scholarly journals On warped string vacuum profiles and cosmologies. Part II. Non-supersymmetric strings

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
J. Mourad ◽  
A. Sagnotti
Keyword(s):  
Exact Solutions ◽  
The Other ◽  
Initial Singularity ◽  
Warped Products ◽  
Cosmological Expansion ◽  
Finite Distance ◽  
General Setup ◽  
Single Coordinate

Abstract We investigate the effects of the leading tadpole potentials of 10D tachyon-free non-supersymmetric strings in warped products of flat geometries of the type Mp+1× R × T10−p−2 depending on a single coordinate. In the absence of fluxes and for p < 8, there are two families of these vacua for the orientifold disk-level potential, both involving a finite internal interval. Their asymptotics are surprisingly captured by tadpole-free solutions, isotropic for one family and anisotropic at one end for the other. In contrast, for the heterotic torus-level potential there are four types of vacua. Their asymptotics are always tadpole-dependent and isotropic at one end lying at a finite distance, while at the other end, which can lie at a finite or infinite distance, they can be tadpole-dependent isotropic or tadpole-free anisotropic. We then elaborate on the general setup for including symmetric fluxes, and present the three families of exact solutions that emerge when the orientifold potential and a seven-form flux are both present. These solutions include a pair of boundaries, which are always separated by a finite distance. In the neighborhood of one, they all approach a common supersymmetric limit, while the asymptotics at the other boundary can be tadpole-free isotropic, tadpole-free anisotropic or again supersymmetric. We also discuss corresponding cosmologies, with emphasis on their climbing or descending behavior at the initial singularity. In some cases the toroidal dimensions can contract during the cosmological expansion.

scholarly journals On warped string vacuum profiles and cosmologies. Part I. Supersymmetric strings

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
J. Mourad ◽  
A. Sagnotti
Keyword(s):  
Upper Bound ◽  
Flat Space ◽  
The Other ◽  
Warped Products ◽  
Limiting Behavior ◽  
The Third ◽  
Finite Distance ◽  
Effective Theories ◽  
Single Coordinate

Abstract We investigate in detail solutions of supergravity that involve warped products of flat geometries of the type Mp+1× R × TD−p−2 depending on a single coordinate. In the absence of fluxes, the solutions include flat space and Kasner-like vacua that break all supersymmetries. In the presence of a symmetric flux, there are three families of solutions that are characterized by a pair of boundaries and have a singularity at one of them, the origin. The first family comprises supersymmetric vacua, which capture a universal limiting behavior at the origin. The first and second families also contain non-supersymmetric solutions whose behavior at the other boundary, which can lie at a finite or infinite distance, is captured by the no-flux solutions. The solutions of the third family have a second boundary at a finite distance where they approach again the supersymmetric backgrounds. These vacua exhibit a variety of interesting scenarios, which include compactifications on finite intervals and p + 1-dimensional effective theories where the string coupling has an upper bound. We also build corresponding cosmologies, and in some of them the string coupling can be finite throughout the evolution.

scholarly journals STATIC CYLINDRICALLY SYMMETRIC INTERIOR SOLUTIONS IN f(R) GRAVITY

2012 ◽  
Vol 27 (25) ◽  
pp. 1250138 ◽  
Author(s):  
M. SHARIF ◽  
SADIA ARIF
Keyword(s):  
Energy Density ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Functional Form ◽  
Ricci Scalar ◽  
The Other ◽  
New Exact Solutions ◽  
Cylindrically Symmetric ◽  
Theory Of Gravity ◽  
Interior Solutions

We investigate some exact static cylindrically symmetric solutions for a perfect fluid in the metric f(R) theory of gravity. For this purpose, three different families of solutions are explored. We evaluate energy density, pressure, Ricci scalar and functional form of f(R). It is interesting to mention here that two new exact solutions are found from the last approach, one is in particular form and the other is in the general form. The general form gives a complete description of a cylindrical star in f(R) gravity.

scholarly journals Comparison between the (G’/G) - expansion method and the modified extended tanh method

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 88-94 ◽  
Author(s):  
Şamil Akçaği ◽  
Tuğba Aydemir
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Expansion Method ◽  
The Other ◽  
Extended Tanh Method ◽  
New Exact Solutions ◽  
Tanh Method

