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This article proposes a novel multivariate generalized autoregressive conditionally heteroscedastic (GARCH) model that incorporates the modified Cholesky decomposition for a covariance matrix in or...

Modeling financial returns is challenging because the correlations and variance of returns are time-varying and the covariance matrices can be quite high-dimensional. In this paper, we develop a Bayesian shrinkage approach with modified Cholesky decomposition to model correlations between financial returns. We reparameterize the correlation parameters to meet their positive definite constraint for Bayesian analysis. To implement an efficient sampling scheme in posterior inference, hierarchical representation of Bayesian lasso is used to shrink unknown coefficients in linear regressions. Simulation results show good sampling properties that iterates from Markov chain Monte Carlo converge quickly. Using a real data example, we illustrate the application of the proposed Bayesian shrinkage method in modeling stock returns in Hong Kong.

We theoretically investigate the hybrid guided modes in a five-layer symmetrical hybrid-metal–dielectric–metal (MDM) plasmonic waveguide. It is a modified-MDM structure that consists of five layers with three-layer (low/high/low) dielectric cladded symmetrically by metal. The hybrid guided mode is characterized and analyzed based on the results obtained from the mode characteristics equations. Such a waveguiding structure can support different types of hybrid-MDM modes at different dielectric thicknesses. Consequently, the optical performance of the hybrid MDM plasmonic waveguide can be controlled by the geometrical parameters and the refractive indices of the dielectric layers, which could be useful for emerging applications in ultracompact nanophotonics.

We presented a comprehensive theoretical study of the hybrid guided mode in a multilayer symmetrical planar plasmoinc waveguide, which is constructed with a thin film metal layer symmetrically sandwiched by three dielectric low/high/low-index layers. The seven-layer planar plasmonic structure can support super long-range plasmonic modes with strong subwavelength confinement in the low-index gap layer. We derived the dispersion equations for the guided mode and characterized the hybrid guided mode based on our derived analytical expressions. We explained how the variations in the thickness of the low-index gap and high-index cladding could change the types of the hybrid mode from strong surface plasmon polariton (SPP)-like mode, to SPP-dielectric waveguide (DW)-like mode, and further to strong-DW-like mode. We also found that by tailoring the geometric dimensions of the waveguide, the plasmonic mode of the multilayer structure can be optimized with the strongest mode confinement at the nanoscale gap. The combination of tight light confinement and long-range propagation length makes the seven-layer plasmonic waveguide an excellent candidate for applications in chip-scale plasmonic integrated circuits. The presented theoretical analysis shall be very useful in the design and optimization of active and passive nanoplasmonic devices.

Proteases play key roles in the regulation of normal cellular function, and thus, their deregulation leads to many disease states. Molecular beacons are promising protease-imaging probes for the detection and characterization of disease as well as for the evaluation of treatment. Inspired by this, we examined the efficiency of zipper molecular beacons (ZMBs) as imaging probes. First, we showed experimentally that the symmetrical ZMB (zip5e5r), bearing 5-arginine and 5-glutamate arms, is as efficient as the asymmetrical zip5e8r in enhancing cell uptake but without the dark toxicity exhibited by the asymmetric zipper. Also, zip5e5r was shown to dissociate more efficiently at pH’s greater than 5. Using a simple two-state binding model, we attributed this to a larger number of charge-pair conformations for zip5e8r. We then measured the ability of soluble matrix metalloproteinases (MMPs) to cleave zip5e5r, and compared their cleavage efficiency with the original photodynamic molecular beacon (PMB). Finally, as a first step toward understanding our observations quantitatively, we simulated the native structures of the peptides GPLGLARK and EGPLGLARRK with charged termini NH3(+) and COO(-) that approximate the PMB and ZMB (with one pair of arginine/glutamate electrostatic zipper), respectively. We concluded that inclusion of the zipper changes the native structure of the MBs, altering the cleavage efficiency of different MMPs.

