This thesis deals with some applications of Regge Theory to K (^+) p and pp elastic scattering. Chapter one is an introduction. The important results and problems of Regge theory are discussed, together with some recent developments. In chapter two a model incorporating doubled trajectories is proposed and compared to K (^+) p elastic scattering data. The model supports t channel helicity conservation for the pomeron near the forward direction. The results for K - p agree in part with those of Heyot and Wavelet at 10 GeV/c, and those For K + p agree well with the CERN beta phase shift solution at 2.5 CeV/c. In chapter three a J-plane analysis technique is introduced. It is applied to pp elastic scattering, where the results do not allow an interpretation in terms of simple poles. Evidence is presented that the curvature of the pp total cross section is not due to exchange degeneracy breaking. In chapter four the J-plane structure of pp scattering in the absorption model is investigated. Many of the puzzling features of the results of chapter three are explained. Chapter five is concerned with the recent data on pp scattering at high energies. Several models which have bean proposed to explain these data are discussed and soma conclusions are drawn.

The bootstrap idea in the sense of finite energy sum rules and the saturation with zero-width resonances are developed further in the thesis for the reaction ƿƿ→ƿo and ƿƿ→ƿy which are identical in all the three channels and therefore provide us with a genuine bootstrap of the Regge trajectories, contrary to, say, the reaction πƿ→ πƿ . A set of fourteen FESR,s for all the invariant amplitudes of the reaction ƿƿ→ƿo and also a set of thirteen FESR,s for ƿƿ→ƿy different steps of approximation have been written down which can be studied further in different aspects. Notice that a previously considered by other authors reaction ππ → πw finally led to a special representation, namely the Veneziano model which has many attractive features. With the appearance of this model and the concept of duality we devoted ourselves to the idea of mass extrapolation along the Regge trajectory, a show-case of which is the annihilation pn-3 π at rest. The Dalitz plot and the overall normalization for this process were obtained with a certain degree of success. An analogous attempt was done for the over all normalization of the annihilation process pp → 4π at rest. The new experimental data on the annihilation process for low laboratory momenta of antiproton P(_lab) = 100 - 700 MeV give a further support to this kind of extrapolation along the Regge trajectory. These data indicate the existence of angular momenta up to l = 3 at these near-threshold energies. An impact parameter picture with the reasonable radius of interaction gives l^1 , while the explanation within the above mode(is very natural since the Regge trajectory a is very near to 3. A step has also been done towards the construction of physical dual resonance models (DRM) with unnatural parity couplings and without the tachyon states. One of the motivations has been to see whether these physical requirements give a natural way to get a double or more degenerate (w - A(_2))-trajectory in 3π-channels when one factorizes the states analogous to the de-generay of the daughters levels. One has to admit that the unitarization of DRM still remains a problem. However, from a theoretical point of view the ZSV-program to consider the model as a Bom term of a field- theoretic expansion is the most attractive one. In admitting this program, the best place to look for its predictions is the field of inclusive experiments both in purely hadronic and photonic processes where one measures the discontinuities. For purely hadronic reactions in DRM Feynman scaling is obtained provided the trajectory exchanged is associated with the Pomeron with unit intercept. For photonic processes in DRM the Bjorken scaling is obtained due to the existence of current algebra fixed pole. The latter question is studied in the thesis in a model where the currents are included into DRM through a minimal gauge interaction prescription, in which one has the minimum amount of freedom, and the dual re-normalization has also been used. With the use of Muellerism the generalized Bjorken scaling for some quasi-inclusive reactions has also been obtained. The motivation for the above analysis has-been the experimental indication that the nondiffractive part of the electroproduction structure functions do show scaling. Without the fixed pole responsibility it would be hard to understand the scaling of the resonant part. Also notice that with the exception of λρ(^3)-theory all the other field-theoretic models have failed to produce Bjorken scaling unless one introduces an unjustified cutoff and therefore one would like to argue that in the DRM the renormalization term as if replaces this cutoff in a more natural way. The above and many other points studied in the young but vast literature may indicate that the DRM might be "not that far" from the real world of hadron physics.

