A variational approach to the stability of an embedded NLS soliton at the edge of the continuum

2005 ◽  
Vol 206 (3-4) ◽  
pp. 166-179 ◽  
Author(s):  
A.A. Minzoni ◽  
Noel F. Smyth ◽  
Annette L. Worthy
Keyword(s):  
Variational Approach ◽  
The Stability ◽  
The Continuum

scholarly journals Устойчивость углеродной нанолуковицы в контакте с графитовой подложкой

2019 ◽  
Vol 45 (12) ◽  
pp. 9
Author(s):  
С.Ш. Рехвиашвили ◽  
М.М. Бухурова
Keyword(s):  
Theoretical Model ◽  
Interaction Potential ◽  
Interatomic Interaction ◽  
Continuum Approximation ◽  
Graphite Phase ◽  
Interatomic Interaction Potential ◽  
The Stability ◽  
The Continuum

AbstractA theoretical model describing the stability of a carbon nano-onion in the presence of a bulk catalytic graphite phase is constructed based on the continuum approximation of interatomic interaction potential and mechanics of deformed systems. It is shown that a carbon nano-onion becomes unstable when its radius exceeds double value of the radius of a fullerene C_60 molecule.

scholarly journals The X-Ray Nova GRO J0422+32 in Decline and Quiescence

1996 ◽  
Vol 158 ◽  
pp. 399-400
Author(s):  
M. R. Garcia ◽  
P. J. Callanan ◽  
J. E. McClintock ◽  
P. Zhao
Keyword(s):  
Emission Line ◽  
Emission Region ◽  
Dwarf Novae ◽  
X Ray ◽  
First Order ◽  
Band Emission ◽  
Line Region ◽  
Hα Emission ◽  
The Stability ◽  
The Continuum

We have followed the X-ray nova GRO J0422+32, spectroscopically and photometrically, throughout the decline to quiescence.In the final stages of decay (days 430…880 after the outburst, see Callanan et al. (1995) for the epoch 1995), the equivalent width (EW) of the Hα emission increases monotonically and the R magnitude decreases monotonically. This suggests that the flux in the Hα line is constant, while the continuum fades. The Hα flux is the product of the R band flux (F(R), arbitrarily scaled to 100 at R = 19 mag) and the EW, and is shown in the last column of the table below. The Hα flux varies by only ~ 30% while the continuum fades by a factor of eight (from R = 19 mag to R = 21.3 mag). So, to first order, the Hα luminosity is constant in the final stages of decay. While it is generally the case that the emission line EWs in individual dwarf novae also increase during the decay, the exact behavior seen in GRO J0422+32 is not what is seen for dwarf novae (on average). Using the relation between EW[Hβ] and Mv given in figure 6 of Patterson (1984), we would expect a factor of ~ 5 variation in the Hα flux during days 430…880. The stability of the Hα flux implies that somehow the emission line region is ‘disconnected’ from the continuum (R–band) emission region.

The Stability of the Low Temperature Surface Reconstruction in Au(111)

2000 ◽  
Vol 648 ◽  
Author(s):  
Todd M. Trimble ◽  
Robert C. Cammarata
Keyword(s):  
Surface Reconstruction ◽  
Stability Criterion ◽  
Continuum Model ◽  
Lattice Parameter ◽  
Surface Strain ◽  
The Stability ◽  
Computer Simulation Studies ◽  
Physical Quantities ◽  
Temperature Surface ◽  
The Continuum

AbstractWe have performed computer simulation studies on the 22×√3 surface reconstruction of Au(111). This reconstruction involves a uniaxial contraction of the top monolayer corresponding to a surface strain of about 4.3% and has been observed to be the stable structure for clean surfaces at low temperatures. A continuum model yields a stability criterion that depends on the knowledge of a small number of measurable physical quantities: surface stress f, surface free energy γ, lattice parameter a0 and shear modulus µ. The simulations using EAM potentials accurately reproduce many observed features of the reconstruction and tend to support the continuum model and the resulting stability criterion.

GROUND STATE PROPERTIES OF SUPERHEAVY NUCLEI IN RELATIVISTIC MEAN FIELD THEORY

2006 ◽  
Vol 15 (07) ◽  
pp. 1613-1624
Author(s):  
H. F. ZHANG ◽  
J. Q. LI ◽  
W. ZUO ◽  
X. H. ZHOU ◽  
Z. G. GAN ◽  
...  
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Decay Chain ◽  
Stable Region ◽  
Bcs Theory ◽  
Heavy Nuclei ◽  
Relativistic Mean Field ◽  
The Stability ◽  
Super Heavy Nuclei ◽  
The Continuum

In the framework of the relativistic mean field (RMF) theory, the stability and ground properties of super-heavy nuclei are discussed. Our study indicated that the current synthesized super-heavy nuclei (SHN) actually appear in the stable region, and adding more neutrons will not increase their stability. The study of nuclei from 287115 α decay chain showed that they are usually deformed, the magnitudes of their shell gaps are much smaller than those of nuclei before the actinium region, so that the shell effect is weakened, and SHN are usually not stable. A common phenomenon is that the Fermi surface of the proton is close to the continuum, the resonant continuums exist in SHN, because the SHN are usually neutron deficient. Although bulk properties can be described by the RMF+BCS theory, further study is needed. Density dependent delta pairing interaction can improve the treatment of the pairing and thus improve the level distribution in the continuum.