The permeability of the bacterial outer membrane, enclosing Gram-negative bacteria, depends on the interactions of the outer, lipopolysaccharide (LPS) layer, with surrounding ions and molecules. We present a coarse-grained model for describing how cationic amphiphilic molecules (e.g., antimicrobial peptides) interact with and perturb the LPS layer in a biologically relevant medium, containing monovalent and divalent salt ions (e.g., ${\text{Mg}}^{\text{2+}}$). In our approach, peptide binding is driven by electrostatic and hydrophobic interactions and is assumed to expand the LPS layer, eventually priming it for disruption. Our results suggest that in parameter ranges of biological relevance (e.g., at micromolar concentrations) the antimicrobial peptide magainin 2 effectively disrupts the LPS layer, even though it has to compete with ${\text{Mg}}^{\text{2+}}$ for the layer. They also show how the integrity of LPS is restored with an increasing concentration of ${\text{Mg}}^{\text{2+}}$. Using the approach, we make a number of predictions relevant for optimizing peptide parameters against Gram-negative bacteria and for understanding bacterial strategies to develop resistance against cationic peptides.

We presented the propagation characteristics of the hybrid guided mode in a 5-layer metal/low-index/high-index/low-index/metal waveguide based on our derived analytical equations. The optical properties of the dielectric layers have played an important role on the optical performance of the hybrid mode. In this study, we investigated the effect of the refractive index of the high index dielectric core layer on the propagation length enhancement.

A hybrid plasmonic waveguide is considered as one of the most promising architectures for long-range subwavelength guiding. The objective of this paper is to present a theoretical analysis of plasmonic guided modes in a symmetric conductor–gap–dielectric (SCGD) system. It consists of a thin metal conductor symmetrically sandwiched by two-layer dielectrics with low-index nanoscale gaps inside. The SCGD waveguide can support ultra-long range surface plasmon-polariton mode when the thickness of a low-index gap is smaller than a cutoff gap thickness. For relatively high index contrast ratios of the cladding to gap layers, the cutoff gap thickness is only a few nanometers, within which the electric field of the guided SCGD mode is tightly confined. The dispersion equations and approximate analytical expressions of the cutoff gap thickness are derived in order to characterize the properties of the guided mode. Our simulation results show that the cutoff gap thickness can be tailored by the metal film thickness and the indices of the cladding and gap materials. The geometrical scheme for lateral confinement is also presented. Such a structure with unique features of low-loss and strong confinement has applications in the fabrication of active and passive plasmonic devices.

In this paper we provide a systematic method of finding the higher order asymptotic expansion of the Keldysh integral using the hydrogen atom as an example. Comparisons with exact numerical integration shows that the second-order correction improves the the first-order results significantly. We extend this method to molecular ionisation in H and calculate the total ionisation rate. The results are in good agreement with the exact solution of the time-dependent Schrodinger equation.

We present an all-fiber sensor for simultaneous measurement of temperature and strain. The sensing head is formed by introducing a fiber Bragg grating into a high-birefringence fiber loop mirror that acts as a Mach-Zehnder interferometer for temperature and strain discrimination. A sensing resolution of ±1 °C in temperature and ±21 μe in strain has been experimentally achieved over a temperature range of 60 °C and strain range of 600 μe.

We presented a comprehensive theoretical analysis of hybrid guided modes in a 7-layer symmetrical plasmonic waveguide, which consists of a thin metal film sandwiched symmetrically by three low/high/low-index dielectric layers. The dispersion equation for the hybrid guided mode is derived which allows us to numerically calculate the mode index and the propagation length. We have thoroughly characterized the hybrid guided modes based on our derived analytical expressions.

We report a computational study of the small peptide Met-enkephalin based on the ECEPP/2 and ECEPP/3 force fields using the basin paving method. We have located a new global minimum when using the ECEPP/3 force field with peptide angles omega fixed at 180 degrees. With this new result, we can conclude that the lowest energy configurations of Met-enkephalin predicted based on all four versions of ECEPP have a classic gamma-turn centered at residue Gly3 and a beta-turn at residues Gly3-Phe4. However, minor differences between the structures also exist.

The classical deterministic dynamics of a Brownian particle with a time-dependent periodic perturbation in a spatially periodic potential is investigated. We have constructed a perturbed chaotic solution near the heteroclinic orbit of the nonlinear dynamics system by using the Constant-Variation method. Theoretical analysis and numerical result show that the motion of the Brownian particle is a kind of chaotic motion. The corresponding chaotic region in parameter space is obtained analytically and numerically.

