2.13. Search the Internet and find out more about Dr Sykes’ nanotechnology device. Share what you discover with your partner. Make a presentation about nanotechnology. (See Appendix 1)

2.14. Answer the questions.

1. How do you think scientists can work with and make things that are a billionth of a metre wide?

2. What is nanotechnology? Do you know of any examples of it

3. What uses do you think the motor will have for mankind?

4. When do you think nanotechnology will be a widely used part of our life?

5. Do you think it’s possible to get smaller than nano?

6. How might nanotechnology change things like computers and iPads?

2.15. Make a summary of the texts. (See Appendix 4)

Text A. Russian mathematician receives the 2014 Abel Prize (1,800 characters).

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2014 to Yakov G. Sinai of Princeton University, USA, and the Landau Institute for Theoretical Physics, Russian Academy of Sciences, "for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics".

The Abel Prize recognizes contributions of extraordinary depth and influence to the mathematical sciences and has been awarded annually since 2003. It carries a cash award of NOK 6,000,000 (about EUR 750,000 or USD 1 million).

Yakov Sinai is one of the most influential mathematicians of the twentieth century. He has achieved numerous groundbreaking results in the theory of dynamical systems, in mathematical physics and in probability theory. Many mathematical results are named after him, including Kolmogorov–Sinai entropy, Sinai’s billiards, Sinai’s random walk, Sinai-Ruelle-Bowen measures, and Pirogov-Sinai theory.

Sinai is highly respected in both physics and mathematics communities as the major architect of the most bridges connecting the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. During the past half-century Yakov Sinai has written more than 250 research papers and a number of books.

Yakov G. Sinai has received many distinguished international awards. In 2013 he was awarded the Leroy P. Steele Prize for Lifetime Achievement from the American Mathematical Society. Other awards include the Wolf Prize in Mathematics (1997), the Nemmers Prize in Mathematics (2002), the Henri Poincaré Prize from the International Association of Mathematical Physics (2009) and the Dobrushin International Prize from the Institute of Information Transmission of the Russian Academy of Sciences (2009).

The Abel Prize is awarded by the Norwegian Academy of Science and Letters. The choice of the Abel Laureate is based on the recommendation of the Abel Committee, which is composed of five internationally recognized mathematicians. The Abel Prize and associated events are funded by the Norwegian Government.

Text B. Poincare conjecture (2,000 characters).

In mathematics, the Poincare conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states:

Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.

Originally conjectured by Henri Poincare, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincare conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv. The proof followed on from the program of Richard Hamilton to use the Ricci flow to attempt to solve the problem. Perelman introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way. Several teams of mathematicians have verified that Perelman's proof is correct.

The Poincare conjecture, before being proven, was one of the most important open questions in topology. It is one of the seven Millennium Prize Problems, for which the Clay Mathematics Institute offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006, leading to his being offered a Fields Medal, which he declined. Perelman was awarded the Millennium Prize on March 18, 2010. On July 1, 2010, he turned down the prize saying that he believes his contribution in proving the Poincare conjecture was no greater than that of Hamilton's (who first suggested using the Ricci flow for the solution). The Poincare conjecture is the only solved Millennium problem.

In 2006, the journal Science honored Perelman's proof of the Poincare conjecture as the scientific "Breakthrough of the Year", the first time this had been bestowed in the area of mathematics.

Text C. Wavelet theory (2, 500 characters).

A wavelet is a wave-likeoscillationwith anamplitudethat begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by aseismographorheart monitor. Generally, wavelets are purposefully crafted to have specific properties that make them useful forsignal processing. Wavelets can be combined, using a "reverse, shift, multiply and integrate" technique calledconvolution, with portions of a known signal to extract information from the unknown signal.

For example, a wavelet could be created to have a frequency of Middle C and a short duration of roughly a 32nd note. If this wavelet was to be convolved with a signal created from the recording of a song, then the resulting signal would be useful for determining when the Middle C note was being played in the song. Mathematically, the wavelet will correlate with the signal if the unknown signal contains information of similar frequency. This concept ofcorrelationis at the core of many practical applications of wavelet theory.