scholarly journals Stability of disk-like galaxies – Part I: Stability via reduction

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Roman Fiřt ◽  
Gerhard Rein
Keyword(s):  
Stability Problem ◽  
Variational Approach ◽  
Steady States ◽  
Poisson System ◽  
Reduction Procedure ◽  
Analogous Question ◽  
Existence And Stability ◽  
The Stability

We prove the existence and stability of flat steady states of the Vlasov–Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by GUO and REIN [5, 6, 7] for this type of problems and extend previous results of REIN [11]. In particular, we employ a reduction procedure which relates the stability problem for the Vlasov–Poisson system to the analogous question for the Euler–Poisson system.

The Stability of a Dislocation Threading a Strained Layer on a Substrate

1987 ◽  
Vol 54 (3) ◽  
pp. 553-557 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Optical Properties ◽  
Critical Thickness ◽  
Continuum Theory ◽  
Threading Dislocation ◽  
Critical Layer Thickness ◽  
Strained Layer ◽  
Mismatch Strain ◽  
The Stability ◽  
Work Done ◽  
The Continuum

The continuum theory of elastic dislocations is applied to estimate the critical thickness of a strained layer bonded to a substrate for a given mismatch strain. The formation of strained epitaxial layers is of interest due to their special electronic or optical properties, and critical thickness is understood to be the smallest thickness at which interface dislocations con form “spontaneously.” The criterion invoked here is based on the work done by the layer stress in driving a threading dislocation to lay down a misfit dislocation along the layer-substrate interface, and it is applied in a way that leads to a result that is independent of the deflected shape of the threading dislocation. The general form of the dependence of critical layer thickness on mismatch strain is similar to that based on equilibrium dislocation analysis.

BUCKLING AND POSTBUCKLING ANALYSIS OF MULTI-WALLED CARBON NANOTUBES BASED ON THE CONTINUUM SHELL MODEL

2007 ◽  
Vol 07 (04) ◽  
pp. 629-645 ◽  
Author(s):  
X. Q. HE ◽  
C. QU ◽  
Q. H. QIN ◽  
C. M. WANG
Keyword(s):  
Carbon Nanotubes ◽  
Shallow Shell ◽  
Compressive Force ◽  
Postbuckling Behavior ◽  
Steep Gradient ◽  
Multi Walled Carbon Nanotubes ◽  
The Stability ◽  
Walled Carbon Nanotubes ◽  
The Continuum ◽  
Vdw Interaction

Buckling and postbuckling behaviors of multi-walled carbon nanotubes (MWCNTs) under a compressive force are studied. MWCNTs are modeled by Donnell's shallow shell nonlinear theory with the allowance of van der Waals (vdW) interaction between the walls. It is shown herein that the buckling load decreases while the buckling strain increases as the innermost radius of MWCNT increases. For the postbuckling behavior, the shortening-load curves show an initial steep gradient that gradually level up when the radius of the innermost tube changes from a small value to a large value. However, the deflection-load curves are almost level for various radii of MWCNTs. In addition, the analytical results showed that the shortening-load curves are almost linear but the deflection-load curves are nonlinear and the stability of MWCNTs can be enhanced by adding tubes.

Softening Instability: Part I—Localization Into a Planar Band

1988 ◽  
Vol 55 (3) ◽  
pp. 517-522 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Strain Softening ◽  
Geometrical Nonlinearity ◽  
Small Strain ◽  
Minimum Thickness ◽  
Infinite Layer ◽  
The Stability ◽  
Conditions Of Stability ◽  
Range Part ◽  
Homogeneous Strain ◽  
The Continuum

Distributed damage such as cracking in heterogeneous brittle materials may be approximately described by a strain-softening continuum. To make analytical solutions feasible, the continuum is assumed to be local but localization of softening strain into a region of vanishing volume is precluded by requiring that the softening region, assumed to be in a state of homogeneous strain, must have a certain minimum thickness which is a material property. Exact conditions of stability of an initially uniform strain field against strain localization are obtained for the case of an infinite layer in which the strain localizes into an infinite planar band. First, the problem is solved for small strain. Then a linearized incremental solution is obtained taking into account geometrical nonlinearity of strain. The stability condition is shown to depend on the ratio of the layer thickness to the softening band thickness. It is found that if this ratio is not too large compared to 1, the state of homogeneous strain may be stable well into the softening range. Part II of this study applies Eshelby’s theorem to determine the conditions of localization into ellipsoidal regions in infinite space, and also solves localization into circular or spherical regions in finite bodies.

scholarly journals TIME-DEPENDENT VARIATIONAL APPROACH TO BOSE–EINSTEIN CONDENSATION

2000 ◽  
Vol 14 (01) ◽  
pp. 1-11 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Variational Approach ◽  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Collective Oscillations ◽  
The Stability ◽  
Bose Einstein

We discuss the mean-field approximation for a trapped weakly-interacting Bose–Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross–Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.

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