The potential for selectively controlling the excitation and dissociation of the two bonds of the linear triatomic molecule HCN using short laser pulses is studied. We show that intramolecular vibrational redistribution (IVR) has strong influence on the controlling process: at low excitation level, IVR is slow and it is easy to control the excitation of either bond, whereas at higher exitation, IVR causes rapid leakage into the unexcited bond, making control more difficult. Simple linearly chirped pulses are effective in exciting and dissociating the weaker C-H bond. In an attempt to excite the stronger C-N bond, we found that although linearly chirped pulses can transfer energy to the C-N bond, they cannot compete with the much faster internal energy redistribution, and the C-N bond cannot be dissociated because the weaker C-H bond will always break first. To overcome this problem, we construct an optimization scheme and use it to find pulses that do effect C-N dissociation. These pulses however are very short (less than 0.5 ps) and too intense (with brief peaks in the low 10 1 5 W/cm 2 range) so that the molecule will be ionized before dissociation into neutral fragments can occur.

In this letter, we present the first experimental results of climbing a vibrational ladder by Raman chirped adiabatic rapid passage. We obtain the bandwidth necessary for this experiment by utilizing pulses from a unique dual-wavelength high-intensity laser. The vibrationally excited molecules are field ionized by an intense 180 fs laser pulse, enabling us to probe the extent of the vibrational excitation of the symmetric stretch based on an enhanced ionization calculation.

We demonstrated a novel graphene Q-switched erbium-doped fiber laser with wide pulse-repetition-rate range. The Q-switched fiber laser is constructed with a 37-cm linear cavity formed by two fiber Bragg gratings, a section of highly doped erbium fiber, and a graphene saturable absorber. The laser has a low pump threshold of 16.9 mW, a wide range of repetition rate from 31.7 to 236.3 kHz, and minimum pulse duration of 206 ns. The short-cavity laser structure enables laser action free of self-mode-locking effects.

We present detailed numerical results on the ground state structures of metallic clusters. The Gupta-type many-body potential is used to account for the interactions between atoms in the cluster. Both the genetic algorithm technique and the basin hopping method have been applied to search for the global energy minima of clusters. The excellent agreement found in both schemes for the global energy minima gives credence to the optimized energy values obtained. For four monovalent and one polyvalent metals studied in this work and within the accuracy of the energies presented here, we find that the global energy minima predicted by the basin hopping method are the same as those values obtained by the genetic algorithm. Our calculations for the ground state energies of alkali metallic clusters show regularities in the energy differences, and the cluster growth pattern manifested by this same group of clusters is generally icosahedral, which is quite different from the close-packed and decahedral preferentially exhibited by the tetravalent lead clusters. Considering the inherent disparities in the electronic properties and the bulk structures in these metals (body-centered cubic for alkali metals and face-centered cubic for the lead metal), it is not unreasonable to conjecture that the valence electrons do play a subtle role in the conformation of metallic clusters.

After a review of the ”bucket dynamics” which classically accounts for the efficiency of chirped laser pulse excitation of the vibrations of a diatomic molecule, quantum mechanical results for the dissociation of diatomic molecules by a chirped pulse followed by a second laser pulse are presented. It is demonstrated that by using a second fixed-frequency laser, dissociation without ionization is possible which each laser by itself would not suffice to dissociate the molecules. By using a second chirped laser pulse, additional excitation and dissociation of the molecule is observed. Similar to vibrational excitation, rotational excitation of a diatomic molecule can be accomplished by using a circularly polarized chirped laser pulse. Results of our quantum mechanical calculations show that coherent control of the rotational motion of a diatomic molecule is achievable.

Quantum mechanical close-coupling calculations of pressure broadened and pressure shifting coefficients for polarized vibrational Raman Q1(j) and pure rotational S0(j) Raman transitions of H2–Ar and D2–Ar have been performed using the empirically determined three-dimensional ‘XC(fit)’ potential energy surface. While the calculated Q1(j) vibrational line shifting coefficients, and both the shifting and broadening coefficients for the pure rotational S0(j) lines agree well with experiment, broadening coefficients calculated for the Q1(j) transitions are substantially smaller than the measured values. Test calculations using ad hoc modifications of the XC(fit) potential indicate that the diatom stretching dependence of that potential energy surface needs further refinement.

