Terms Of Solitons Research Articles

Kink Formation Dynamics in a Single α-helical Protein

Protein folding remains an open problem despite the progress in understanding the process rate and the success in folding prediction for some small proteins. The reason is the absence of a constructive theoretical framework, both general and specific enough.In earlier papers, we have argued that protein-folding dynamics can be described in terms of solitons of a generalized discrete non-linear Schrodinger equation (GDNLSE) obtained from the energy function in terms of bond and torsion angles [1]. The soliton manifestation is the pattern helix--loop--helix in the secondary structure of the protein, which explains the importance of understanding loop formation in helical proteins and the kink assignment to it [2]. We propose a new mechanism for this process based on the energy transmission along the chain---a disturbance in the latter leads to energy accumulation sufficient to form a kink. We present first insights into the process dynamics by all-atom molecular-dynamics analysis of unfolding of a single alpha-helical protein–--one chain of the core structure of gp41 from the HIV envelope glycoprotein (PDB ID: 1AIK). We suggest an adequate quantification of the side-chain orientation dynamics and also identify some force-field related artefacts.

Surface multipole solitons on photorefractive media with Bessel optical lattices

We find the existence conditions for new surface crescent, dipole, tripole, and quadrupole solitons formed at the interface of a focusing photorefractive medium and a medium imprinted with a Bessel optical lattice. We demonstrate by using numerical simulations that the crescent and the dipole solitons show oscillatory behaviors in their amplitude and shape while the tripole and the quadrupole solitons maintain a remarkable rigidity during propagation. Based on a linear stability analysis, we classify the stability region of the tripole and the quadrupole surface solitons in terms of the Bessel optical lattice strength and the Bessel index.

Multireference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model

The few determinant (FED) approximation introduced in our previous work [Phys. Rev. B 87, 235129 (2013)] is used to describe the ground state, characterized by well-defined spin and space group symmetry quantum numbers as well as doping fractions ${N}_{e}/{N}_{\mathrm{sites}}$, of one-dimensional Hubbard lattices with nearest-neighbor hopping and periodic boundary conditions. Within this multireference scheme, each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry-projected configurations. The results obtained for the ground-state and correlation energies of half-filled and doped lattices with 30, 34, and 50 sites compare well with the exact Lieb-Wu solutions as well as with those obtained with other state-of-the-art approximations. The structure of the intrinsic symmetry-broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations. It is also shown that in the case of doped one-dimensional lattices, a part of such fluctuations can also be interpreted in terms of polarons. In addition to momentum distributions, both spin-spin and density-density correlation functions are studied as functions of doping. The spectral functions and density of states, computed with an ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the ${N}_{e}\ifmmode\pm\else\textpm\fi{}1$ electron systems, display features beyond a simple quasiparticle distribution, as well as spin-charge separation trends.

Nonlinear dynamics of inhomogeneous antiferromagnetic system with Dzyaloshinski–Moriya interactions

Soliton excitation in a one-dimensional antiferromagnet with Dzyaloshinski–Moriya interaction has been studied using the Holstein–Primakoff representation, the coherent-state ansatz and the time-dependent variational principle. The dynamics is found to be governed by a set of coupled nonlinear partial differential equations. Employing the sine–cosine function method with minimal algebra, we analyse the effect of inhomogeneity in terms of soliton under perturbation and it is found that inhomogeneity causes splitting in soliton and hence a disorder in the system.

Tau functions of KP solitons realized in Wiener space

In this paper, a probabilistic representation of the tau functions of KP (Kadomtsev-Petviashvili) solitons in terms of stochastic areas will be presented.

Dynamical Self-organization in Protein Folding

We propose that protein folding is due to a self-organization process, that can be described in terms of solitons, the paradigm self-organizers in numerous physical scenarios. We present a simple Hamiltonian energy function that supports solitons, and show how these solitons can be utilized to describe protein collapse. As an example, we consider two proteins, the myoglobin and a mainly-beta-stranded protein with PDB code 3LL1 and show how in both cases the process of collapse can be modeled, with sub-atomic precision, in terms of explicit soliton profiles.

