Thermal partition functions for gravitational systems have traditionally been studied using Euclidean path integrals. But in Euclidean signature the gravitational action suffers from the conformal factor problem, which renders the action unbounded below. This makes it difficult to take the Euclidean formulation as fundamental. However, despite their familiar association with periodic imaginary time, thermal gravitational partition functions can also be described by real-time path integrals over contours defined by real Lorentzian metrics. The one caveat is that we should allow certain codimension-2 singularities analogous to the familiar Euclidean conical singularities. With this understanding, we show that the usual Euclidean-signature black holes (or their complex rotating analogues) define saddle points for the real-time path integrals that compute our partition functions. Furthermore, when the black holes have positive specific heat, we provide evidence that a codimension-2 subcontour of our real Lorentz-signature contour of integration can be deformed so as to show that these black holes saddles contribute with non-zero weight to the semiclassical limit, and that the same is then true of the remaining two integrals.

Dense and Small Object Detection in UAV-Vision Based on a Global-Local Feature Enhanced Network

Unmanned aerial vehicles (UAVs) have been widely used in post-disaster search and rescue operations, object tracking, and other tasks. Therefore, the autonomous perception of UAVs based on computer vision has become a research hotspot in recent years. However, UAV images include dense objects, small objects, and arbitrary object directions, which bring about significant challenges to existing object detection methods. To alleviate these issues, we propose a global-local feature enhanced network (GLF-Net). Considering the difficulty of processing UAV images with complex scenes and dense objects, we designed a backbone based on an involution and self-attention that can extract effective features from complex objects. A multiscale feature fusion module is also proposed to address the presence of numerous small objects in UAV images through multiscale object detection and feature fusion. To accurately detect rotated objects, a rotated regional proposal network was designed based on the midpoint offset representation, which can apply a rotated box to determine the real direction and contour of an object. GLF-Net achieves a state-of-the-art detection accuracy (86.52% mAP) on our created RO-UAV dataset, while achieving 96.95% and 97% mAP on the public datasets HRSC2016 and UCAS-AOU, respectively. The experimental results demonstrate that our method achieves a high detection accuracy and generalization, which can meet the practical requirements of UAVs under various complex scenarios.

Construction of a mechanical model of the human heart left ventricle in the process of its contraction

A detailed analysis of previous works on modeling the left ventricle (LV) of the human heart, starting with mechanical models in the form of the simplest three-dimensional figures (cylinder, sphere, ellipsoid of rotation) and ending with models using real contours of the human heart obtained by ultrasound examination of the human heart. A way of constructing a mechanical LV model based on the processing of its dynamic images obtained using computer and magnetic resonance imaging was proposed. Digitization of these images was carried out using numerical methods developed to create a finite element model were implemented in the CMISS system, which allows the use of finite element analysis methods to solve various complex problems. To avoid the need to operate with huge arrays of numbers (up to 10 thousand numerical values at each time of the MRI study) characteristic points of the three-dimensional LV image were selected and spline interpolation of the model framework written in C++ using the Cmgui module was performed. To describe the work of the mechanical model of LV reduction, the main components of this process were identified: transverse compression, longitudinal contraction and twisting. To describe them, simple mathematical characteristics were used.

The Economic and political components of diplomatic discourse: State actors in Morocco-UK Free Trade Agreement as a case study

Morocco is the UK’s 58 th largest trading partner (ONS, 2019). Based on this fact, a new perception of the state actors’ role in diplomacy should be brought into play and transformational force of economic actors may be the appraiser and monitor of international relations. Diplomatic and economic actors’ effective performance lies on their capacity to go beyond the usual standards of the main institutional narrative and reshape their own narrative. What are the real contours of the state actors’ instrumentality under the pressure of institutional directives? And how are institutional pressures constructed and the extent to which they shape the state actors’ discourse? We have conducted a textual analysis of political discourse based on the interventions made by three interveners to understand and analyse the interests of the UK and Morocco as determined by their institutional logics. State actors’ effective performance on a diplomatic scale seems practicably incapable to go beyond the usual standards of the main institutional narrative and reshape their own narrative. State actors are indeed far from bringing about change and consolidate a more harmonious standpoint vis-a-vis the official diplomatic and economic perspective.

