1,223 research outputs found
Energy absorption by polymer crazing
During the past thirty years, a tremendous amount of research was done on the development of crazing in polymers. The phenomenon of crazing was recognized as an unusual deformation behavior associated with a process of molecular orientation in a solid to resist failure. The craze absorbs a fairly large amount of energy during the crazing process. When a craze does occur the surrounding bulk material is usually stretched to several hundred percent of its original dimension and creates a new phase. The total energy absorbed by a craze during the crazing process in creep was calculated analytically with the help of some experimental measurements. A comparison of the energy absorption by the new phase and that by the original bulk uncrazed medium is made
Pancharatnam and Berry Phases in Three-Level Photonic Systems
A theoretical analysis of Pancharatnam and Berry phases is made for biphoton
three-level systems, which are produced via frequency degenerate co-linear
spontaneous parametric down conversion (SPDC). The general theory of
Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in
Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical
phases are derived for the transformations produced by linear phase-converters.
The problem of gauge invariance is treated along all the article
Seismic Safety Analysis of Earth Dam — Case History Studies
The method of seismic safety analysis for earth dam was examined by using actual performances of earth dams during the Chi-Chi Earthquake. Results of analysis under design earthquakes were also collected and compared with the performance records of earth dams. From the results of these studies, it appears that the Seed-Lee-Idriss approach can provide reasonable predictions on the dynamic responses and post-earthquake performance of well-compacted earth dam
Concise theory of chiral lipid membranes
A theory of chiral lipid membranes is proposed on the basis of a concise free
energy density which includes the contributions of the bending and the surface
tension of membranes, as well as the chirality and orientational variation of
tilting molecules. This theory is consistent with the previous experiments
[J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector
\textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.},
Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral
lipid membranes of DCPC. A torus with the ratio between its two
generated radii larger than is predicted from the Euler-Lagrange
equations. It is found that tubules with helically modulated tilting state are
not admitted by the Euler-Lagrange equations, and that they are less
energetically favorable than helical ripples in tubules. The pitch angles of
helical ripples are theoretically estimated to be about 0 and
35, which are close to the most frequent values 5 and
28 observed in the experiment [N. Mahajan \textit{et al.}, Langmuir
\textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted
ribbons of achiral cationic amphiphiles interacting with chiral tartrate
counterions. The ratio between the width and pitch of twisted ribbons is
predicted to be proportional to the relative concentration difference of left-
and right-handed enantiomers in the low relative concentration difference
region, which is in good agreement with the experiment [R. Oda \textit{et al.},
Nature (London) \textbf{399}, 566 (1999)].Comment: 14 pages, 7 figure
Conditional linearizability criteria for a system of third-order ordinary differential equations
We provide linearizability criteria for a class of systems of third-order
ordinary differential equations (ODEs) that is cubically semi-linear in the
first derivative, by differentiating a system of second-order quadratically
semi-linear ODEs and using the original system to replace the second
derivative. The procedure developed splits into two cases, those where the
coefficients are constant and those where they are variables. Both cases are
discussed and examples given
Oscillatons formed by non linear gravity
Oscillatons are solutions of the coupled Einstein-Klein-Gordon (EKG)
equations that are globally regular and asymptotically flat. By means of a
Legendre transformation we are able to visualize the behaviour of the
corresponding objects in non-linear gravity where the scalar field has been
absorbed by means of the conformal mapping.Comment: Revtex file, 6 pages, 3 eps figure; matches version published in PR
The geometric sense of R. Sasaki connection
For the Riemannian manifold two special connections on the sum of the
tangent bundle and the trivial one-dimensional bundle are constructed.
These connections are flat if and only if the space has a constant
sectional curvature . The geometric explanation of this property is
given. This construction gives a coordinate free many-dimensional
generalization of the connection from the paper: R. Sasaki 1979 Soliton
equations and pseudospherical surfaces, Nuclear Phys., {\bf 154 B}, pp.
343-357. It is shown that these connections are in close relation with the
imbedding of into Euclidean or pseudoeuclidean -dimension
spaces.Comment: 7 pages, the key reference to the paper of Min-Oo is included in the
second versio
Self-gravitating branes of codimension 4 in Lovelock gravity
We construct a familly of exact solutions of Lovelock equations describing
codimension four branes with discrete symmetry in the transverse space. Unlike
what is known from pure Einstein gravity, where such brane solutions of higher
codimension are singular, the solutions we find, for the complete Lovelock
theory, only present removable singularities. The latter account for a
localised tension-like energy-momentum tensor on the brane, in analogy with the
case of a codimension two self-gravitating cosmic string in pure Einstein
gravity. However, the solutions we discuss present two main distinctive
features : the tension of the brane receives corrections from the induced
curvature of the brane's worldsheet and, in a given Lovelock theory, the
spectrum of possible values of the tension is discrete. These solutions provide
a new framework for the study of higher codimension braneworlds.Comment: 22 page
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
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