Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Dynamic method of stiffness identification in impacting systems for percussive drilling applications

Peer reviewed

Dual self-image technique for beam collimation

We propose an accurate technique for obtaining highly collimated beams, which also allows testing the collimation degree of a beam. It is based on comparing the period of two different self-images produced by a single diffraction grating. In this way, variations in the period of the diffraction grating do not affect to the measuring procedure. Self-images are acquired by two CMOS cameras and their periods are determined by fitting the variogram function of the self-images to a cosine function with polynomial envelopes. This way, loss of accuracy caused by imperfections of the measured self-images is avoided. As usual, collimation is obtained by displacing the collimation element with respect to the source along the optical axis. When the period of both self-images coincides, collimation is achieved. With this method neither a strict control of the period of the diffraction grating nor a transverse displacement, required in other techniques, are necessary. As an example, a LED considering paraxial approximation and point source illumination is collimated resulting a resolution in the divergence of the beam of σ φ = ± μrad.

Polarimetric sensitivity to hydrostatic pressure and temperature in birefringent dual-core microstructured polymer fiber

We experimentally characterized a birefringent microstructured polymer fiber of specific construction, which allows for single mode propagation in two cores separated by a pair of large holes. The fiber exhibits high birefringence in each of the cores as well as relatively weak coupling between the cores. Spectral dependence of the group and the phase modal birefringence was measured using an interferometric method. We have also measured the sensing characteristics of the fiber such as the polarimetric sensitivity to hydrostatic pressure and temperature. © 2010 SPIE.

Periodic nonlinear Fourier transform for fiber-optic communications, Part I:theory and numerical methods

In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.

Periodic nonlinear Fourier transform for fiber-optic communications, Part II:eigenvalue communication

In this paper we propose the design of communication systems based on using periodic nonlinear Fourier transform (PNFT), following the introduction of the method in the Part I. We show that the famous "eigenvalue communication" idea [A. Hasegawa and T. Nyu, J. Lightwave Technol. 11, 395 (1993)] can also be generalized for the PNFT application: In this case, the main spectrum attributed to the PNFT signal decomposition remains constant with the propagation down the optical fiber link. Therefore, the main PNFT spectrum can be encoded with data in the same way as soliton eigenvalues in the original proposal. The results are presented in terms of the bit-error rate (BER) values for different modulation techniques and different constellation sizes vs. the propagation distance, showing a good potential of the technique.

Optical wave turbulence and wave condensation in a nonlinear optical experiment

We present theory, numerical simulations and experimental observations of a 1D optical wave system. We show that this system is of a dual cascade type, namely, the energy cascading directly to small scales, and the photons or wave action cascading to large scales. In the optical context the inverse cascade is particularly interesting because it means the condensation of photons. We show that the cascades are induced by a six-wave resonant interaction process described by weak turbulence theory. We show that by starting with weakly nonlinear randomized waves as an initial condition, there exists an inverse cascade of photons towards the lowest wavenumbers. During the cascade nonlinearity becomes strong at low wavenumbers and, due to the focusing nature of the nonlinearity, it leads to modulational instability resulting in the formation of solitons. Further interaction of the solitons among themselves and with incoherent waves leads to the final condensate state dominated by a single strong soliton. In addition, we show the existence of the direct energy cascade numerically and that it agrees with the wave turbulence prediction.

Effective Dose Estimation in Fast-kV Switch Dual Energy Computed Tomography

Purpose

The objective of our study was to test a new approach to approximating organ dose by using the effective energy of the combined 80kV/140kV beam used in fast kV switch dual-energy (DE) computed tomography (CT). The two primary focuses of the study were to first validate experimentally the dose equivalency between MOSFET and ion chamber (as a gold standard) in a fast kV switch DE environment, and secondly to estimate effective dose (ED) of DECT scans using MOSFET detectors and an anthropomorphic phantom.

Materials and Methods

A GE Discovery 750 CT scanner was employed using a fast-kV switch abdomen/pelvis protocol alternating between 80 kV and 140 kV. The specific aims of our study were to (1) Characterize the effective energy of the dual energy environment; (2) Estimate the f-factor for soft tissue; (3) Calibrate the MOSFET detectors using a beam with effective energy equal to the combined DE environment; (4) Validate our calibration by using MOSFET detectors and ion chamber to measure dose at the center of a CTDI body phantom; (5) Measure ED for an abdomen/pelvis scan using an anthropomorphic phantom and applying ICRP 103 tissue weighting factors; and (6) Estimate ED using AAPM Dose Length Product (DLP) method. The effective energy of the combined beam was calculated by measuring dose with an ion chamber under varying thicknesses of aluminum to determine half-value layer (HVL).

