scholarly journals Curvature Invariants for the Accelerating Natário Warp Drive

Particles ◽  
2020 ◽  
Vol 3 (3) ◽  
pp. 642-659
Author(s):  
Brandon Mattingly ◽  
Abinash Kar ◽  
Matthew Gorban ◽  
William Julius ◽  
Cooper K. Watson ◽  
...  
Keyword(s):  
Mathematical Description ◽  
Skin Depth ◽  
Ricci Scalar ◽  
Curvature Invariant ◽  
Curvature Invariants ◽  
Internal Structures ◽  
Coordinate Mapping ◽  
Key Features

A process for using curvature invariants is applied to evaluate the accelerating Natário warp drive. Curvature invariants are independent of coordinate bases and plotting the invariants is free of coordinate mapping distortions. While previous works focus mainly on the mathematical description of the warp bubble, plotting curvature invariants provides a novel pathway to investigate the Natário spacetime and its characteristics. For warp drive spacetimes, there are four independent curvature invariants the Ricci scalar, r1, r2, and w2. The invariant plots demonstrate how each curvature invariant evolves over the parameters of time, acceleration, skin depth and radius of the warp bubble. They show that the Ricci scalar has the greatest impact of the invariants on the surrounding spacetime. They also reveal key features of the Natário warp bubble such as a flat harbor in the center of it, a dynamic wake, and the internal structures of the warp bubble.

scholarly journals Curvature Invariants for the Alcubierre and Natário Warp Drives

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 21 ◽  
Author(s):  
Brandon Mattingly ◽  
Abinash Kar ◽  
Matthew Gorban ◽  
William Julius ◽  
Cooper K. Watson ◽  
...  
Keyword(s):  
Constant Curvature ◽  
Constant Velocity ◽  
Shape Function ◽  
Skin Depth ◽  
Safe Harbor ◽  
Field Equations ◽  
Curvature Invariants ◽  
Unique Effect ◽  
Coordinate Mapping ◽  
Faster Than Light

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natário warp drives at a constant velocity. Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes, such as warp drives. Warp drives are the theoretical solutions to Einstein’s field equations that allow for the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter’s unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natário warp drive do not contain a wake or a constant curvature, indicating that these are unique features of the accelerating Natário warp drive.

scholarly journals Curvature Invariants for Lorentzian Traversable Wormholes

Universe ◽  
2020 ◽  
Vol 6 (1) ◽  
pp. 11 ◽  
Author(s):  
Brandon Mattingly ◽  
Abinash Kar ◽  
William Julius ◽  
Matthew Gorban ◽  
Cooper Watson ◽  
...  
Keyword(s):  
Spherically Symmetric ◽  
Curvature Invariant ◽  
Invariant Functions ◽  
Curvature Invariants ◽  
Traversable Wormholes ◽  
Nonzero Curvature ◽  
Coordinate Mapping ◽  
Line Elements ◽  
Coordinate Basis ◽  
Exponential Metric

The curvature invariants of three Lorentzian wormholes are calculated and plotted in this paper. The plots may be inspected for discontinuities to analyze the traversability of a wormhole. This approach was formulated by Henry, Overduin, and Wilcomb for black holes (Henry et al., 2016). Curvature invariants are independent of coordinate basis, so the process is free of coordinate mapping distortions and the same regardless of your chosen coordinates (Christoffel, E.B., 1869; Stephani, et al., 2003). The four independent Carminati and McLenaghan (CM) invariants are calculated and the nonzero curvature invariant functions are plotted (Carminati et al., 1991; Santosuosso et al., 1998). Three traversable wormhole line elements analyzed include the (i) spherically symmetric Morris and Thorne, (ii) thin-shell Schwarzschild wormholes, and (iii) the exponential metric (Visser, M., 1995; Boonserm et al., 2018).

scholarly journals Gravity mode offset and properties of the evanescent zone in red-giant stars

