Positive vector solutions for a Schrödinger system with external source terms

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Wei Long ◽  
Shuangjie Peng
Keyword(s):  
External Source ◽  
Source Terms ◽  
Positive Vector ◽  
Schrödinger System

Quantum mechanics

2018 ◽  
Author(s):  
Michael Kachelriess
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Transition Amplitude ◽  
External Source ◽  
Quantum Field ◽  
Damping Term ◽  
Relativistic Quantum Theory ◽  
Generating Functional

After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory should be based on quantum fields is explained.

scholarly journals Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1799
Author(s):  
Irene Gómez-Bueno ◽  
Manuel Jesús Castro Díaz ◽  
Carlos Parés ◽  
Giovanni Russo
Keyword(s):  
High Order ◽  
Collocation Methods ◽  
Quadrature Formulas ◽  
Balance Laws ◽  
Source Terms ◽  
Time Step ◽  
Systems Of Balance Laws ◽  
Reconstruction Operator ◽  
Non Linear ◽  
Linear Problems

In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced reconstruction operator. Moreover, they introduced a procedure to modify any standard reconstruction operator, like MUSCL, ENO, CWENO, etc., in order to be well-balanced. This strategy involves a non-linear problem at every cell at every time step that consists in finding the stationary solution whose average is the given cell value. In a recent paper, a fully well-balanced method is presented where the non-linear problems to be solved in the reconstruction procedure are interpreted as control problems. The goal of this paper is to introduce a new technique to solve these local non-linear problems based on the application of the collocation RK methods. Special care is put to analyze the effects of computing the averages and the source terms using quadrature formulas. A general technique which allows us to deal with resonant problems is also introduced. To check the efficiency of the methods and their well-balance property, they have been applied to a number of tests, ranging from easy academic systems of balance laws consisting of Burgers equation with some non-linear source terms to the shallow water equations—without and with Manning friction—or Euler equations of gas dynamics with gravity effects.

scholarly journals New general decay result for a system of two singular nonlocal viscoelastic equations with general source terms and a wide class of relaxation functions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Adel M. Al-Mahdi ◽  
Salim A. Messaoudi
Keyword(s):  
Wide Class ◽  
Relaxation Function ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
General Assumption ◽  
General Decay ◽  
Source Terms ◽  
Relaxation Functions ◽  
Viscoelastic Equations ◽  
General Source

Abstract This work is concerned with a system of two singular viscoelastic equations with general source terms and nonlocal boundary conditions. We discuss the stabilization of this system under a very general assumption on the behavior of the relaxation function $k_{i}$ k i , namely, $$\begin{aligned} k_{i}^{\prime }(t)\le -\xi _{i}(t) \Psi _{i} \bigl(k_{i}(t)\bigr),\quad i=1,2. \end{aligned}$$ k i ′ ( t ) ≤ − ξ i ( t ) Ψ i ( k i ( t ) ) , i = 1 , 2 . We establish a new general decay result that improves most of the existing results in the literature related to this system. Our result allows for a wider class of relaxation functions, from which we can recover the exponential and polynomial rates when $k_{i}(s) = s^{p}$ k i ( s ) = s p and p covers the full admissible range $[1, 2)$ [ 1 , 2 ) .

scholarly journals Properties of Extruded Snacks Prepared from Corn and Carrot Powder with Ascorbic Acid Addition

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1367
Author(s):  
Valentina Obradović ◽  
Jurislav Babić ◽  
Verica Dragović-Uzelac ◽  
Antun Jozinović ◽  
Đurđica Ačkar ◽  
...  
Keyword(s):  
Ascorbic Acid ◽  
Temperature Regime ◽  
External Source ◽  
Single Screw Extruder ◽  
Functional Value ◽  
Temperature Regimes ◽  
Starting Point ◽  
Extruded Snacks ◽  
New Type ◽  
Corn Snacks

The objective of this research was to investigate the potentiality of carrot powder (CP) utilization at levels 4, 6, or 8% as ingredient of corn snacks and evaluation of the extrusion influence on functionally important ingredients such as carotenoids (color), polyphenols, fiber, fat, and antioxidant activity. The influence of ascorbic acid (AA) as an external source at levels 0.5 and 1% on this particular extrusion was also investigated. A single-screw extruder at two temperature regimes (135/170/170 °C (E1) and 100/150/150 °C (E2)) carried out extrusion. The E1 temperature regime acted favorably on total polyphenol content and crude fiber, but fat preferred the E2 regime. Extrusion, especially the E1 temperature regime, increased the extractability of carotenoids. Ascorbic acid degraded during extrusion, but it still provided protection to carotenoids and color attributes of extrudates. Snacks with increased nutritional and functional value due to carrot powder addition were successfully produced, which is a starting point for production of a new type of extruded snacks.

scholarly journals “Don’t Worry, We Are Here for You”: Brands as External Source of Control during the Covid-19 Pandemic

2021 ◽  
pp. 1-9
Author(s):  
Peeter W. J. Verlegh ◽  
Stefan F. Bernritter ◽  
Verena Gruber ◽  
Noud Schartman ◽  
Francesca Sotgiu
Keyword(s):  
External Source
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