Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization

Towards Positive Geometry of Multi Scalar Field Amplitudes : Accordiohedron and Effective Field Theory

The geometric structure of S-matrix encapsulated by the "Amplituhedron program" has begun to reveal itself even in non-supersymmetric quantum field theories. Starting with the seminal work of Arkani-Hamed, Bai, He and Yan it is now understood that for a wide class of scalar quantum field theories, tree-level amplitudes are canonical forms associated to polytopes known as accordiohedra. Similarly the higher loop scalar integrands are canonical forms associated to so called type-D cluster polytopes for cubic interactions or recently discovered class of polytopes termed pseudo-accordiohedron for higher order scalar interactions. In this paper, we continue to probe the universality of these structures for a wider class of scalar quantum field theories. More in detail, we discover new realisations of the associahedron in planar kinematic space whose canonical forms generate (colour-ordered) tree-level S matrix of external massless particles with $n-4$ massless poles and one massive pole at $m^{2}$. The resulting amplitudes are associated to $\lambda_{1}\, \phi_{1}^{3}\, +\, \lambda_{2}\, \phi_{1}^{2}\phi_{2}$ potential where $\phi_{1}$ and $\phi_{2}$ are massless and massive scalar fields with bi-adjoint colour indices respectively. We also show how in the "decoupling limit" (where $m \rightarrow \infty, \lambda_{2} \rightarrow \infty$ such that $g := \frac{\lambda_{2}}{m} = \textrm{finite}$) these associahedra project onto a specific class of accordiohedron which are known to be positive geometries of amplitudes generated by $\lambda \phi_{1}^{3} + g \phi_{1}^{4}$.Comment: 43 pages, 11 Figure

HISTOPATHOLOGICAL STUDY OF ENDOMETRIUM IN ABNORMAL UTERINE BLEEDING IN REFERENCE TO DIFFERENT AGE GROUPS, PARITY AND CLINICAL SYMPTOMATOLOGY

Background: Abnormal uterine bleeding is the commonest presenting symptom and major gynecological problem responsible for as many as one-third of all out patient gynecologic visit. An understanding of the varieties in the normal morphological appearance of the endometrium provides an essential background for the evaluation of endometrial pathology. Aims: To study the histopathology of endometrial biopsies in patients presenting with abnormal uterine bleeding and its correlation with age, parity and bleeding pattern Methods: This was a study done at tertiary care hospital from 2012-2014. Endometrial biopsies obtained from 100 cases of patients presenting with abnormal uterine bleeding were studied followed by correlation of endometrial histopathology with parity, age and bleeding pattern. Results: The most common age group presenting with abnormal uterine bleeding was 41-50 years (31%).The commonest pathology was proliferative endometrium (29%).The commonest bleeding pattern was menorrhagia (88%) and highest incidence was seen in multiparous women(58%).Conclusion: Endometrial biopsy should be recommended during the workup of patients presenting with abnormal uterine bleeding to exclude organic pathology of endometrium KEYWORDS: Abnormal uterine bleeding; Menorrhagia; Endometrium; Endometrial biopsy

Positive Geometries of S-matrix without Color

In this note, we prove that the realization of associahedron discovered by Arkani-Hamed, Bai, He, and Yun (ABHY) is a positive geometry for tree-level S-matrix of scalars which have no color and which interact via cubic coupling. More in detail, we consider diffeomorphic images of the ABHY associahedron. The diffeomorphisms are linear maps parametrized by the right cosets of the Dihedral group on n elements. The set of all the boundaries associated with these copies of ABHY associahedron exhaust all the simple poles. We prove that the sum over the diffeomorphic copies of ABHY associahedron is a positive geometry and the total volume obtained by summing over all the dual associahedra is proportional to the tree-level S matrix of (massive or massless) scalar particles with cubic coupling. We then provide non-trivial evidence that the projection of the planar scattering forms parametrized by the Stokes polytope on these realizations of the associahedron leads to the tree-level amplitudes of scalar particles, which interact via quartic coupling. Our results build on ideas laid out in our previous works, leading to further evidence that a large class of positive geometries which are diffeomorphic to the ABHY associahedron defines an ``amplituhedron" for a tree-level S matrix of some local and unitary scalar theory. We also highlight a fundamental obstruction in applying these ideas to discover positive geometry for the one loop integrand when propagating states have no color.Comment: 33 Pages, 4 Figure