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In this thesis we consider supersymmetric probes in backgrounds sourced by an M5-brane which is wrapped on holomorphic 2-cycles in C(^2) and C(^3), respectively. For the first case, we use M2-brane probes to compute the BPS spectra of the corresponding N = 2 gauge theory, as well as M5-brane probes to calculate field theory parameters such as the gauge coupling, theta angle and complex scalar moduli space metric. This background describes a large class of Hanany-Witten models when dimensionally reduced to Type IIA ten-dimensional supergravity. We calculate the instanton action using a Euclidean DO-brane probe in this limit. For the case of an M5-brane wrapping a 2-cycle in C(^3), we firstly show an alternative method of deriving this solution which involves the projection conditions and certain spinor bilinear differential equations. We also consider M5-brane probes in this background, and analyse the corresponding N = I MQCD gauge theory parameters, in direct analogy with the N = 2 case. We then move on to consider the central charges of the supersymmetry algebra of brane probes in the two backgrounds under consideration. For the case of an M5-brane wrapping a 2-cycle in c2, we find it allows for M2- braneร representing BPS monopoles and vortices. There is also the possibility of a "hidden" M5-brane which is similar to the M2-brane, but which includes a rotation in the complex structure and an extra volume modulus. For the N = I case, we find it allows for a supersymmetric M5-brane probe wrapping a Cayley calibrated 4-cycle, which is interpreted as a system of intersecting domain walls. These results are geometrically linked to M-theory structure groups.

This thesis is concerned with dual resonance models, especially the Neveu-Schwarz and Ramond Models. The first chapter is an introduction to the subject of dual models and is concerned with the concepts that lead to them and early ideas of dual models. Chapter two presents, in the operator formalism, the Conventional Dual Model and then the Neveu-Schwarz and Eamond Models and is meant to indicate the more important features of these models. The: first part of chapter three deals with the string pictures of dual models and various ways of considering dual models which can be considered to be related to the string pictures. The latter half of chapter three deals with the formulation of the Neveu-Schwarz Model by the use of a finite Grassmann algebra which extends the Conventional Dual Model, in Koba-Nielsen variables, directly into the Neveu-Schwarz Model. The tree graph and one loop diagrams are calculated explicitly while the form for higher order terms is given in terms of automorphic functions. The first part of chapter four presents a method of obtaining the functions, involved in one loop meson and fermion diagrams with external mesons, by the use of Neumann functions on an annulus, the boundary conditions on the annulus giving the different loop diagrams. The second part of chapter four deals with, the calculation of the Neumann function for one loop diagrams with external fermions and an attempt to obtain the partition function which is necessary to write down the complete amplitude at the one loop level. Chapter four is completed by the construction of the one loop amplitude for four external fermions.

This thesis has two main themes: on the one hand, in Chapters 3 and 5 we study some effects of the presence of timelike boundaries on linear classical and quantum field theories; the second theme is the analysis of technical issues with the paper B.S. Kay and R.M. Wald, Phys. Rep. 207, 49-136 (1991), which is carried out in parts of Chapter 2 and in Chapter 4. Chapter 2 contains a novel result on the characteristic initial value problem on globally hyperbolic spacetimes. In Chapter 3, we conjecture that (when the notion of a Hadamard state is suitably adapted to spacetimes with timelike boundaries) there is no isometry-invariant Hadamard state for the Klein-Gordon equation defined on the region of the Kruskal spacetime 'to the left of' a surface of constant Schwarzschild radius in the right Schwarzschild wedge, if Dirichlet boundary conditions are imposed there. We also prove that, under a suitable notion for 'boost-invariant Hadamard state' which also takes into account the special infra-red pathology of massless fields in 1+1 dimensions, there is no such state for the massless 1+1 wave equation on the region of Minkowski space to the left of an eternally uniformly accelerating mirror – with Dirichlet boundary conditions at the mirror. Chapter 5 collects and extends results of Solis about the causal structure of spacetimes with timelike boundaries, and deals with algebraic aspects of the interplay between Green hyperbolicity and boundary conditions in classical field theory. It also outlines a plan for generalizing the established work on wave-like equations from globally hyperbolic spacetimes to 'globally hyperbolic spacetimes-with-timelike-boundaries'. Appendix B contains a non-existence result for boost-invariant Hadamard states of a massless scalar field in (1+1)-dimensional Minkowski spacetime.

A probability distribution encodes all the statistics of its corresponding random variable, hence it encodes all one can learn about the system via the random variable. In the theoretical part of this thesis, we discuss several equivalent representations of probability distributions in physics which establishes their roles as complete information measures in their own contexts. In particular, we show how Rényi entropies (as well as relative Rényi entropies) completely characterise the uncertainty of a system, hence implies the insufficiency of Shannon entropy (as well as relative entropy) in capturing the information in the presence of strong fluctuation. We also generalise Jarzynski equality in terms of relative Rényi entropies and show the equivalence between the generalised equality and the work distribution. As a consequence, an equivalence between a monotonic property of relative Rényi entropies and a kind of second law relations is revealed. In the experimental part, we study the non-equilibrium dynamics of an optically levitated nanosphere system in Knudsen regime and discover that, even though the system is not in equilibrium, the dynamics can still be treated as a Brownian motion with an effective temperature and an effective coefficient. Due to the Gaussian statistics of the levitated sphere, we show how some relevant non-equilibrium properties of the system, including several local temperatures, can be analysed from its power spectrum.

