184 research outputs found
Supersymmetric version of a Gaussian irrotational compressible fluid flow
The Lie point symmetries and corresponding invariant solutions are obtained
for a Gaussian, irrotational, compressible fluid flow. A supersymmetric
extension of this model is then formulated through the use of a superspace and
superfield formalism. The Lie superalgebra of this extended model is determined
and a classification of its subalgebras is performed. The method of symmetry
reduction is systematically applied in order to derive special classes of
invariant solutions of the supersymmetric model. Several new types of
algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are
obtained in explicit form.Comment: Expanded introduction and added new section on classical Gaussian
fluid flow. Included several additional reference
Generalization of the Darboux transformation and generalized harmonic oscillators
The Darbroux transformation is generalized for time-dependent Hamiltonian
systems which include a term linear in momentum and a time-dependent mass. The
formalism for the -fold application of the transformation is also
established, and these formalisms are applied for a general quadratic system (a
generalized harmonic oscillator) and a quadratic system with an inverse-square
interaction up to N=2. Among the new features found, it is shown, for the
general quadratic system, that the shape of potential difference between the
original system and the transformed system could oscillate according to a
classical solution, which is related to the existence of coherent states in the
system
BCS-BEC crossover at finite temperature in the broken-symmetry phase
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry
phase between zero temperature and the critical temperature. This study bridges
two regimes where quantum and thermal fluctuations are, respectively,
important. The theory is implemented on physical grounds, by adopting a
fermionic self-energy in the broken-symmetry phase that represents fermions
coupled to superconducting fluctuations in weak coupling and to bosons
described by the Bogoliubov theory in strong coupling. This extension of the
theory beyond mean field proves important at finite temperature, to connect
with the results in the normal phase. The order parameter, the chemical
potential, and the single-particle spectral function are calculated numerically
for a wide range of coupling and temperature. This enables us to assess the
quantitative importance of superconducting fluctuations in the broken-symmetry
phase over the whole BCS-BEC crossover. Our results are relevant to the
possible realizations of this crossover with high-temperature cuprate
superconductors and with ultracold fermionic atoms in a trap.Comment: 21 pages, 15 figure
Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry
At arbitrary temperature , we solve for the dynamics of single molecule
magnets composed of three classical Heisenberg spins either on a chain with two
equal exchange constants , or on an isosceles triangle with a third,
different exchange constant . As T\rightrarrow\infty, the Fourier
transforms and long-time asymptotic behaviors of the two-spin time correlation
functions are evaluated exactly. The lack of translational symmetry on a chain
or an isosceles triangle yields time correlation functions that differ
strikingly from those on an equilateral trinagle with . At low ,
the Fourier transforms of the two autocorrelation functions with
show one and four modes, respectively. For a semi-infinite range, one
mode is a central peak. At the origin of this range, this mode has a novel
scaling form.Comment: 9 pages, 14 figures, accepted for publication in Phys. Rev.
Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases
This paper presents a conserving gapless mean-field theory for weakly
interacting Bose gases. We first construct a mean-field Luttinger-Ward
thermodynamic functional in terms of the condensate wave function and
the Nambu Green's function for the quasiparticle field. Imposing its
stationarity respect to and yields a set of equations to
determine the equilibrium for general non-uniform systems. They have a
plausible property of satisfying the Hugenholtz-Pines theorem to provide a
gapless excitation spectrum. Also, the corresponding dynamical equations of
motion obey various conservation laws. Thus, the present mean-field theory
shares two important properties with the exact theory: ``conserving'' and
``gapless.'' The theory is then applied to a homogeneous weakly interacting
Bose gas with s-wave scattering length and particle mass to clarify its
basic thermodynamic properties under two complementary conditions of constant
density and constant pressure . The superfluid transition is predicted
to be first-order because of the non-analytic nature of the order-parameter
expansion near inherent in Bose systems, i.e., the Landau-Ginzburg
expansion is not possible here. The transition temperature shows quite
a different interaction dependence between the -fixed and -fixed cases.