Joint statistical description of the distribution of ion charge states and the spatial structure of a cluster, made of heavy ions, allows a self-consistent generalization of the Brandt–Kitagawa variational theory, including dynamically-screened inter-ionic interactions, in a form of a non-linear integral equation. Solution of such an equation for fast clusters passing very thin foils shows the familiar reduction of charge per ion, compared to the charge on an isotachic ion, which is rather non-homogeneously distributed throughout the volume of the cluster. As a consequence, the distribution of individual ion charges in the cluster exhibits large dispersion around an average value, which drops with the increasing cluster size.

We describe the evolution of the charge state of a fast ion in a thin solid foil by a non-stationary continuous-time Markov process which takes two discrete values, appropriate for H and He projectiles. General expression is presented for the ion energy distribution after traversing the foil and is used to derive the expectation values for the ion stopping power and the energy-loss straggling. A careful analysis of the time auto-correlation function for the ion charge state in a non-stationary regime reveals that, in addition to the familiar exponential transient regime, the initial charge effects exhibit a long-time algebraic decay, inversely proportional to the penetration time through the foil.

Based on the assumption that the probability density of finding a free particle is independent of position, we infer the form of the eigenfunction for the free particle, $\bra{x} p > = \exp(ipx/\hbar)/\sqrt{2��\hbar}$. The canonical commutation relation between the momentum and position operators and the Ehrenfest theorem in the free particle case are derived solely from differentiation of the delta function and the form of $\bra{x} p >$., 3 pages

International audience; We study the break up of OCS in intense femtosecond laser radiation using the FEMPULS technique to vary the laser pulse duration from 7 fs to 200 fs. Newton and Dalitz plots show the progression of molecular deformation and break up for OCS$^{3+}$ and OCS$^{4+}$. For increasing pulse length, the concerted three body dissociation exhibits increasing bending, and the amount of stepwise dissociation decreases. For the longest pulses however the stepwise process increases again. Both phenomena can be interpreted in terms of the effect of the laser field on lower charge states and the behaviour of a wave packet on a saddle point potential. The experiment illustrates the ability of the Coulomb imaging method to track molecular geometry and dynamics and indicates a new path to laser control of molecular parameters.

Employing the recent XC(fit) intermolecular potential for H2-Ar, we have presented the results of the spectral parameters for the D2-Ar Raman Q1 branch, obtained from quantum mechanical close-coupled calculations. While the theoretical line shifts of the polarized Raman spectra were found to agree with experiments, the corresponding widths were smaller than the measured values by as much as 56%. We observed that the shifts and the widths depend on the vibrational dependence of the potential in their own separate ways, and our results suggested that the anisotropic vibrational dependence of the XC(fit) potential requires improvement, in conjunction with further fine-tuning of the isotropic part. Even though there is no experimental data for comparison, we have computed the line-mixing parameters of the polarized Raman Q1 branch, as well as the depolarized line widths and shifts for the Q1(j) lines. These results showed the same trends as the corresponding ones for D2-He.

Just as a helium atom is a prototype for atoms, a hydrogen molecular ion is a prototype for chemical bonding in molecules. In the presence of an external field, the latter also serves as a prototype for which field-induced ionization and dissociation compete with each other. Pauli was the first to examine the nature of chemical bonding in terms of the old quantum theory. In view of the recent developments of nonlinear dynamics and quantum chaos, we re-examine the negative conclusion that he reached in his thesis. In particular, we are interested in finding out whether the classical three-body system is stable and whether any part of the chemical bonding can be attributed to its classical stability. Our result shows that indeed classical phase space structures exist which contribute to chemical bonding, when quantized semiclassically. Thus chemical bonding is not a purely quantum phenomenon, as generally believed. We also examine the classical dynamical behavior of this three-body system in the presence of an external field beyond the Born-Oppenheimer approximation. Interesting competition exists between ionization, dissociation, and Coulomb explosion. Although ionization dominates over dissociation at high laser fields, there exists a range of laser intensity below 150 TW/cm2 for which we can concentrate on dissociation alone without significant interference from the ionization process.