As a mathematical tool, wavelets can be used to extract information from many different kinds of data, including – but certainly not limited to – audio signals and images. Sets of wavelets are generally needed to analyze data fully. A set of "complementary" wavelets will decompose data without gaps or overlap so that the decomposition process is mathematically reversible. Thus, sets of complementary wavelets are useful in wavelet based compression/decompression algorithms where it is desirable to recover the original information with minimal loss.

In formal terms, this representation is a wavelet seriesrepresentation of asquare-integrable functionwith respect to either acomplete,orthonormalset ofbasis functions, or anovercompleteset orframe of a vector space, for theHilbert spaceof square integrable functions.

Wavelet theory is applicable to several subjects. All wavelet transforms may be considered forms of time-frequency representation for continuous-time (analog) signals and so are related to harmonic analysis. Almost all practically useful discrete wavelet transforms use discrete-time filterbanks. These filter banks are called the wavelet and scaling coefficients in wavelets nomenclature. These filterbanks may contain either finite impulse response (FIR) or infinite impulse response (IIR) filters. The wavelets forming a continuous wavelet transform (CWT) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event. The product of the uncertainties of time and frequency response scale has a lower bound. Thus, in the scaleogram of a continuous wavelet transform of this signal, such an event marks an entire region in the time-scale plane, instead of just one point. Also, discrete wavelet bases may be considered in the context of other forms of the uncertainty principle.

Wavelet transforms are broadly divided into three classes: continuous, discrete and multiresolution-based.

TEXT D. The Motion in Place Platform: capturing the relationship between human movement and site (2,500 characters).

Through Digital and Social Media, researchers at Sussex are developing technology to communicate across space and society.

The Motion in Place Platform brings together a cross-disciplinary group to develop new technologies allowing researchers to move out of the studio, to map and measure the human experience and response when moving through places.

Over centuries, societies have built up a wealth of written knowledge of human behaviour and emotion in response to specific environments. Such narratives are, however, subjective and not necessarily quantifiable. At the same time, the physical study of a site or the cataloguing of material objects often falls short of capturing the human experience of a site. In an effort to develop new tools for recording and articulating the human physical and emotional response to specific environments, the Motion in Place Platform (MiPP) is developing technologies and research strategies to enable the study of how people understand a site by moving through it.

The MiPP team will use two tracking systems to capture different forms of movement data on site. The first system will be developed in collaboration with Brighton-based motion-capture company Animazoo, who will adapt their IGS-190m, currently the most advanced inertial motion-capture system on the market, for use outside a studio. Using gyroscopic sensors attached to flexible suits, this system will allow the collection of high-resolution, full-body data from two people in a fixed area over limited time periods, recording, for example, the movements needed to collect water from a well. The second system will use software developed for the Apple iPhone to capture positional data from large numbers of people moving over a large areas within extended time scales. The goal of MiPP is to develop low-cost and user-friendly systems for generating motion data with a greater degree of flexibility than current research tools such as cameras and GPS loggers. These tools will also provide additional information on aspects of human behaviour and responses to place that is often lost when using written texts, 3-D models and virtual recreations.

MiPP is funded in part through a grant from the Arts and Humanities Research Council's (AHRC) Digital Equipment and Database Enhancement for Impact (DEDEFI) scheme, and brings together a cross-disciplinary team of researchers directed by Kirk Woolford.

The team has an initial year to develop the Platform, and conduct tests in conjunction with the University of Reading's Silchester Field School. At the completion of this pilot phase, the Platform will be hosted until 2013 through the ACCA, a cutting-edge research and teaching infrastructure with a strong focus on creative arts, performance and technology. Ultimately, this hardware, software, and data will be made available to researchers throughout the UK as part of the programme of the AHRC to develop digital resources for the wider academic community.

http://www.sussex.ac.uk/research/about/researchreview/2010/digitalsocialmedia

UNIT 3. INTERDISCIPLINARY RESEARCHES IN PHYSICS AND MATHEMATICS