Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Numerical methods for second-order stochastic differential equations

We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Direct second-order elastic analysis for steel frame design

The traditional structural design procedure, especially for the large-scale and complex structures, is time consuming and inefficient. This is due primarily to the fact that the traditional design takes the second-order effects indirectly by virtue of design specifications for every member instead of system analysis for a whole structure. Consequently, the complicated and tedious design procedures are inevitably necessary to consider the second-order effects for the member level in design specification. They are twofold in general: 1) Flexural buckling due to P-d effect, i.e. effective length. 2) Sway effect due to P-D effect, i.e. magnification factor. In this study, a new system design concept based on the second-order elastic analysis is presented, in which the second-order effects are taken into account directly in the system analysis, and also to avoid the tedious member-by-member stability check. The plastic design on the basis of this integrated method of direct approach is ignored in this paper for simplicity and clarity, as the only emphasis is placed on the difference between the second-order elastic limit-state design and present system design approach. A practical design example, a 57m-span dome steel skylight structure, is used to demonstrate the efficiency and effectiveness of the proposed approach. This skylight structure is also designed by the traditional design approach BS5950-2000 for comparison on which the emphasis of aforementioned P-d and P-D effects is placed.

Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

Analysis of a second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer

A novel second-order polarization-independent filter made of a single ring resonator and a Sagnac interferometer (SRRSI) is proposed, and its filtering characteristics are investigated. By using birefringence in waveguide, a single ring resonator can be used to synthesize a filter with second-order response. Analytical formulas are derived for characteristics of the SRRSI varied with waveguide parameters.. such as the coupling coefficient; and the critical condition of a second-order Butterworth filter is given. The influence of loss in the ring resonator is also analyzed. (c) 2005 Elsevier B.V. All rights reserved.

Two-photon asymmetric color-locking second-order stochastic correlation of attosecond polarization beats

Based on the phase-conjugation polarization interference between two two-photon processes, we theoretically investigated the attosecond scale asymmetry sum-frequency polarization beat in four-level system (FASPB). The field correlation has weak influence on the FASPB signal when the laser has narrow bandwidth. Conversely, when the laser has broadband linewidth, the FASPB signal shows resonance-nonresonance cross correlation. The two-photon signal exhibits hybrid radiation-matter detuning terahertz; damping oscillation, i.e., when the laser frequency is off resonance from the two-photon transition, the signal exhibits damping oscillation and the profile of the two-photon self-correlation signal also exhibits zero time-delay asymmetry of the maxima. We have also investigated the asymmetry of attosecond polarization beat caused by the shift of the two-photon self-correlation zero time-delay phenomenon, in which the maxima of the two two-photon signals are shifted from zero time-delay point to opposite directions. As an attosecond ultrafast modulation process, FASPB can be intrinsically extended to any level-summation systems of two dipolar forbidden excited states.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

Typability and Type Checking in the Second-Order Λ-Calculus Are Equivalent and Undecidable (Preliminary Draft)

We consider the problems of typability[1] and type checking[2] in the Girard/Reynolds second-order polymorphic typed λ-calculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pure λ -terms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lower-bound complexity results for System F have been achieved, but they have remained "embarrassing open problems"[3] for System F itself. We first prove that type checking in System F is undecidable by a reduction from semi-unification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructing λ-terms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specific subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment may be simulated. We develop this method, which we call "constants for free", for both the λK and λI calculi.

First- and second-order phase transitions in the adlayer of biadipate on Au(111)

The adsorption of biadipate on Au(111) was studied by cyclic voltammetry and chronocoulometry. The biadipate adlayer undergoes a potential-driven phase transition. It is shown that the phase transition can be either of the first- or second-order depending on the biadipate concentration. At low surfactant concentrations, the first-order transition is characterised by a discontinuity in the charge density-potential curve and by the presence of very sharp peaks in the voltammetric response. At higher concentrations, these peaks are no longer observed but a discontinuity in the capacity curve is still noticeable, in agreement with a second-order transition. © the Owner Societies.

An evaluation of the Socrative (personal response system) app for increasing student engagement and learning in an undergraduate psychology curriculum.

Personal response systems using hardware such as 'clickers' have been around for some time, however their use is often restricted to multiple choice questions (MCQs) and they are therefore used as a summative assessment tool for the individual student. More recent innovations such as 'Socrative' have removed the need for specialist hardware, instead utilising web-based technology and devices common to students, such as smartphones, tablets and laptops. While improving the potential for use in larger classrooms, this also creates the opportunity to pose more engaging open-response questions to students who can 'text in' their thoughts on questions posed in class. This poster will present two applications of the Socrative system in an undergraduate psychology curriculum which aimed to encourage interactive engagement with course content using real-time student responses and lecturer feedback. Data is currently being collected and result will be presented at the conference.
The first application used Socrative to pose MCQs at the end of two modules (a level one Statistics module and level two Individual Differences Psychology module, class size N≈100), with the intention of helping students assess their knowledge of the course. They were asked to rate their self-perceived knowledge of the course on a five-point Likert scale before and after completing the MCQs, as well as their views on the value of the revision session and any issues that had with using the app. The online MCQs remained open between the lecture and the exam, allowing students to revisit the questions at any time during their revision.
This poster will present data regarding the usefulness of the revision MCQs, the metacognitive effect of the MCQs on student's judgements of learning (pre vs post MCQ testing), as well as student engagement with the MCQs between the revision session and the examination. Student opinions on the use of the Socrative system in class will also be discussed.
The second application used Socrative to facilitate a flipped classroom lecture on a level two 'Conceptual Issues in Psychology' module, class size N≈100). The content of this module requires students to think critically about historical and contemporary conceptual issues in psychology and the philosophy of science. Students traditionally struggle with this module due to the emphasis on critical thinking skills, rather than simply the retention of concrete knowledge. To prepare students for the written examination, a flipped classroom lecture was held at the end of the semester. Students were asked to revise their knowledge of a particular area of Psychology by assigned reading, and were told that the flipped lecture would involve them thinking critically about the conceptual issues found in this area. They were informed that questions would be posed by the lecturer in class, and that they would be asked to post their thoughts using the Socrative app for a class discussion. The level of preparation students engaged in for the flipped lecture was measured, as well as qualitative opinions on the usefulness of the session. This poster will discuss the level of student engagement with the flipped lecture, both in terms of preparation for the lecture, and engagement with questions posed during the lecture, as well as the lecturer's experience in facilitating the flipped classroom using the Socrative platform.