An all-fiber tunable passively Q-switched erbium-doped fiber (EDF) laser is presented. Saturable absorbers are constructed by optically driven deposition of single-wall carbon nanotubes on fiber connectors. A low pump threshold of 11.1 mW is achieved. Self-mode-locking effect is also observed, and it could be suppressed by splicing an extra unpumped EDF into the laser ring cavity. The laser can be tuned by applying axial strain on the fiber Bragg grating which serves as a narrowband external mirror of the cavity.

Using a planar model beyond the Born–Oppenheimer approximation, we study classically the dynamics of a hydrogen molecular ion interacting with an intense laser field. Regularized coordinates are used to remove the singularity of the electron–proton Coulomb interaction. We have calculated the probabilities of ionization and dissociation as functions of time, and obtained the photoelectron and the nuclear fragmentation kinetic energy distribution spectra as well as the harmonic generation spectra.

The effects of the rotational degrees of freedom in the photodissociation dynamics of diatomic molecules by a chirped laser pulse is studied. In general, the inclusion of rotational degrees of freedom reduces the efficiency of the chirping excitations relative to that found for nonrotating molecules. However, using classical 2D and 3D rotating Morse oscillator models we demonstrate that field polarization can cause dramatic enhancements of the dissociation probabilities, with circularly polarized chirped pulses inducing dissociation in rotating molecules almost as efficiently as that previously seen for nonrotating Morse oscillators. We suggest reasons for such improvement in efficiency and discuss the validity of the bucket dynamics model for rotating Morse oscillators.

A new all-fiber sensor capable of simultaneous measurement of strain and temperature is presented. The sensor system is formed by a fiber Bragg grating and two sections of multimode fibers (MMFs). One section of the MMF is isolated from strain and acts as a temperature-dependent edge filter, while the other is isolated from both strain and temperature changes. By monitoring the optical power changes, it is feasible to obtain information that permits simultaneous measurement of strain and temperature with a low-cost and simple structure.

The dynamics of the vibrational excitation and dissociation of a diatomic molecule by infrared laser pulses is studied classically. The system is modeled by a Morse oscillator interacting with a classical electric field. A chirped infrared laser pulse with realistic pulse shape and time-dependent frequency is very efficient to pump the molecule to highly excited states. The addition of a second fixed-frequency laser pulse is found to drastically enhance the dissociation probabilities.

The classical and quantum dynamics of diatomic molecules driven by chirped laser pulses are investigated, with particular attention given to the dependence of the classical-quantum correspondence on the microscopic parameters of the systems. For this purpose, several molecules with different effective Planck’s constants are employed and their respective results are compared. Based on the bucket dynamics which has been successfully applied to explain the dissociation mechanism, we propose a criterion that determines whether a particular molecule will show a good correspondence between classical and quantum calculations in a given parameter region. It is found that, when the size of the bucket is bigger than the effective Planck’s constant, the classical predictions of dissociation probabilities agree well with the quantum mechanical results.

We simulate the Coulomb explosion patterns for swift H2+ ions penetrating through solids by solving the motion equations. The forces acting on the individual H+ fragments are given by the stopping force and the dynamic interacting force. With the plasmon-pole approximation (PLA) dielectric function, the linear-response dielectric theory is used to determine the dynamic interacting force. The initial directions of the molecular axis with respect to the beam direction are assumed to be random. It is found that due to the dynamic-interaction effects, the molecular axes tend to align to the beam direction and the energy losses of the trailing ions are larger than that of the leading ions.

We investigate the effectiveness of chirped laser pulses in exciting a multimode system, where a vibrational mode is coupled to a large number of bath modes. We solve the Liouville equation for this model numerically to investigate the roles played by laser frequency, laser intensity, pulse width, frequency sweeping rate, and bath relaxation times in inducing vibrational excitation. We investigate the range of parameters for which chirping excitation is efficient for multimode systems. In addition, we study constant-frequency excitations using the present model, revealing the special effects of phase relaxation time and the phenomenon of molecular bistability. Furthermore, we present results on quantum decoherence and assess the validity of an effective Hamiltonian method.