2018 ◽  
Vol 610 ◽  
pp. A80 ◽  
Author(s):  
S. Hekker ◽  
Y. Elsworth ◽  
G. C. Angelou
Keyword(s):  
Mathematical Description ◽  
Physical Parameters ◽  
Full Potential ◽  
Coupling Term ◽  
Giant Stars ◽  
Internal Structures ◽  
Mixed Modes ◽  
Red Giant Stars ◽  
Red Giant ◽  
Gravity Mode

Context. The wealth of asteroseismic data for red-giant stars and the precision with which these data have been observed over the last decade calls for investigations to further understand the internal structures of these stars. Aim. The aim of this work is to validate a method to measure the underlying period spacing, coupling term, and mode offset of pure gravity modes that are present in the deep interiors of red-giant stars. We subsequently investigate the physical conditions of the evanescent zone between the gravity mode cavity and the pressure mode cavity. Methods. We implement an alternative mathematical description compared to what is used in the literature to analyse observational data and to extract the underlying physical parameters that determine the frequencies of mixed modes. This description takes the radial order of the modes explicitly into account, which reduces its sensitivity to aliases. Additionally, and for the first time, this method allows us to constrain the gravity mode offset ϵg for red-giant stars. Results. We find that this alternative mathematical description allows us to determine the period spacing ΔΠ and the coupling term q for the dipole modes within a few percent of values found in the literature. Additionally, we find that ϵg varies on a star-by-star basis and should not be kept fixed in the analysis. Furthermore, we find that the coupling factor is logarithmically related to the physical width of the evanescent region normalised by the radius at which the evanescent zone is located. Finally, the local density contrast at the edge of the core of red-giant branch models shows a tentative correlation with the offset ϵg. Conclusions. We are continuing to exploit the full potential of the mixed modes to investigate the internal structures of red-giant stars; in this case we focus on the evanescent zone. It remains, however, important to perform comparisons between observations and models with great care as the methods employed are sensitive to the range of input frequencies.

A COMPLEX FINSLER APPROACH OF GRAVITY

2012 ◽  
Vol 09 (07) ◽  
pp. 1250058 ◽  
Author(s):  
GHEORGHE MUNTEANU ◽  
NICOLETA ALDEA
Keyword(s):  
Gordon Equation ◽  
Finsler Metric ◽  
Energy Relation ◽  
Two Dimensional ◽  
Curvature Invariant ◽  
Plane Wave Solution ◽  
Curvature Invariants ◽  
Complex Finsler Metric ◽  
Klein Gordon ◽  
Special Case

In this paper our aim is mainly to obtain a two-dimensional complex Finsler model of the real gravitation space-time. We prove that, at least in the special case of the weakly gravitational field, this is possible and it leads to some interesting geometrical and physical aspects, such as the study of curvature invariants with respect to complex Berwald frame, intensively studied recently by us for a two-dimensional complex Finsler space. A generalization of the Klein–Gordon equation is proposed and we find solutions which are in concordance to the classical plane wave solution of momentum-energy relation. The last part of the paper is devoted to some applications in which the complex gravitational potential leads to the Bergman metric and to a more general case which leads to a non-purely Hermitian complex Finsler metric, with negative curvature invariant.

Ultrastructure of Giant Mitochondria and Their Inclusions in Schwann Cells of Bovine Splenic Nerve

1974 ◽  
Vol 32 ◽  
pp. 194-195
Author(s):  
Å. Thureson-Klein
Keyword(s):  
Schwann Cells ◽  
Cell Organelles ◽  
Giant Mitochondria ◽  
Matrix Density ◽  
Physiological Conditions ◽  
Unmyelinated Axons ◽  
Internal Structures ◽  
Structural Abnormalities ◽  
Cytotoxic Compounds ◽  
Cell Components

Giant mitochondria of various shapes and with different internal structures and matrix density have been observed in a great number of tissues including nerves. In most instances, the presence of giant mitochondria has been associated with a known disease or with abnormal physiological conditions such as anoxia or exposure to cytotoxic compounds. In these cases degenerative changes occurred in other cell organelles and, therefore the giant mitochondria also were believed to be induced structural abnormalities.Schwann cells ensheating unmyelinated axons of bovine splenic nerve regularly contain giant mitochondria in addition to the conventional smaller type (Fig. 1). These nerves come from healthy inspected animals presumed not to have been exposed to noxious agents. As there are no drastic changes in the small mitochondria and because other cell components also appear reasonably well preserved, it is believed that the giant mitochondria are normally present jin vivo and have not formed as a post-mortem artifact.

