227 research outputs found
Kramers-Kronig constrained variational analysis of optical spectra
A universal method of extraction of the complex dielectric function
from
experimentally accessible optical quantities is developed. The central idea is
that is parameterized independently at each node of a
properly chosen anchor frequency mesh, while is
dynamically coupled to by the Kramers-Kronig (KK)
transformation. This approach can be regarded as a limiting case of the
multi-oscillator fitting of spectra, when the number of oscillators is of the
order of the number of experimental points. In the case of the normal-incidence
reflectivity from a semi-infinite isotropic sample the new method gives
essentially the same result as the conventional KK transformation of
reflectivity. In contrast to the conventional approaches, the proposed
technique is applicable, without readaptation, to virtually all types of
linear-response optical measurements, or arbitrary combinations of
measurements, such as reflectivity, transmission, ellipsometry {\it etc.}, done
on different types of samples, including thin films and anisotropic crystals.Comment: 10 pages, 7 figure
Ab initio study of alanine polypeptide chains twisting
We have investigated the potential energy surfaces for alanine chains
consisting of three and six amino acids. For these molecules we have calculated
potential energy surfaces as a function of the Ramachandran angles Phi and Psi,
which are widely used for the characterization of the polypeptide chains. These
particular degrees of freedom are essential for the characterization of
proteins folding process. Calculations have been carried out within ab initio
theoretical framework based on the density functional theory and accounting for
all the electrons in the system. We have determined stable conformations and
calculated the energy barriers for transitions between them. Using a
thermodynamic approach, we have estimated the times of characteristic
transitions between these conformations. The results of our calculations have
been compared with those obtained by other theoretical methods and with the
available experimental data extracted from the Protein Data Base. This
comparison demonstrates a reasonable correspondence of the most prominent
minima on the calculated potential energy surfaces to the experimentally
measured angles Phi and Psi for alanine chains appearing in native proteins. We
have also investigated the influence of the secondary structure of polypeptide
chains on the formation of the potential energy landscape. This analysis has
been performed for the sheet and the helix conformations of chains of six amino
acids.Comment: 24 pages, 10 figure
Central factorials under the Kontorovich-Lebedev transform of polynomials
We show that slight modifications of the Kontorovich-Lebedev transform lead
to an automorphism of the vector space of polynomials. This circumstance along
with the Mellin transformation property of the modified Bessel functions
perform the passage of monomials to central factorial polynomials. A special
attention is driven to the polynomial sequences whose KL-transform is the
canonical sequence, which will be fully characterized. Finally, new identities
between the central factorials and the Euler polynomials are found.Comment: also available at http://cmup.fc.up.pt/cmup/ since the 2nd August
201
Modes of Oscillation in Radiofrequency Paul Traps
We examine the time-dependent dynamics of ion crystals in radiofrequency
traps. The problem of stable trapping of general three-dimensional crystals is
considered and the validity of the pseudopotential approximation is discussed.
We derive analytically the micromotion amplitude of the ions, rigorously
proving well-known experimental observations. We use a method of infinite
determinants to find the modes which diagonalize the linearized time-dependent
dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov')
transformation to coordinates of decoupled linear oscillators. We demonstrate
the utility of the method by analyzing the modes of a small `peculiar' crystal
in a linear Paul trap. The calculations can be readily generalized to
multispecies ion crystals in general multipole traps, and time-dependent
quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction
Dynamic Phase Transition in a Time-Dependent Ginzburg-Landau Model in an Oscillating Field
The Ginzburg-Landau model below its critical temperature in a temporally
oscillating external field is studied both theoretically and numerically. As
the frequency or the amplitude of the external force is changed, a
nonequilibrium phase transition is observed. This transition separates
spatially uniform, symmetry-restoring oscillations from symmetry-breaking
oscillations. Near the transition a perturbation theory is developed, and a
switching phenomenon is found in the symmetry-broken phase. Our results confirm
the equivalence of the present transition to that found in Monte Carlo
simulations of kinetic Ising systems in oscillating fields, demonstrating that
the nonequilibrium phase transition in both cases belongs to the universality
class of the equilibrium Ising model in zero field. This conclusion is in
agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He,
Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss,
C.J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E (submitted)].
