the calculation of thermoacoustic oscillations thermoacoustic oscillations occur in a wide variety of practical applications in which heat is supplied to an acoustic resonator a simple geometry is investigated systematically to determine the importance of various flow parameters on the frequency of the oscillations detailed consideration of elementary examples shows that the form of the coupling between the heat input and the unsteady flow has a crucial effect on the frequency of oscillation the same elementary examples are used to compare how well if at all different calculation methods in the literature account for this influence a mean flow and a distributed region of heat input significantly complicate the analysis of thermoacoustic oscillations and are often neglected model problems are used to illustrate that mean flow effects can become significant even at modest inlet mach numbers and to indicate circumstances under which a distributed heat input may be treated as concentrated

reflection functors and symplectic reflection algebras for wreath products we construct reflection functors on categories of modules over deformed wreath products of the preprojective algebra of a quiver these functors give equivalences of categories associated to generic parameters which are in the same orbit under the weyl group action we give applications to the representation theory of symplectic reflection algebras of wreath product groups

fuzzy smooth preproximity spaces abstract the concept of a fuzzy smooth preproximity space is introduced and studied also some particular constructions of fuzzy smooth preproximity are given a natural link is established between this concept and the concept of fuzzy pretopological spaces and fuzzy preuniform spaces

an exact solution for one dimensional acoustic fields in ducts with an axial temperature gradient abstract in this paper an approach is presented for obtaining exact analytical solutions for sound propagation in ducts with an axial mean temperature gradient the one dimensional wave equation for ducts with an axial mean temperature gradient is derived the analysis neglects the effects of mean flow and therefore the solutions obtained are valid only for mean mach numbers that are less than 0 1 the derived wave equation is then transformed to the mean temperature space it is shown that by use of suitable transformations the derived wave equation can be reduced to analytically solvable equations e g bessel s differential equation the applicability of the developed technique is demonstrated by obtaining a solution for ducts with a linear temperature profile this solution is then applied to investigate the dependence of sound propagation in a quarter wave tube upon the mean temperature profile furthermore the developed analytical solution is used to extend the classical impedance tube technique to the determination of admittances of high temperature systems e g flames the results obtained using the developed analytical solution are in excellent agreement with experimental as well as numerical results analytical solutions were also obtained for a duct with an exponential temperature profile and also for a temperature profile that corresponds to a constant convective heat transfer coefficient at the wall

reconstruction of acoustic transfer matrices by instationary computational fluid dynamics thermoacoustic combustion instabilities are a frequently encountered problem in the operation of combustion equipment the brute force application of computational fluid dynamics to the analysis of thermoacoustic instabilities is estimated to be forbiddingly expensive for many systems of technical interest due to the high computational demands of a time and space accurate simulation of a low mach number compressible reacting flow in a complex geometry thermoacoustic systems can be modelled efficiently as networks of acoustic multi ports where each multi port corresponds to a certain component of the system e g air or fuel supply burner flame combustor and suitable terminations and is represented mathematically by its transfer matrix for some multi ports the transfer matrix can be derived analytically from first principles i e the equations of fluid motions and suitable approximations however the acoustic behavior of more complicated components e g a burner or a flame has to be determined by empirical methods by using a black box approach common in communications engineering in this work a method is introduced which allows one to reconstruct the transfer matrix of an acoustic two port from an instationary computation of the response of the two port to an imposed perturbation of the steady state firstly from the time series data of fluctuating velocity and pressure on both sides of the two port the auto and cross correlations of the fluctuations are estimated then the unit impulse responses of the multi port are computed by inverting the wiener hopf equation finally the unit impulse responses are z transformed to yield the coefficients of the transfer matrix the method is applied to the one dimensional model of a heat source with time delay placed in a low mach number compressible flow for which an analytical description can be derived from first principles computational predictions of the transfer matrix have been validated successfully against these analytical results furthermore a comparison of the novel approach presented in this paper with a method for computing the frequency response of a flame by laplace transforming its step response is carried out

on plane wave propagation in a uniform pipe in the presence of a mean flow and a temperature gradient a theoretical study on the propagation of plane waves in the presence of a hot mean flow in a uniform pipe is presented the temperature variation in the pipe is taken to be a linear temperature gradient along the axis the theoretical studies include the formulation of a wave equation based on continuity momentum and state equation and derivation of a general four pole matrix which is shown to yield the well known transfer matrices for several other simpler cases