AbstractIn this paper, firstly, we give a connection between well known and commonly used methods called the $\left( {{{G'} \over G}} \right)$ -expansion method and the modified extended tanh method which are often used for finding exact solutions of nonlinear partial differential equations (NPDEs). We demonstrate that giving a convenient transformation and formula, all of the solutions obtained by using the $\left( {{{G'} \over G}} \right)$ - expansion method can be converted the solutions obtained by using the modified extended tanh method. Secondly, contrary to the assertion in some papers, the $\left( {{{G'} \over G}} \right)$-expansion method gives neither all of the solutions obtained by using the other method nor new solutions for NPDEs. Namely, while the modified extended tanh method gives more solutions in a straightforward, concise and elegant manner without reproducing a lot of different forms of the same solution. On the other hand, the $\left( {{{G'} \over G}} \right)$-expansion method provides less solutions in a rather cumbersome form. Lastly, we obtain new exact solutions for the Lonngren wave equation as an illustrative example by using these methods.

1a. Qualified Quantitative Geography

10.1068/d292 ◽  
2001 ◽  
Vol 19 (5) ◽  
pp. 555-572 ◽  
Author(s):  
Marcus A Doel
Keyword(s):  
The Other ◽  
Opening Scene ◽  
Qualitative Approaches ◽  
Ethical Status ◽  
Other Hand ◽  
The One ◽  
Ethical Response ◽  
General Setup ◽  
The Way

The rapprochement of humanism and structuralism on the one hand, and quantitative and qualitative approaches on the other hand, has not addressed an implacable difficulty which continues to haunt both spatial science and ‘critical’ human geographies. That difficulty concerns the ontological and ethical status of numbers, and their relationship to concepts, events, and sensations. The paper engages with this difficulty through a combination of theoretical and literary writings, most notably Woody Allen's film Deconstructing Harry, Samuel Beckett's play Not I, and Derrida's work of Dissemination. Insofar as ‘one’ lacks consistency—by disavowing difference, alterity, and innumerable numbers—its deployment is invariably unbecoming, repressive, and ill-mannered. The ethical response is to divine ‘another way of working with numbers’, as Derrida once intimated; to prevent some ones from taking hold. The outcome is a form of poststructuralist geography that takes flight from all kinds of pointillism. After an opening scene that lays out the general setup of quantification and its qualification, the first section of the paper employs the notion of a soft ontology in order to prepare the way for ‘another way of working with numbers’ that is occasioned by a sensitivity towards the ontological buzzing and solicitation that accompanies processes of subjectification, objectification, identification, and enumeration. The paper concludes with an affirmation of a ‘disturbing geography’ that leaves everything in perpetual suspense.

Cosmological expansion and local systems: exact solutions

2008 ◽  
Vol 86 (4) ◽  
pp. 663-667
Author(s):  
V Faraoni
Keyword(s):  
Exact Solutions ◽  
Coupled Systems ◽  
De Sitter ◽  
Strongly Coupled ◽  
New Exact Solutions ◽  
Cosmological Expansion ◽  
Weakly Coupled ◽  
Weakly Coupled Systems ◽  
Sitter Background ◽  
04.20 Jb

We study the competition between cosmological expansion and local attraction for relativistic objects embedded in a generic Friedmann universe. The recently discovered “all or nothing” behaviour (i.e., weakly coupled systems are comoving while strongly coupled ones do not expand at all) is found to be limited to the de Sitter background. New exact solutions are presented describing black holes co-moving with a surrounding universe.PACS Nos.: 98.80.–k,04.20.Jb, 04.20.–q

scholarly journals The new exact solitary solutions for the (3+1)-dimensional Zakharov-Kuznetsov equation using the Riccati equation