We study the effects on the electronic stopping power of large clusters in solids, resulting from multiple elastic scattering of each particle in the cluster by the target atoms, in the small-angle approximation. Evaluation of the cluster vicinage self-energy at the entrance of the target shows that large clusters may stabilize against the Coulomb explosion for a range of cluster sizes and speeds, so that the change of the cluster structure, due to multiple scattering, may have a noticeable influence on the vicinage, or interference, energy losses of clusters due to collective electronic excitations in the target. Stopping power calculations are presented for ${\mathrm{C}}_{60}$ and $({\mathrm{H}}_{2}{)}_{50}$ clusters in an Al target, together with the results on stabilization conditions against the Coulomb explosion for $({\mathrm{H}}_{2}{)}_{{N}_{m}}$, based on self-energy considerations.

The dynamical interaction effects on the Coulomb explosion and the stopping power are studied for MeV ${\mathrm{H}}_{2}^{+}$ ions in grazing collisions with a solid surface. The surface dynamical potential induced by the molecular ions is obtained by using a local frequency-dependent dielectric function for a semi-infinite electron gas with damping. A set of equations describing the motion of the center of mass and the Coulomb explosion is obtained by including the repulsive force of the surface atoms, the bare Coulomb force, and the dynamical forces. The total energy loss for the molecular ion is calculated, taking into account a contribution from both the collective excitations of the conduction electrons and the single-electron excitations of each of the substrate atoms.

The dissociation of a diatomic molecule by a chirped infrared laser pulse is modeled by a Morse oscillator interacting with a classical electric field with a time-dependent frequency. Our previous classical analysis in terms of bucket dynamics, in which systems within the single-node separatrices (buckets) in phase space are trapped and undergo convection to highly excited states, is found to be applicable to the more general cases of nonlinear chirping and using a realistic dipole moment function for the molecule. This route of excitation leads to a much lower dissociation threshold laser intensity when compared to the chaotic diffusion route for monochromatic excitation. Time-dependent quantum mechanical calculations of the dissociation probability based on the split-operator method are performed. It is found that the classical and quantum results agree well, and the classical resonances appear also in the quantum probabilities. Hence the classical method can be used to investigate various characteristics of the chirped pulse excitation and dissociation processes.

The dephasing and energy relaxation contributions to the line width in infrared (IR) and sum-frequency generation (SFG) spectra of adsorbates are derived from the generalized master equation approach. Expression for the line shift is also obtained. The anharmonic interaction between the adsorbate and the substrate is expanded in a polynomial in terms of the adsorbate and phonon coordinates, and the dephasing is shown to be mainly due to two-phonon processes, while two-phonon, three-phonon or four-phonon processes can contribute to energy relaxation, depending on the relative values of the adsorbate vibrational and the phonon frequencies. The temperature-dependence data of the IR absorption for C(111):H is found to be consistent with the theory, and the large line width for C(111):D can be accounted for by the efficient two-phonon energy relaxation process which is not available for C(111):H due to the higher adsorbate vibrational frequency for C(111):H.

We have made a series of measurements, as a function of pulse duration, of ionization and fragmentation of the asymmetric molecule N2O in intense femtosecond laser radiation. The pulse length was varied from 7 fs to 500 fs with intensity ranging from 4 × 10(15) to 2.5 × 10(14) W∕cm(2). Time and position sensitive detection allows us to observe all fragments in coincidence. By representing the final dissociation geometry with Dalitz plots, we can identify the underlying breakup dynamics. We observe for the first time that there are two stepwise dissociation pathways for N2O(3+): (1) N2O(3+) → N(+) + NO(2+) → N(+) + N(+) + O(+) and (2) N2O(3+) → N2 (2+) + O(+) → N(+) + N(+) + O(+) as well as one for N2O(4+) → N(2+) + NO(2+) → N(2+) + N(+) + O(+). The N2 (2+) stepwise channel is suppressed for longer pulse length, a phenomenon which we attribute to the influence which the structure of the 3+ potential has on the dissociating wave packet propagation. Finally, by observing the total kinetic energy released for each channel as a function of pulse duration, we show the increasing importance of charge resonance enhanced ionization for channels higher than 3+.

The electric potential induced by a slow ion moving parallel to a solid surface is calculated based on the specular-reflection model. The effect of exchange-correlation interactions of electrons in the solid is taken into account by the local-field correction (LFC) dielectric theory, and comparison is made with the random-phase approximation (RPA) to the solid response function. It is found that the magnitude of the induced potential calculated using the LFC is always larger than that from the RPA, and hence the effect of electronic exchange-correlation interactions is important for low ion velocities.