In the former case increases from the ideal gas value as
, whereas it decreases in the latter as
. Temperature dependences of
basic thermodynamic quantities are clarified explicitly.Comment: 19 pages, 8 figure
Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence of partial sums, but also explicit estimates
for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of
Mathematical Physic
Extreme genetic fragility of the HIV-1 capsid
Genetic robustness, or fragility, is defined as the ability, or lack thereof, of a biological entity to maintain function in the face of mutations. Viruses that replicate via RNA intermediates exhibit high mutation rates, and robustness should be particularly advantageous to them. The capsid (CA) domain of the HIV-1 Gag protein is under strong pressure to conserve functional roles in viral assembly, maturation, uncoating, and nuclear import. However, CA is also under strong immunological pressure to diversify. Therefore, it would be particularly advantageous for CA to evolve genetic robustness. To measure the genetic robustness of HIV-1 CA, we generated a library of single amino acid substitution mutants, encompassing almost half the residues in CA. Strikingly, we found HIV-1 CA to be the most genetically fragile protein that has been analyzed using such an approach, with 70% of mutations yielding replication-defective viruses. Although CA participates in several steps in HIV-1 replication, analysis of conditionally (temperature sensitive) and constitutively non-viable mutants revealed that the biological basis for its genetic fragility was primarily the need to coordinate the accurate and efficient assembly of mature virions. All mutations that exist in naturally occurring HIV-1 subtype B populations at a frequency >3%, and were also present in the mutant library, had fitness levels that were >40% of WT. However, a substantial fraction of mutations with high fitness did not occur in natural populations, suggesting another form of selection pressure limiting variation in vivo. Additionally, known protective CTL epitopes occurred preferentially in domains of the HIV-1 CA that were even more genetically fragile than HIV-1 CA as a whole. The extreme genetic fragility of HIV-1 CA may be one reason why cell-mediated immune responses to Gag correlate with better prognosis in HIV-1 infection, and suggests that CA is a good target for therapy and vaccination strategies
Field-induced delocalization and Zener breakdown in semiconductor superlattices
We investigate the energy spectrum and the electron dynamics of a band in a semiconductor superlattice as a function of the electric field. Linear optical spectroscopy shows that, for high fields, the well-known localization of the Bloch states is followed by a field-induced delocalization, associated with Zener breakdown. Using time-resolved measurements, we observe Bloch oscillations in a regime where they are damped by Zener breakdown
Assisted evolution enables HIV-1 to overcome a high trim5α-imposed genetic barrier to rhesus macaque tropism
Diversification of antiretroviral factors during host evolution has erected formidable barriers to cross-species retrovirus transmission. This phenomenon likely protects humans from infection by many modern retroviruses, but it has also impaired the development of primate models of HIV-1 infection. Indeed, rhesus macaques are resistant to HIV-1, in part due to restriction imposed by the TRIM5α protein (rhTRIM5α). Initially, we attempted to derive rhTRIM5α-resistant HIV-1 strains using two strategies. First, HIV-1 was passaged in engineered human cells expressing rhTRIM5α. Second, a library of randomly mutagenized capsid protein (CA) sequences was screened for mutations that reduced rhTRIM5α sensitivity. Both approaches identified several individual mutations in CA that reduced rhTRIM5α sensitivity. However, neither approach yielded mutants that were fully resistant, perhaps because the locations of the mutations suggested that TRIM5α recognizes multiple determinants on the capsid surface. Moreover, even though additive effects of various CA mutations on HIV-1 resistance to rhTRIM5α were observed, combinations that gave full resistance were highly detrimental to fitness. Therefore, we employed an 'assisted evolution' approach in which individual CA mutations that reduced rhTRIM5α sensitivity without fitness penalties were randomly assorted in a library of viral clones containing synthetic CA sequences. Subsequent passage of the viral library in rhTRIM5α-expressing cells resulted in the selection of individual viral species that were fully fit and resistant to rhTRIM5α. These viruses encoded combinations of five mutations in CA that conferred complete or near complete resistance to the disruptive effects of rhTRIM5α on incoming viral cores, by abolishing recognition of the viral capsid. Importantly, HIV-1 variants encoding these CA substitutions and SIVmac239 Vif replicated efficiently in primary rhesus macaque lymphocytes. These findings demonstrate that rhTRIM5α is difficult to but not impossible to evade, and doing so should facilitate the development of primate models of HIV-1 infection
NIH Workshop 2018: Towards Minimally Invasive or Noninvasive Approaches to Assess Tissue Oxygenation Pre- and Post-transfusion
Because blood transfusion is one of the most common therapeutic interventions in hospitalized patients, much recent research has focused on improving the storage quality in vitro of donor red blood cells (RBCs) that are then used for transfusion. However, there is a significant need for enhancing our understanding of the efficacy of the transfused RBCs in vivo. To this end, the NIH sponsored a one-and-a-half-day workshop that brought together experts in multiple disciplines relevant to tissue oxygenation (eg, transfusion medicine, critical care medicine, cardiology, neurology, neonatology and pediatrics, bioengineering, biochemistry, and imaging). These individuals presented their latest findings, discussed key challenges, and aimed to identify opportunities for facilitating development of new technologies and/or biomarker panels to assess tissue oxygenation in a minimally-invasive to non-invasive fashion, before and after RBC transfusion
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