2020 ◽  
Vol 24 (6 Part B) ◽  
pp. 3995-4000
Author(s):  
Xiao-Jun Yin ◽  
Quan-Sheng Liu ◽  
Lian-Gui Yang ◽  
N Narenmandula
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Electrostatic Potential ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
The Other ◽  
Equation Method ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, a non-linear (3+1)-dimensional Zakharov-Kuznetsov equation is investigated by employing the subsidiary equation method, which arises in quantum magneto plasma. The periodic solutions, rational wave solutions, soliton solutions for the quantum Zakharov-Kuznetsov equation which play an important role in mathematical physics are obtained with the help of the Riccati equation expan?sion method. Meanwhile, the electrostatic potential can be accordingly obtained. Compared to the other methods, the exact solutions obtained will extend on earlier reports by using the Riccati equation.

scholarly journals Vanishing or non-vanishing rainbow? Reduction formulas of electric dipole moment

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Motoko Fujiwara ◽  
Junji Hisano ◽  
Takashi Toma
Keyword(s):  
Electric Dipole ◽  
Dipole Moments ◽  
Form Factors ◽  
The Other ◽  
Vertex Correction ◽  
Electric Dipole Moments ◽  
Self Energy ◽  
The Standard Model ◽  
General Setup ◽  
Exact Cancellation

Abstract In this paper, we derive a simplified formula of electric dipole moments (EDMs) of a fermion. In the Standard Model, it is well-known that non-trivial cancellations between some rainbow-type diagrams induced by W boson exchanges occur in the calculation of the neutron EDM at the two-loop level due to the gauge symmetry. The fermion self-energy and the vertex correction are related through the Ward-Takahashi identity, and this relation causes the exact cancellation of the EDM. We derive EDM formulas for a more general setup by introducing the form factors for the fermion self-energy and the vertex correction so that the derived formulas can be applicable to a larger class of models. We conclude that the non-zero EDM contributions are induced from rainbow-type diagrams with the chirality flipping effects for internal fermions. We also discuss the other possible generalization of the EDM calculation which is applicable to the other classes of models.

Application of Improved (G′/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

2012 ◽  
Vol 4 (1) ◽  
pp. 122-130 ◽  
Author(s):  
Xiaohua Liu ◽  
Weiguo Zhang ◽  
Zhengming Li
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Nonlinear Evolution Equations ◽  
The Other ◽  
Wave Solutions

AbstractIn this work, the improved (G′/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.

On the Correspondence between Exact Solutions in Kaluza–Klein Theory and in Scalar–Tensor Theories

1997 ◽  
Vol 12 (28) ◽  
pp. 2121-2132 ◽  
Author(s):  
Andrew Billyard ◽  
Alan Coley
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
The Other ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Formal Equivalence ◽  
Higher Dimensional ◽  
Klein Theory ◽  
Dimensional Version ◽  
Kaluza Klein

Using the formal equivalences between Kaluza–Klein gravity, Brans–Dicke theory and general relativity coupled to a massless scalar field, exact solutions obtained in one theory will correspond to analogous solutions in the other two theories. Often exact solutions in one theory are "rediscovered" since theory are not recognized as analogs of the corresponding solutions in one of the other theories. We review here a number of exact solutions in each of the theories, with an emphasis on identifying and presenting the higher-dimensional version of the solutions. We also briefly comment upon the formal equivalence between Kaluza–Klein theory and scalar–tensor theories in general.

Delving Deeper: A Specific Construction of a Conic From An Ellipse

2004 ◽  
Vol 98 (2) ◽  
pp. 98-103
Author(s):  
J. Todd Lee
Keyword(s):  
Mathematics Teacher ◽  
Major Axis ◽  
Geometric Construction ◽  
The Other ◽  
Conic Section ◽  
Center Point ◽  
Variable Point ◽  
Specific Construction ◽  
General Setup

Consider the interesting geometric construction given by Manuel Santos-Trigo in the “Technology Tips” in the January 2004 Mathematics Teacher (Santos-Trigo 2004). He starts with an ellipse, its center point O, a variable point R on the line along the major axis of the ellipse, and variable points S and S', which are points on the ellipse that are reflections with respect to the major axis. Figure 1 shows the general setup and various placements of S. Santos-Trigo constructs a pair of lines, one through R and S and the other through O and S'. He describes a set of discovery exercises involving the locus of points generated by the intersection of these lines as the point S roams around the ellipse. The empirical conclusion of these exercises is that the locus is a conic section, the nature of which is determined in a fairly simple way by the location of R relative to O and the major vertices of the ellipse.

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