A new approach to capture heterogeneity in groundwater problem: An illustration with an Earth equation

2019 ◽  
Vol 14 (3) ◽  
pp. 313 ◽  
Author(s):  
Abdon Atangana ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Exact Solution ◽  
Numerical Scheme ◽  
Differential Operators ◽  
New Approach ◽  
Flow Problems ◽  
The Earth ◽  
Time Differential ◽  
Geological Formation ◽  
Non Local ◽  
Real World Problems

One of the major problem faced in modeling groundwater flow problems is perhaps how to capture heterogeneity of the geological formation within which the flow takes place. In this paper, we suggested applied a newly established approach to model real world problems that combines the concept of stochastic modeling in which parameters inputs are converted into distributions and the time differential operator is replaced by non-local differential operators. We illustrated this method with the Earth equation of groundwater recharge. For each case, we provided numerical and exact solution using the newly established numerical scheme and Laplace transform. We presented some numerical simulations. The numerical graphical representations let no doubt to think that this approach is the future way of modeling complex problems.

A new approach to flow problems past a screen

1985 ◽  
Author(s):  
O. INOUE ◽  
K. KUWAHARA
Keyword(s):  
New Approach ◽  
Flow Problems

A new approach to the hydraulic fracture geometric dimensions determination

2017 ◽  
Vol 12 (1) ◽  
pp. 126-134
Author(s):  
A.M. Ilyasov
Keyword(s):  
Exact Solution ◽  
Hydraulic Fracture ◽  
Pressure Gauge ◽  
Hyperbolic Type ◽  
Fluid Injection ◽  
Fracturing Fluid ◽  
New Approach ◽  
Gauge Data ◽  
Bottomhole Pressure ◽  
Half Length

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.

Review of Network Flow Algorithms David P. Williamson

2021 ◽  
Vol 52 (1) ◽  
pp. 12-15
Author(s):  
S.V. Nagaraj
Keyword(s):  
Graduate Students ◽  
Real World ◽  
Network Flow ◽  
Network Flows ◽  
Optimization Problems ◽  
Capacity Constraints ◽  
Incoming Flow ◽  
Network Flow Problems ◽  
Flow Problems ◽  
Real World Problems

This book is on algorithms for network flows. Network flow problems are optimization problems where given a flow network, the aim is to construct a flow that respects the capacity constraints of the edges of the network, so that incoming flow equals the outgoing flow for all vertices of the network except designated vertices known as the source and the sink. Network flow algorithms solve many real-world problems. This book is intended to serve graduate students and as a reference. The book is also available in eBook (ISBN 9781316952894/US$ 32.00), and hardback (ISBN 9781107185890/US$99.99) formats. The book has a companion web site www.networkflowalgs.com where a pre-publication version of the book can be downloaded gratis.

On the Free Vibration of Mono-Coupled Periodic Distributed Parameter Systems

1993 ◽  
Author(s):  
Gerhard G. G. Lueschen ◽  
Lawrence A. Bergman
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Periodic Structure ◽  
Classical Result ◽  
Discrete Systems ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
New Approach

Abstract A new approach to the exact solution is given for the free vibration of a periodic structure comprised of a multiplicity of identical linear distributed parameter substructures, closely coupled through identical linear springs. The method used is an extension of a classical result for periodic discrete systems.

scholarly journals Gravitational differentiation in the regimes from stokes settling to Rayleigh–Raylor flows

2019 ◽  
pp. 15-30
Author(s):  
V. P. Trubitsyn
Keyword(s):  
Viscous Fluid ◽  
Interacting Particles ◽  
Small Particles ◽  
Continuous Transition ◽  
New Approach ◽  
Earth's Core ◽  
The Core ◽  
The Earth ◽  
Large Particles ◽  
Two Component

The Earth’s core was formed under gravitational differentiation in the course of the separation of iron and silicates. Most of the iron has gone into the core as early as when the Earth was growing. However, iron continued to precipitate even during the subsequent partial solidification which developed from the bottom upwards. At the different stages and in the different layers of the mantle, iron was deposited in different regimes. In this paper, the mechanisms of the deposition of a cloud of heavy interacting particles (or drops) in a viscous fluid are considered. A new approach suitable for analytical and numerical tracing the changes in the structure of the flows in a two-component suspension under continuous transition from the Stokessettling (for the case of a cloud of large particles) to the Rayleigh–Taylor flows and heavy diapirs (for the case of a cloud of small particles) is suggested. It is numerically and analytically shown that the both regimes are the different limiting cases of the sedimentation convection in suspensions.