A Review Paper on Big data & Hadoop

Big data is dataset that having the ability to capture, manage & process the data in elapsed time .Managing the data is the big issue. And now days the huge amount of data is produced in the origination so the big data concept is in picture. It is data set that can manage and process the data. For managing the data the big data there are many technique are used .One of this technique is Hadoop. Hadoop can handle the huge amount of data, it is very cost effective, and it can handle huge amount of data so processing speed is very fast, and also it can create a duplicate copy of data in case of system failure or to prevent the loss of data.This paper contains the Introduction of big data and Hadoop, characteristics of big data ,problem associated with big data, architecture of big data and Hadoop, other component of hadoop, advantages, disadvantages and applications of Hadoop and also the conclusion

An In-Depth Statistical Review of Retinal Image Processing Models from a Clinical Perspective

The burgeoning field of retinal image processing is critical in facilitating early diagnosis and treatment of retinal diseases, which are amongst the leading causes of vision impairment globally. Despite rapid advancements, existing machine learning models for retinal image processing are characterized by significant limitations, including disparities in pre-processing, segmentation, and classification methodologies, as well as inconsistencies in post-processing operations. These limitations hinder the realization of accurate, reliable, and clinically relevant outcomes. This paper provides an in-depth statistical review of extant machine learning models used in retinal image processing, meticulously comparing them based on their internal operating characteristics and performance levels. By adopting a robust analytical approach, our review delineates the strengths and weaknesses of current models, offering comprehensive insights that are instrumental in guiding future research and development in this domain. Furthermore, this review underscores the potential clinical impacts of these models, highlighting their pivotal role in enhancing diagnostic accuracy, prognostic assessments, and therapeutic interventions for retinal disorders. In conclusion, our work not only bridges the existing knowledge gap in the literature but also paves the way for the evolution of more sophisticated and clinically-aligned retinal image processing models, ultimately contributing to improved patient outcomes and advancements in ophthalmic care

HISTOPATHOLOGICAL STUDY OF ENDOMETRIUM IN ABNORMAL UTERINE BLEEDING IN REFERENCE TO DIFFERENT AGE GROUPS, PARITY AND CLINICAL SYMPTOMATOLOGY

Background: Abnormal uterine bleeding is the commonest presenting symptom and major gynecological problem responsible for as many as one-third of all out patient gynecologic visit. An understanding of the varieties in the normal morphological appearance of the endometrium provides an essential background for the evaluation of endometrial pathology. Aims: To study the histopathology of endometrial biopsies in patients presenting with abnormal uterine bleeding and its correlation with age, parity and bleeding pattern Methods: This was a study done at tertiary care hospital from 2012-2014. Endometrial biopsies obtained from 100 cases of patients presenting with abnormal uterine bleeding were studied followed by correlation of endometrial histopathology with parity, age and bleeding pattern. Results: The most common age group presenting with abnormal uterine bleeding was 41-50 years (31%).The commonest pathology was proliferative endometrium (29%).The commonest bleeding pattern was menorrhagia (88%) and highest incidence was seen in multiparous women(58%).Conclusion: Endometrial biopsy should be recommended during the workup of patients presenting with abnormal uterine bleeding to exclude organic pathology of endometrium KEYWORDS: Abnormal uterine bleeding; Menorrhagia; Endometrium; Endometrial biopsy

Characterization of wheat (Triticum aestivum L.) genotypes unraveled by molecular markers considering heat stress

204-213The current study focuses and emphasis on the potential of heat stress to negatively affect crop physiology. Here, we have screened 19 wheat (Triticum aestivum L.) genotypes for their tolerance of heat stress. Significant differences were observed among the genotypes for all the traits under consideration. Exploitable extent of genetic variability amongst the entries was present as revealed by considerably higher estimates of mean percentage. On the basis of heat susceptibility index genotypes, Halna, Mon’s Ald’s, Cuo/79/Prulla and K 307 were identified as heat-tolerant whereas SAWSN 3041, SAWSN 3101 and K 0583 were identified as heat-susceptible. Seventeen wheat microsatellite markers were capable of detecting 89 alleles with an average of 4.6 alleles per locus. Polymorphism information content (PIC) value ranged from 0.16 for the primer XGWM 516 to 0.83 for DUPW 117 with an average of 0.60. A perusal of similarity coefficients clearly reflected that a very high degree of similarity exists between wheat variety Mon’s Ald’s and SAWSN 3101 (0.70). On the other hand, the two most distantly related cultivars were found to be AKAW 4008 and PBW 343 (0.034). Marker BARC 4, BARC 170, BARC 311, PSP 3058, WHE014. H04 and GWM 458 were strongly associated with the heat tolerance for traits TGW and BARC 311 were strongly associated with terminal heat tolerance for number of grains/plant, respectively. Considering all the parameters it is adjudged that relatively stable genotypes may be evaluated at various agro-climatic regions for grain yield and heat tolerance along with other contributing characters and ideal plant type