Mitochondria in Cardiomyopathy: Alterations in Size, Number and Internal Structures

1968 ◽  
Vol 26 ◽  
pp. 126-127
Author(s):  
George Hug ◽  
William K. Schubert
Keyword(s):  
Heart Failure ◽  
Biochemical Analysis ◽  
Left Ventricular ◽  
Size Number ◽  
Internal Structures ◽  
Left Ventricular Outflow ◽  
Chest X Ray ◽  
Myocardial Fibers ◽  
Muscle Biopsies ◽  
Needle Liver Biopsy

A white boy six months of age was hospitalized with respiratory distress and congestive heart failure. Control of the heart failure was achieved but marked cardiomegaly, moderate hepatomegaly, and minimal muscular weakness persisted.At birth a chest x-ray had been taken because of rapid breathing and jaundice and showed the heart to be of normal size. Clinical studies included: EKG which showed biventricular hypertrophy, needle liver biopsy which showed toxic hepatitis, and cardiac catheterization which showed no obstruction to left ventricular outflow. Liver and muscle biopsies revealed no biochemical or histological evidence of type II glycogexiosis (Pompe's disease). At thoracotomy, 14 milligrams of left ventricular muscle were removed. Total phosphorylase activity in the biopsy specimen was normal by biochemical analysis as was the degree of phosphorylase activation. By light microscopy, vacuoles and fine granules were seen in practically all myocardial fibers. The fibers were not hypertrophic. The endocardium was not thickened excluding endocardial fibroelastosis. Based on these findings, the diagnosis of idiopathic non-obstructive cardiomyopathy was made.

SKIN DEPTH EFFECT IN THE RF COLLAPSE STUDIES

1980 ◽  
Vol 41 (C1) ◽  
pp. C1-217-C1-218 ◽  
Author(s):  
G. Karczewski ◽  
M. Kopcewicz ◽  
A. Kotlicki
Keyword(s):  
Skin Depth ◽  
Depth Effect

Working up to the wire…

2019 ◽  
Vol 13 (2) ◽  
pp. 198-206
Author(s):  
Philippa Smethurst
Keyword(s):  
Psychotherapeutic Processes ◽  
Internal Structures ◽  
The Wire ◽  
Power And Energy ◽  
Time Boundary ◽  
The Way

This is a reflection on the power of endings and time boundaries, exploring the way that time can act as a catalyst in psychotherapeutic processes. The article describes the ending processes with five clients. These occurred simultaneously due to the author’s relocation. Some responses illuminate hitherto hidden and intractable internal structures, and in others the intensity of the limit acts an impetus for the client to grasp something new. Drawing on Power’s comprehensive book: Forced Endings in Psychotherapy and Psychoanalysis (2016), the author reflects on the power and energy springing from the setting of the time boundary and the different dynamics created in client and therapist. There is acknowledgement of the pressure that this can create in the therapist and also there are reflections about what ultimately may be achieved.

Review of the Current State and Future Development in Standardising Artificial Lighting

2019 ◽  
pp. 4-44 ◽  
Author(s):  
Peter Thorns
Keyword(s):  
Internet Of Things ◽  
Future Development ◽  
Best Practice ◽  
The Internet ◽  
Artificial Lighting ◽  
Current State ◽  
Internal Structures ◽  
European Regulations ◽  
The Internet Of Things

This paper discusses the organisations involved in the development of application standards, European regulations and best practice guides, their scope of work and internal structures. It considers their respective visions for the requirements for future standardisation work and considers in more detail those areas where these overlap, namely human centric or integrative lighting, connectivity and the Internet of Things, inclusivity and sustainability.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

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