Simultaneous Continuation of Infinitely Many Sinks Near a Quadratic Homoclinic Tangency

We prove that the $C^3$ diffeomorphisms on surfaces, exhibiting infinitely many sinksnear the generic unfolding of a quadratic homoclinic tangency of a dissipative saddle, can be perturbed along an infinite dimensional manifold of $C^3$ diffeomorphisms such that infinitely many sinks persist simultaneously. On the other hand, if they are perturbed along one-parameter families that unfold generically the quadratic tangencies, then at most a finite number of those sinks have continuation

Adaptive Deconvolution to Improve Resolution

Deconvolution applied to ultrasonic flaw detection offers the possibility of greatly improved resolution through the elimination of the transducer response. Seydel has previously demonstrated that at least a modest increase in resolution is possible provided the signal-to-noise ratio of the signal being deconvolved is large enough. The random signal flaw detection system can be shown to be ideally suited to deconvolution since it provides enormous signal-to-noise ratio enhancement. Furthermore, the bandwidth compression inherent in this system allows A-D conversion of the output at a rate several orders of magnitude lower than the transmitted ultrasonic frequency. The computer program created to implement the deconvolution procedure also utilizes elementary pattern recognition techniques to deal with the remaining signal noise and ensure a good signal-tonoise ratio for the deconvolution output. The operation of this program was discussed and some preliminary results were presented which showed that at least a ten-fold increase in resolution is possible. At present this processing technique is restricted to a special class of targets, those composed of a series of plane surfaces

Deconvolution Processing for Flaw Signatures

The ultimate resolution of all ultrasonic flaw detection systems is limited by transducer response. Although the system output contains detailed information about the target structure, these details are masked by the system characteristics. Since the output can be described as the convolution of the target response and the impulse response of the system, it should- in principle - be possible to reverse this operation and extract the target response. In practice, it is found that the presence of even relatively small amounts of noise make the deconvolution process impossible. If, however, the flaw detection system has an extremely high output signal-to-noise ratio it is possible to use estimation techniques in the deconvolution process to achieve a good approximation to the actual target response. Results are presented that demonstrate these techniques applied to both simulated and experimental data. Coupling deconvolution processing with feature extraction is shown to yield an order of magnitude increase in range resolution

The Use of Noise Signals for Multi-Mode Beam Shaping

Noise as a transmitted signal has been used in radar, ultrasonic Doppler flow measurement, and ultrasonic flaw detection. In each of these applications, the unique properties of noise have mainly influenced the design and operation of the signal processing portions of the system in which it was used. Our present work shows that the use of noise as a transmitted signal may also benefit the properties of phased array transducers used in imaging systems. Some imaging systems excite the transducer array sequentially in several modes. The echoes resulting from each of the transmitted modes are stored separately and then processed together to yield an effective beam pattern which cannot be realized by any elementary mode of the array. Although phased arrays are frequently used to simultaneously receive in a number of modes, it has not, up to now, been possible for an array to transmit more than one mode at a time. A technique is described which allows several modes to be transmitted simultaneously from a transducer array. This is achieved by exciting each mode with its own independent random signal. The echoes corresponding to each transmitted signal can then be unambiguously identified by correlation with the desired reference signal. This technique generally leads to simplified system design and permits operation in real time. Preliminary results for a small random signal phased array system will be described

Random Noise Signal Processing

Pulse echo flaw detection systems have found extensive use in industry for quality control of many types of metal and ceramic components. The random signal flaw detection system described in this paper provides an increase in sensitivity of several orders of magnitude compared to conventional pulse echo systems. Following a review of the theory of system operation, we present some recently obtained results of our system on materials which are strongly sound absorbing, including ceramics, plastics and metals as well as material s which have large grains. In addition to detecting flaws in strongly absorbing materials we feel that this system might also be utilized as a way of estimating grain size, inclusion size or porosity

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure

Use of the TIDier checklist to describe an online structured education programme for type 2 diabetes

Objectives: The aim of structured education for type 2 diabetes is to improve knowledge, skills and confidence in self-management. It is recommended in the UK for everyone who is newly diagnosed with type 2 diabetes. We developed an on-line programme called HeLP-Diabetes: Starting Out to address poor uptake of face-to-face structured education. The aim of this paper is to describe the intervention in line with the Template for Intervention Description and Replication guide, which calls for better reporting of interventions. Methods: The Template for Intervention Description and Replication guide provided the item headings for the description. These included the theoretical underpinning, materials, procedures, providers, and mode of delivery. Results: The programme was developed to meet NICE requirements for structured education and therefore followed a structured curriculum with four sessions covering content such as what diabetes is and how it is treated, possible complications, and how lifestyle changes can improve health. Content was delivered in text, images and video, and behaviour change techniques, self-assessment and feedback were used to help people target key health behaviours. The programme was delivered entirely online, but the team were available for support via telephone. Email feedback and reminders were sent. Conclusions: The TIDieR checklist allowed us to provide a clear structure for the description of the intervention. However, it could not capture the full complexity of the programme, and intervention developers considering using it in the future may find that it needs to be adapted to make it more specific to their intervention