feedback control of combustion instabilities from within limit cycle oscillations using h loop shaping and the ν gap metric combustion instabilities arise owing to a two way coupling between acoustic waves and unsteady heat release oscillation amplitudes successively grow until nonlinear effects cause saturation into limit cycle oscillations feedback control in which an actuator modifies some combustor input in response to a sensor measurement can suppress combustion instabilities linear feedback controllers are typically designed using linear combustor models however when activated from within limit cycle the linear model is invalid and such controllers are not guaranteed to stabilize this work develops a feedback control strategy guaranteed to stabilize from within limit cycle oscillations a low order model of a simple combustor exhibiting the essential features of more complex systems is presented linear plane acoustic wave modelling is combined with a weakly nonlinear describing function for the flame the latter is determined numerically using a level set approach its implication is that the open loop transfer function oltf needed for controller design varies with oscillation level the difference between the mean and the rest of the oltfs is characterized using the gap metric providing the minimum required robustness margin for an formula see text loop shaping controller such controllers are designed and achieve stability both for linear fluctuations and from within limit cycle oscillations

representations of symplectic reflection algebras and resolutions of deformations of symplectic quotient singularities we give an equivalence of triangulated categories between the derived category of finitely generated representations of symplectic reflection algebras associated with wreath products with parameter t 0 and the derived category of coherent sheaves on a crepant resolution of the spectrum of the centre of these algebras

exact solutions to one dimensional acoustic fields with temperature gradient and mean flow an exact solution for one dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper the analysis is valid for mean mach numbers such that the square of the mean mach number is much less than one the one dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived by appropriate transformations the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile the developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow the results obtained using the analytical solution compare very well with the numerical results the developed solution is also compared with an existing analytical solution

generalized double affine hecke algebras of rank 1 and quantized del pezzo surfaces abstract let d be a simply laced dynkin diagram of rank r whose affinization has the shape of a star i e d 4 e 6 e 7 e 8 to such a diagram one can attach a group g whose generators correspond to the legs of the affinization have orders equal to the leg lengths plus 1 and the product of the generators is 1 the group g is then a 2 dimensional crystallographic group g z l z 2 where l is 2 3 4 and 6 respectively in this paper we define a flat deformation h t q of the group algebra c g of this group by replacing the relations saying that the generators have prescribed orders by their deformations saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots which are deformation parameters the algebra h t q for d 4 is the cherednik algebra of type c c 1 which was studied by noumi sahi and stokman and controls askey wilson polynomials we prove that h t q is the universal deformation of the twisted group algebra of g and that this deformation is compatible with certain filtrations on c g we also show that if q is a root of unity then for generic t the algebra h t q is an azumaya algebra and its center is the function algebra on an affine del pezzo surface for generic q the spherical subalgebra e h t q e provides a quantization of such surfaces we also discuss connections of h t q with preprojective algebras and painleve vi

pbw deformation theory and regular central extensions a deformation u of a graded k algebra a is said to be of pbw type if gru is a it has been shown for koszul and n koszul algebras that the deformation is pbw if and only if the relations of u satisfy a jacobi type condition in particular for these algebras the determination of the pbw property is a finite and explicitly determined linear algebra problem we extend these results to an arbitrary graded k algebra using the notion of central extensions of algebras and a homological constant attached to a which we call the complexity of a

exact solution for one dimensional acoustic fields in ducts with a quadratic mean temperature profile the purpose of this letter is to present an exact analytical solution for sound propagation in ducts with a quadratic mean temperature profile using appropriate transformations the one dimensional wave equation for ducts with an axial mean temperature gradient was reduced to the hypergeometric differential equation whose solution can be expressed in terms of hypergeometric functions the analysis neglects the effects of mean flow and is therefore valid only for small mean mach numbers

stratifications of marsden weinstein reductions for representations of quivers and deformations of symplectic quotient singularities we investigate the poisson geometry of the marsden weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver we show that the stratification by representation type equals the stratification by symplectic leaves the deformed symplectic quotient singularities spectra of centres of symplectic reflection algebras associated to a wreath product are shown to be isomorphic to reductions of a certain quiver this establishes a method to calculate when these deformations are smooth furthermore the isomorphism identifies symplectic leaves and so one can give a description of their symplectic leaves in terms of roots of the quiver