On the role of thermal backbone fluctuations in myoglobin ligand gate dynamics

We construct an energy function that describes the crystallographic structure of sperm whale myoglobin backbone. As a model in our construction, we use the Protein Data Bank entry 1ABS that has been measured at liquid helium temperature. Consequently, the thermal B-factor fluctuations are very small, which is an advantage in our construction. The energy function that we utilize resembles that of the discrete nonlinear Schrödinger equation. Likewise, ours supports topological solitons as local minimum energy configurations. We describe the 1ABS backbone in terms of topological solitons with a precision that deviates from 1ABS by an average root-mean-square distance, which is less than the experimentally observed Debye-Waller B-factor fluctuation distance. We then subject the topological multi-soliton solution to extensive numerical heating and cooling experiments, over a very wide range of temperatures. We concentrate in particular to temperatures above 300 K and below the Θ-point unfolding temperature, which is around 348 K. We confirm that the behavior of the topological multi-soliton is fully consistent with Anfinsen's thermodynamic principle, up to very high temperatures. We observe that the structure responds to an increase of temperature consistently in a very similar manner. This enables us to characterize the onset of thermally induced conformational changes in terms of three distinct backbone ligand gates. One of the gates is made of the helix F and the helix E. The two other gates are chosen similarly, when open they provide a direct access route for a ligand to reach the heme. We find that out of the three gates we investigate, the one which is formed by helices B and G is the most sensitive to thermally induced conformational changes. Our approach provides a novel perspective to the important problem of ligand entry and exit.

A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons

We give a sharp lower bound for the scalar curvature of a steady gradient Ricci soliton in terms of the hyperbolic secant of the distance from a fixed point under the assumption that 2 | R c | 2 ≤ R 2 2|Rc|^2\leq R^2 , a condition that is satisfied by any steady gradient Ricci soliton with nonnegative sectional curvature.

Simulation of electromagnetic soliton radiography under laser-produced proton beam

During propagating through an underdense plasma, a laser will experience significant energy loss and will be trapped in the plasma as the frequency undergoing a redshift. Thus the electromagnetic (EM) soliton is formed. EM field distribution at different stage is constructed for the soliton in terms of primary theory and particle in cell (PIC) simulation. Radiography of solitons produced by laser accelerated MeV protons is investigated using Monte Carlo methods. The influencing fact or such as proton energy and source size is analyzed. Time-resolved radiography of the soliton is also carried out as the protons accelerated by the target normal sheath acceleration (TNSA) mechanism have a wide energy spectrum. Results validate the static electric field model of the soliton, and provide the basis for the future experiments.

Protein loops, solitons, and side-chain visualization with applications to the left-handed helix region

Folded proteins have a modular assembly. They are constructed from regular secondary structures like α helices and β strands that are joined together by loops. Here we develop a visualization technique that is adapted to describe this modular structure. In complement to the widely employed Ramachandran plot that is based on toroidal geometry, our approach utilizes the geometry of a two sphere. Unlike the more conventional approaches that describe only a given peptide unit, ours is capable of describing the entire backbone environment including the neighboring peptide units. It maps the positions of each atom to the surface of the two-sphere exactly how these atoms are seen by an observer who is located at the position of the central C_{α} atom. At each level of side-chain atoms we observe a strong correlation between the positioning of the atom and the underlying local secondary structure with very little if any variation between the different amino acids. As a concrete example we analyze the left-handed helix region of nonglycyl amino acids. This region corresponds to an isolated and highly localized residue independent sector in the direction of the C_{β} carbons on the two-sphere. We show that the residue independent localization extends to C_{γ} and C_{δ} carbons and to side-chain oxygen and nitrogen atoms in the case of asparagine and aspartic acid. When we extend the analysis to the side-chain atoms of the neighboring residues, we observe that left-handed β turns display a regular and largely amino acid independent structure that can extend to seven consecutive residues. This collective pattern is due to the presence of a backbone soliton. We show how one can use our visualization techniques to analyze and classify the different solitons in terms of selection rules that we describe in detail.

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schroedinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing new mechanisms of decay of antidark solitons.

Ab initiodissipative solitons in an all-photonic crystal resonator

We identify dissipative solitons in a Kerr-nonlinear all-photonic crystal resonator by solving Maxwell's equations directly. The photonic crystal allows for diffraction management, leading to solitons with unique properties. These results are compared to a mean-field model based on Bloch waves, finding excellent agreement even for a high-contrast photonic crystal. By adjusting the quality factor and resonance frequencies of the resonator, optimal Bloch cavity solitons in terms of width and pump energy are identified. In particular, the width is independent of the quality factor, in contrast to the usual homogeneous cavity.