Results

The effective energy of the combined dual-energy beams was found to be 42.8 kV. After calibration, tissue dose in the center of the CTDI body phantom was measured at 1.71 ± 0.01 cGy using an ion chamber, and 1.73±0.04 and 1.69±0.09 using two separate MOSFET detectors. This result showed a -0.93% and 1.40 % difference, respectively, between ion chamber and MOSFET. ED from the dual-energy scan was calculated as 16.49 ± 0.04 mSv by the MOSFET method and 14.62 mSv by the DLP method.

Extended nonlinear analytical models of compliant parallelogram mechanisms: third-order models

This paper proposes extended nonlinear analytical models, third-order models, of compliant parallelogram mechanisms. These models are capable of capturing the accurate effects from the very large axial force within the transverse motion range of 10% of the beam length through incorporating the terms associated with the high-order (up to third-order) axial force. Firstly, the free-body diagram method is employed to derive the nonlinear analytical model for a basic compliant parallelogram mechanism based on load-displacement relations of a single beam, geometry compatibility conditions, and load-equilibrium conditions. The procedures for the forward solutions and inverse solutions are described. Nonlinear analytical models for guided compliant multi-beam parallelogram mechanisms are then obtained. A case study of the compound compliant parallelogram mechanism, composed of two basic compliant parallelogram mechanisms in symmetry, is further implemented. This work intends to estimate the internal axial force change, the transverse force change, and the transverse stiffness change with the transverse motion using the proposed third-order model in comparison with the first-order model proposed in the prior art. In addition, FEA (finite element analysis) results validate the accuracy of the third-order model for a typical example. It is shown that in the case study the slenderness ratio affects the result discrepancy between the third-order model and the first-order model significantly, and the third-order model can illustrate a non-monotonic transverse stiffness curve if the beam is thin enough.

Joint Compensation of I/Q Impairments and PA Nonlinearity for Concurrent Dual-Band Transmitters using Two-Box Model

A novel two-box model for joint compensation of nonlinear distortion introduced from both in-phase/quadrature modulator and power amplifier is proposed for concurrent dual-band wireless transmitters. Compensation of nonlinear distortion is accomplished in two phases, where phases are identified separately. It is shown that complexity of the digital predistortion is reduced. The performance of the proposed model is evaluated in terms of ACPR, EVM and NMSE improvements using 1.4 MHz LTE and WCDMA signals.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Building Support Vector Machines in the Context of Regularised Least Squares

This paper formulates a linear kernel support vector machine (SVM) as a regularized least-squares (RLS) problem. By defining a set of indicator variables of the errors, the solution to the RLS problem is represented as an equation that relates the error vector to the indicator variables. Through partitioning the training set, the SVM weights and bias are expressed analytically using the support vectors. It is also shown how this approach naturally extends to Sums with nonlinear kernels whilst avoiding the need to make use of Lagrange multipliers and duality theory. A fast iterative solution algorithm based on Cholesky decomposition with permutation of the support vectors is suggested as a solution method. The properties of our SVM formulation are analyzed and compared with standard SVMs using a simple example that can be illustrated graphically. The correctness and behavior of our solution (merely derived in the primal context of RLS) is demonstrated using a set of public benchmarking problems for both linear and nonlinear SVMs.

Dual stimulation of antigen presenting cells using carbon nanotube-based vaccine delivery system for cancer immunotherapy