poincare birkhoff witt theorem for quadratic algebras of koszul type abstract in this paper we prove a general poincare birkhoff witt theorem for quadratic koszul algebras the result is similar to that obtained by polischuk and positselsky but the proof is entirely different and uses algebraic deformation theory in particular we obtain a new proof of the classical pbw theorem for lie algebras based on deformation theory

quantized multiplicative quiver varieties abstract beginning with the data of a quiver q and its dimension vector d we construct an algebra d q d q mat d q which is a flat q deformation of the algebra of differential operators on the affine space mat d q the algebra d q is equivariant for an action by a product of quantum general linear groups acting by conjugation at each vertex we construct a quantum moment map for this action and subsequently define the hamiltonian reduction a d q of d q with moment parameter we show that a d q is a flat formal deformation of lusztig s quiver varieties and their multiplicative counterparts for all dimension vectors satisfying a flatness condition of crawley boevey indeed the product on a d q yields a fedosov quantization the of symplectic structure on multiplicative quiver varieties as an application we give a description of the category of representations of the spherical double affine hecke algebra of type a n 1 and its generalization constructed by etingof oblomkov and rains in terms of a quotient of the category of equivariant d q modules by a serre subcategory of aspherical modules

on smooth preproximity spaces abstract in this paper we introduce some properties of fuzzy smooth preproximity spaces and we study the cuts of fuzzy smooth preproximity spaces the product and sum of these spaces are given

symplectic reflection algebras calogero moser space and deformed harish chandra homomorphism to any finite group sp v of automorphisms of a symplectic vector space v we associate a new multi parameter deformation h of the algebra v smash product of with the polynomial algebra on v the parameter runs over points of r where r number of conjugacy classes of symplectic reflections in the algebra h called a symplectic reflection algebra is related to the coordinate ring of a poisson deformation of the quotient singularity v this leads to a symplectic analogue of mckay correspondence which is most complete in case of wreath products if is the weyl group of a root system in a vector space and v then the algebras h are certain rational degenerations of the double affine hecke algebra introduced earlier by cherednik

the one dimensional acoustic field in a duct with arbitrary mean axial temperature gradient and mean flow abstract this paper presents an analytical solution for the one dimensional acoustic field in a duct with arbitrary mean temperature gradient and mean flow a wave equation for the pressure perturbation is derived which relies on very few assumptions an analytical solution for this is derived using an adapted wkb approximation the solution is a superposition of waves travelling in either direction and thus provides physical insight it is also very easy to calculate the proposed solution is applied to ducts with a mean temperature profile which varies axially with i a linear and ii a partial sine wave profile predictions are compared to those obtained by numerically solving the linearised euler equations lees the analytical solution reproduces the acoustic field very accurately across a wide range of flow conditions which span both low and moderate to high subsonic mach numbers it always performs well when the frequency exceeds a certain value when the mean temperature profile is linear it also performs well to very low frequencies this increased frequency range for linear mean temperature profiles leads to its application to more complicated profiles in a piecewise linear manner axially segmenting the temperature profile into regions that can be approximated as linear the acoustic field is predicted very accurately as long as enough segmentation points are used and the condition for the linear mean temperature profile is satisfied k 0 where k0 is the local wave number when there is no mean flow and is the normalised mean density gradient the proposed solution is extensively compared to previous analytical solutions and is found to be more accurate and reliable especially at higher mach numbers the entropy wave generated by communication between the acoustic waves and the distributed mean temperature zone is calculated using the lees it is found to remain very small across all operating conditions such that both the entropy wave and its impact on the acoustic field can be neglected

a family of exact transient solutions for acoustic wave propagation in inhomogeneous non uniform area ducts abstract this paper presents a family of exact solutions for quasi one dimensional transient acoustic wave propagation in ducts with mean temperature and area variations in the absence of mean flow these solutions are obtained using a transformation of the spatial and acoustic variables in a manner suggested by the wkb approximation exact travelling wave type solutions are obtained for a class of temperature and area profiles these solutions differ from the classical travelling wave solution however in that the acoustic pressure and velocity are not algebraically related by the local value of the acoustic impedance x c x although these solutions resemble the approximate high frequency wkb form of solution of the wave equation they have the interesting property that they are exact regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity

deformed preprojective algebras and symplectic reflection algebras for wreath products abstract we determine the pbw deformations of the wreath product of a symmetric group with a deformed preprojective algebra of an affine dynkin quiver in particular we show that there is precisely one parameter which does not come from deformation of the preprojective algebra we prove that the pbw deformation is morita equivalent to a corresponding symplectic reflection algebra for wreath product