Spatial optical solitons in microstructured cavities

We present a detailed study of the dynamics of light in passive nonlinear resonators with shallow and deep intracavity periodic modulation of the refractive index in both longitudinal and transverse directions of the resonator. We investigate solutions localized in the transverse direction (so-called Bloch cavity solitons) by means of envelope equations for underlying linear Bloch modes and solving Maxwell’s equations directly. Using a round-trip model for forward and backward propagating waves we review different types of Bloch cavity solitons supported by both focusing (at normal diffraction) and defocussing (at anomalous diffraction) nonlinearities in a cavity with a weak-contrast modulation of the refractive index. Moreover, we identify Bloch cavity solitons in a Kerr-nonlinear all-photonic crystal resonator solving Maxwell’s equations directly. In order to analyze the properties of Bloch cavity solitons and to obtain analytical access we develop a modified mean-field model and prove its validity. In particular, we demonstrate a substantial narrowing of Bloch cavity solitons near the zero-diffraction regime. Adjusting the quality factor and resonance frequencies of the resonator optimal Bloch cavity solitons in terms of width and pump energy are identified.

Hopf solitons and elastic rods

Hopf solitons in the Skyrme-Faddeev model are stringlike topological solitons classified by the integer-valued Hopf charge. In this paper we introduce an approximate description of Hopf solitons in terms of elastic rods. The general form of the elastic rod energy is derived from the field theory energy and is found to be an extension of the classical Kirchhoff rod energy. Using a minimal extension of the Kirchhoff energy, it is shown that a simple elastic rod model can reproduce many of the qualitative features of Hopf solitons in the Skyrme-Faddeev model. Features that are captured by the model include the buckling of the charge three solution, the formation of links at charges five and six, and the minimal energy trefoil knot at charge seven.

Dynamics of vortex structure formation during the evolution of modulation instability of dark solitons

The nonlinear stage of modulation instability of dark solitons is studied analytically and numerically. We propose an asymptotic description of the dynamics of these solitons in terms of their local velocity and the curvature of the lines at which solitons are concentrated. The features of the destruction of dark solitons (in particular, the formation of vortex structures from them) are analyzed.

Deformed solitons in a 2-dimensional non(anti)commutative Wess–Zumino model

In this paper we examine a deformation of the 1/2 BPS kink solitons of a WZ model with a cubic superpotential in two Euclidean dimensions caused by introducing non(anti)commutativity in the superspace formulation of the theory. The spacetime Lagrangian of the deformed model consists of the ordinary WZ terms plus corrections in the form of a kinetic and a cubic term for the auxiliary field, both in proportion to the determinant of the non(anti)commutativity parameters C α β . We compute the correction to the “orbit” equation, relating the auxiliary and the scalar fields together, and subsequently derive the modifications to the BPS equation and to its solution up to first order in λ ≡ det ( C α β ) . We give a description of the deformed solitons in terms of the 1/2 BPS states of an effective N = 1 supersymmetric non-linear σ-model in two dimensions, using which we derive the first-order correction to the BPS mass formula for these solitons.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19°35′N, 112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Stationary localized structures and pulsing structures in a cavity soliton laser

A cavity soliton laser is a device able to generate single-peak localized structures, also called cavity solitons, without the injection of an external coherent beam. We realized experimentally a cavity soliton laser by mutually coupling in face to face configuration two broad-area vertical cavity surface emitting lasers, one set to work as amplifier while the second, biased below transparency, plays the role of a saturable absorber. We explore the parameter space, showing the robustness of cavity solitons in this system, and we analyze their switching process. We also report on structures pulsing at the roundtrip time of the compound cavity defined by the two devices. Despite these structures look very similar to cavity solitons in terms of the time-averaged intensity profile, they cannot be interpreted as pulsing cavity solitons since there is no bistability associated with them.

Existence Conditions for Stable Stationary Solitons of the Cubic-Quintic Complex Ginzburg-Landau Equation with a Viscosity Term

We report the existence of a new family of stable stationary solitons in the one-dimensional cubicquintic complex Ginzburg-Landau equation with the viscosity term. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We find the bistable solitons in the presence of the small viscosity term.We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons. We conclude that the existence condition obtained by the paraxial method may serve as physically more reliable initial condition for stable stationary soliton propagation in the optical system modeled by the one-dimensional cubic-quintic complex Ginzburg-Landau equation with the viscosity term, of which analytical solution is not obtainable with all nonzero parameters.

Stable Stationary Solitons of the One-Dimensional Modified Complex Ginzburg-Landau Equation

We report on the existence of a new family of stable stationary solitons of the one-dimensional modified complex Ginzburg-Landau equation. By applying the paraxial ray approximation, we obtain the relation between the width and the peak amplitude of the stationary soliton in terms of the model parameters. We verify the analytical results by direct numerical simulations and show the stability of the stationary solitons.