Vectorized instance segmentation using periodic B-splines based on cascade architecture

Instance segmentation is an essential part of image semantic understanding. In this paper we propose a novel cascade framework for instance segmentation. Unlike some existing methods that only output contour discrete coordinates, our approach obtains a vectorized representation of contours using periodic B-splines. In order to make better use of geometry and appearance information, we consider the global and local features of objects and introduce two types of graph structures, the star graph and circular graph, for feature extraction. Thereby, we develop a neural network, termed the mix network, to better exploit extracted features. Specifically, we first regress the spline control points to an object boundary via the mix network, then perform spline sampling to obtain the initial predictions of contours, and finally deform the predicted contours to the real contours of the objects. In addition, we add a regularization to further constrain the fairness of contour splines. Experiments show that our approach achieves 34.6% in mask mAP, Mean Average Precision, with a ResNet-101-FPN-DCN backbone on the challenging COCO benchmark, which significantly improves the performance of contour-based methods.

FEMOSSA: Patient-specific finite element simulation of the prostate-rectum spacer placement, a predictive model for prostate cancer radiotherapy.

Major advances in delivery systems in recent years have turned radiotherapy (RT) into a more effective way to manage prostate cancer. Still, adjacency of organs at risk (OARs) can severely limit RT benefits. Rectal spacer implant in recto-prostatic space provides sufficient separation between prostate and rectum, and therefore, the opportunity for potential dose escalation to the target and reduction of OAR dose. Pretreatment simulation of spacer placement can potentially provide decision support to reduce the risks and increase the efficacy of the spacer placement procedure. A novel finite element method-oriented spacer simulation algorithm, FEMOSSA, was developed in this study. We used the finite element (FE) method to model and predict the deformation of rectum and prostate wall, stemming from hydrogel injection. Ten cases of prostate cancer, which undergone hydrogel placement before the RT treatment, were included in this study. We used the pre-injection organ contours to create the FE model and post-injection spacer location to estimate the distribution of the virtual spacer. Material properties and boundary conditions specific to each patient's anatomy were assigned. The FE analysis was then performed to determine the displacement vectors of regions of interest (ROIs), and the results were validated by comparing the virtually simulated contours with the real post-injection contours. To evaluate the different aspects of our method's performance, we used three different figures of merit: dice similarity coefficient (DSC), nearest neighbor distance (NND), and overlapped volume histogram (OVH). Finally, to demonstrate a potential dosimetric application of FEMOSSA, the predicted rectal dose after virtual spacer placement was compared against the predicted post-injection rectal dose. Our simulation showed a realistic deformation of ROIs. The post-simulation (virtual spacer) created the same separation between prostate and rectal wall, as post-injection spacer. The average DSCs for prostate and rectum were 0.87 and 0.74, respectively. Moreover, there was a statistically significant increase in rectal contour similarity coefficient (P<0.01). Histogram of NNDs showed the same overall shape and a noticeable shift from lower to higher values for both post-simulation and post-injection, indicative of the increase in distance between prostate and rectum. There was less than 2.2- and 2.1-mm averaged difference between the mean and fifth percentile NNDs. The difference between the OVH distances and the corresponding predicted rectal dose was, on average, less than 1mm and 1.5Gy, respectively. FEMOSSA provides a realistic simulation of the hydrogel injection process that can facilitate spacer placement planning and reduce the associated uncertainties. Consequently, it increases the robustness and success rate of spacer placement procedure that in turn improves prostate cancer RT quality.

Numerical modeling of an outdoor unit heat exchanger for residential heat pump systems with nonuniform airflow and refrigerant distribution

Multirow finned tube heat exchangers have been extensively used as an outdoor unit in heat pump applications. Several factors, including nonuniform airflow distribution, refrigerant circuitry arrangement, fin and tube configurations, and operating conditions, have a significant influence on its thermohydraulic performance. For accurate outdoor unit heat exchanger modeling and analysis, developing a robust and experimentally validated numerical model reflecting the influence of realistic nonuniform airflow and refrigerant distribution is necessary. This paper presents a general-purpose numerical model, implemented in MATLAB, for a multirow finned tube heat exchanger using a tube-by-tube modeling approach based on the log mean enthalpy difference method. State-of-the-art heat transfer and pressure drop correlations are used for each refrigerant-side's flow regime and airside fin configuration. An alternative iteration loop is also incorporated to solve the complex circuitry of the heat exchanger under wet conditions. Simulation results of the current model yield consistent and more real heat transfer, pressure drop, and temperature contours using nonuniform airflow velocity profiles than those of the simplified models that assumed uniform airflow. Therefore, higher accuracy of the performance evaluation for complex refrigerant circuitry was achieved. Furthermore, current model is able to identify the exit vapor quality that allows proper selection of tubes and mass flow rates to avoid unnecessary superheat or sub cooling. The model is also validated with available experimental data, and the maximum error is within ±10.0%.

Real-time gravitational replicas: formalism and a variational principle

This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called ‘splitting surface’. This feature is an important hallmark of unitarity in a field theory dual.