Although anti−cancer immuno−based combinatorial therapeutic approaches have shown promising results, efficient tumour eradication demands further intensification of anti−tumour immune response. With the emerging field of nanovaccinology, multi−walled carbon nanotubes (MWNTs) have manifested prominent potentials as tumour antigen nanocarriers. Nevertheless, the utilization of MWNTs in co−delivering antigen along with different types of immunoadjuvants to antigen presenting cells (APCs) has not been investigated yet. We hypothesized that harnessing MWNT for concurrent delivery of cytosine−phosphate−guanine oligodeoxynucleotide (CpG) and anti-CD40 Ig (αCD40), as immunoadjuvants, along with the model antigen ovalbumin (OVA) could potentiate immune response induced against OVA−expressing tumour cells. We initially investigated the effective method to co−deliver OVA and CpG using MWNT to the APC. Covalent conjugation of OVA and CpG prior to loading onto MWNTs markedly augmented the CpG−mediated adjuvanticity, as demonstrated by the significantly increased OVA−specific T cell responses in vitro and in C57BL/6 mice. αCD40 was then included as a second immunoadjuvant to further intensify the immune response. Immune response elicited in vitro and in vivo by OVA, CpG and αCD40 was significantly potentiated by their co−incorporation onto the MWNTs. Furthermore, MWNT remarkably improved the ability of co−loaded OVA, CpG and αCD40 in inhibiting the growth of OVA−expressing B16F10 melanoma cells in subcutaneous or lung pseudo−metastatic tumour models. Therefore, this study suggests that the utilization of MWNTs for the co−delivery of tumour−derived antigen, CpG and αCD40 could be a competent approach for efficient tumours eradication.

Simplified design method for energy dissipating devices in retrofitting of seismically isolated bridges

Abstract: Highway bridges have great values in a country because in case of any natural disaster they may serve as lines to save people’s lives. Being vulnerable under significant seismic loads, different methods can be considered to design resistant highway bridges and rehabilitate the existing ones. In this study, base isolation has been considered as one efficient method in this regards which in some cases reduces significantly the seismic load effects on the structure. By reducing the ductility demand on the structure without a notable increase of strength, the structure is designed to remain elastic under seismic loads. The problem associated with the isolated bridges, especially with elastomeric bearings, can be their excessive displacements under service and seismic loads. This can defy the purpose of using elastomeric bearings for small to medium span typical bridges where expansion joints and clearances may result in significant increase of initial and maintenance cost. Thus, supplementing the structure with dampers with some stiffness can serve as a solution which in turn, however, may increase the structure base shear. The main objective of this thesis is to provide a simplified method for the evaluation of optimal parameters for dampers in isolated bridges. Firstly, performing a parametric study, some directions are given for the use of simple isolation devices such as elastomeric bearings to rehabilitate existing bridges with high importance. Parameters like geometry of the bridge, code provisions and the type of soil on which the structure is constructed have been introduced to a typical two span bridge. It is concluded that the stiffness of the substructure, soil type and special provisions in the code can determine the employment of base isolation for retrofitting of bridges. Secondly, based on the elastic response coefficient of isolated bridges, a simplified design method of dampers for seismically isolated regular highway bridges has been presented in this study. By setting objectives for reduction of displacement and base shear variation, the required stiffness and damping of a hysteretic damper can be determined. By modelling a typical two span bridge, numerical analyses have followed to verify the effectiveness of the method. The method has been used to identify equivalent linear parameters and subsequently, nonlinear parameters of hysteretic damper for various designated scenarios of displacement and base shear requirements. Comparison of the results of the nonlinear numerical model without damper and with damper has shown that the method is sufficiently accurate. Finally, an innovative and simple hysteretic steel damper was designed. Five specimens were fabricated from two steel grades and were tested accompanying a real scale elastomeric isolator in the structural laboratory of the Université de Sherbrooke. The test procedure was to characterize the specimens by cyclic displacement controlled tests and subsequently to test them by real-time dynamic substructuring (RTDS) method. The test results were then used to establish a numerical model of the system which went through nonlinear time history analyses under several earthquakes. The outcome of the experimental and numerical showed an acceptable conformity with the simplified method.

Comparison of three algorithms for nonlinear metal cutting problems

This paper compares three alternative numerical algorithms applied to a nonlinear metal cutting problem. One algorithm is based on an explicit method and the other two are implicit. Domain decomposition (DD) is used to break the original domain into subdomains, each containing a properly connected, well-formulated and continuous subproblem. The serial version of the explicit algorithm is implemented in FORTRAN and its parallel version uses MPI (Message Passing Interface) calls. One implicit algorithm is implemented by coupling the state-of-the-art PETSc (Portable, Extensible Toolkit for Scientific Computation) software with in-house software in order to solve the subproblems. The second implicit algorithm is implemented completely within PETSc. PETSc uses MPI as the underlying communication library. Finally, a 2D example is used to test the algorithms and various comparisons are made.