Merengkuh Bumi Merawat Semesta: Mengupayakan Hermeneutik Ekologis dalam Rangka Menanggapi Kerusakan Lingkungan Dewasa Ini

2021 ◽  
Vol 1 (1) ◽  
pp. 71
Author(s):  
Darius Ade Putra
Keyword(s):  
Biblical Text ◽  
New Paradigm ◽  
New Approach ◽  
Ecological Damage ◽  
The Bible ◽  
The Earth ◽  
The 1960S ◽  
The Universe

Abstract Since the 1960s, started by Lynn White, Christianity has begun to get attacks because it is considered to have triggered ecological damage. Christianity through the teachings of the Bible is accused of legitimizing absolute anthropocentric ideas which then give rise to expansive actions to the environment and nature. In the midst of the massive damage to the environment and in order to fi nd a possible solution to this problem, it is felt necessary to resonance the new approach to the Scriptures that further explores the sound of the earth. One approach that can be developed is ecological hermeneutics. Based on several principles it is possible to see and understand the biblical text from the perspective of the earth. In addittion, this approach will be elaborated with local wisdom so that it can help the text contextualization process. In the end, a new paradigm is expected to encourage awareness of the importance to tend the universe.   Abstrak Sejak tahun 1960an, dimulai oleh Lynn White, Kekristenan mulai mendapat serangan karena dinilai telah menjadi pemicu kerusakan ekologi. Kekristenan melalui ajaran Alkitab dituduh melegitimasi gagasan-gagasan antroposentris absolut yang kemudian melahirkan tinndakan- tindakan ekspansif terhadap lingkungan dan alam. Di tengah masifnya kerusakan lingkungan dan dalam rangka mencari kemungkinan jalan keluar dari persoalan ini, dirasa perlu untuk menggemakan pendekatan baru pada Kitab Suci yang lebih mengeksplorasi suara bumi. Salah satu pendekatan yang bisa dikembangkan adalah hermeneutik ekologi. Berdasarkan beberapa prinsip-prinsipnya memungkinkan untuk melihat dan memahami teks Alkitab dari perspektif bumi. Selain itu, pendekatan ini akan dielaborasi dengan local widom agar membantu proses kontekstualisasi teks. Pada akhirnya diharapkan sebuah paradigma baru yang mendorong kesadaran akan pentingnya merawat alam semesta.

Genetic Algorithms in Fuzzy Engineering Design

1999 ◽  
Author(s):  
Ralf Schleiffer ◽  
Hans-Jürgen Sebastian ◽  
Erik K. Antonsson
Keyword(s):  
Engineering Design ◽  
Clustering Algorithm ◽  
Computer Application ◽  
Test Problems ◽  
Important Class ◽  
New Approach ◽  
Design Task ◽  
Evolutionary Technique ◽  
The Given ◽  
Real World Problems

Abstract Problems in the field of engineering design represent an important class of real world problems that typically require a fuzzy and imprecise representation. This article presents and discusses a new approach to model this type of problem, by incorporating linguistic descriptions together with a variety of user-defined trade-off strategies. An interactive computer application is introduced, using stochastic optimization to solve the design task by producing a specially desired output under the given environmental conditions which are partly caused by the personal preferences of the engineer and by the expectations of the customer. It utilizes a randomized evolutionary technique, made suitable for the class of problems at hand, to generate and to optimize design solutions that are later identified by a clustering algorithm. Moreover test problems that were solved by the application are considered. In all cases the good solutions were obtained by evaluating only an extremely small fraction of all possible designs.

Non-Local Elliptic Boundary-Value Problems

1968 ◽  
Vol 20 ◽  
pp. 1365-1382 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Differential Operators ◽  
Smooth Boundary ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Linear Operators ◽  
Elliptic Boundary Value Problem ◽  
Elliptic Boundary Value ◽  
Open Set ◽  
Non Local ◽  
Image Position

Let G be a bounded open set of Rn with a smooth boundary ∂G. We consider the following elliptic boundary-value problem:where A and Bj are, respectively singular integro-differential operators on G and on ∂G, of orders 2m and rj with rj < 2m; Ck are boundary differential operators, and Ljk are linear operators, bounded in a sense to be specified.

Sign in / Sign up

Export Citation Format

Share Document