Scientific abstract In this dissertation we perform a series of study concerning dualities and integrability properties underlying the AdS3/CFT2 and AdS2/CFT1 correspondences. These are particularly interesting because symmetry do not constrain the dynamics of AdS3 and AdS3 superstrings in the same way as in the higher dimensional instances of AdS/CFT, allowing for novel phenomena such as the presence of massless worldsheet modes or non-coset fermions. We will investigate the self-duality of Green–Schwarz supercoset sigma models on AdSd⇥Sd⇥Sd (d = 2, 3), whose isometry supergroups are (d − 1) copies of the exceptional Lie supergroup D(2, 1; ↵). Our main finding is that additional complex T-dualities along one of the spheres Sd are needed to map the superstring action to itself. Importantly, this proves dual superconformal symmetry of their CFT duals via AdS/CFT. Dual superconformal symmetry is strictly related to integrability, which we study in depth for both AdS3 and AdS2 superstrings. Indeed, we will derive the exact S-matrix conjectured to be related to the massive modes of type IIB AdS2 ⇥ S2 ⇥ T6 superstrings. This S-matrix is psuc(1|1) invariant and it was found to be in perfect agreement with the tree-level result following from string perturbation theory. We also unveil the Yangian algebra ensuring the integrability of the AdS2⇥S2⇥T6 superstring in the planar limit, Y[psu(1|1)c], as well as its secret symmetries. By using the RTT realisation, we provide two di↵erent representations of the Hopf algebra: one is reminiscent of the Yangian underlying AdS5/CFT4, but it is not of evaluation type. The other representation, obtained from co-commutativity, is instead of evaluation type. We explore two limits of the S-matrix for AdS2/CFT1: one is the classical r-matrix, which is the first non-trivial order in the 1/g expansion, with g being the e↵ective tension in the AdS2 ⇥ S2 ⇥ T6 superstring action. In this limit, corresponding to classical strings, we found that secret symmetries not only are present, but also essential to formulate the classical rmatrix in a universal, representation independent form. On the other hand, the limit g ! 0, corresponding to the weakly coupled CFT1, shows that the dual integrable model is described by an e↵ective theory of free fermions on a periodic spin-chain if g = 0, while one obtains a non-trivial spin chain of XYZ type if g 6= 0. Finally, we investigate Yangian and secret symmetries for AdS3 type IIB superstring backgrounds, verifying the persistence of such structures in AdS3/CFT2. Especially, we find that the antipode map, related to crossing symmetry, exchanges in a non-trivial way left and right generators of Y[psu(1|1)2c], the Yangian underlying the integrability of AdS3 superstrings.

Steady state detonations of rate-stick explosives can be modelled via a streamline based approach. The Straight Streamline Approximation (SSA) is a method for predicting the shape of the shock front and sonic surface for an explosive rate-stick. The SSA model is implemented with different explosives models to verify its ability to accurately match high resolution Direct Numerical Simulations (DNS) beyond the simple polytropic EOS (equation of state) and power law reaction rate models. For explosive models using a reaction rate with an induction zone it shown that the SSA is unable to capture diameter effect curves when compared with DNS. The CREST model is implemented into the ZND and Wood-Kirkwood steady- state detonation models. Implementing the CREST model into the steady-state models required the development of a thermodynamic relation not published before. Rate- stick calculations are performed for the SSA model and compared with DNS for various explosive models. With a realistic equation of state there is a limit on the boundary that the SSA model can integrate to, beyond this the streamlines begin to converge and the model equations break down. This places a limit on the SSA’s modelling capabilities not previously reported. Equations for the post-shock streamline curvature with a reaction term are devel- oped. The streamline curvature is calculated for a polytropic EOS with and without reaction at the shock. It is shown that when reaction is a maximum at the shock the magnitude of the streamline curvature is reduced and, in some cases, changes the sign of the curvature. With no reaction at the shock the streamline curvature is signifi- cantly larger. Moreover DNS shows that the streamlines are more curved for reaction rates with induction zones when compared to simple power law reaction rates. The implications for the SSA’s validity are discussed.