Furthermore, a theoretical result for the structure function of the local
magnetization with thermal noise, based on the Ornstein-Zernike approximation,
agrees well with numerical results in one dimension.Comment: 16 pp. RevTex, 9 embedded ps figure
Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential
A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for the nonstationary
Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic
potential. The asymptotic parameter is 1/T, where is the adiabatic
evolution time.
A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Gross-Pitaevskii equation. For the solutions constructed,
the Berry phases are found in explicit form.Comment: 13 pages, no figure
Sufficient conditions for the convergence of the Magnus expansion
Two different sufficient conditions are given for the convergence of the
Magnus expansion arising in the study of the linear differential equation . The first one provides a bound on the convergence domain based on the
norm of the operator . The second condition links the convergence of the
expansion with the structure of the spectrum of , thus yielding a more
precise characterization. Several examples are proposed to illustrate the main
issues involved and the information on the convergence domain provided by both
conditions.Comment: 20 page
Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory
The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parametrized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or a U(2) element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Other components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parametrization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and expresses the theory using only the generalized Twiss function beta. The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice designs in the larger parameter space of general focusing lattices.open3
Missing Links: Referrer Behavior and Job Segregation
How does referral recruitment contribute to job segregation, and what can organizations do about it?
Current theory on network effects in the labor market emphasizes the job-seeker perspective, focusing on the
segregated nature of job-seekers’ information and contact networks, and leaves little role for organizational
influence. But employee referrals are necessarily initiated from within a firm by referrers. We argue that
referrer behavior is the missing link that can help organizations manage the segregating effects of referring.
Adopting the referrer’s perspective of the process, we develop a computational model which integrates a set
of empirically documented referrer behavior mechanisms gleaned from extant organizational case studies.
Using this model, we compare the segregating effects of referring when these behaviors are inactive to the
effects when the behaviors are active. We show that referrer behaviors substantially boost the segregating
effects of referring. This impact of referrer behavior presents an opportunity for organizations. Contrary to
popular wisdom, we show that organizational policies designed to influence referrer behaviors can mitigate
most if not all of the segregating effects of referring
Metalloporphyrin intercalation in liposome membranes: ESR study
Liposomes characterized by membranes featuring diverse fluidity (liquid-crystalline and/or gel phase), prepared from egg yolk lecithin (EYL) and dipalmitoylphosphatidylcholine (DPPC), were doped with selected metalloporphyrins and the time-related structural and dynamic changes within the lipid double layer were investigated. Porphyrin complexes of Mg(II), Mn(III), Fe(III), Co(II), Ni(II), Cu(II), Zn(II), and the metal-free base were embedded into the particular liposome systems and tested for 350 h at 24°C using the electron spin resonance (ESR) spin probe technique. 5-DOXYL, 12-DOXYL, and 16-DOXYL stearic acid methyl ester spin labels were applied to explore the interior of the lipid bilayer. Only the 16-DOXYL spin probe detected evident structural changes inside the lipid system due to porphyrin intercalation. Fluidity of the lipid system and the type of the porphyrin complex introduced significantly affected the intermolecular interactions, which in certain cases may result in self-assembly of metalloporphyrin molecules within the liposome membrane, reflected in the presence of new lines in the relevant ESR spectra. The most pronounced time-related effects were demonstrated by the EYL liposomes (liquid-crystalline phase) when doped with Mg and Co porphyrins, whereas practically no spectral changes were revealed for the metal-free base and both the Ni and Zn dopants. ESR spectra of the porphyrin-doped gel phase of DPPC liposomes did not show any extra lines; however, they indicated the formation of a more rigid lipid medium. Electronic configuration of the porphyrin’s metal center appeared crucial to the degree of molecular reorganization within the phospholipid bilayer system
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