conformal invariance and finite one dimensional quantum chains based on previous work of cardy 1984 the authors show in a systematic way how using conformal invariance one can determine the anomalous dimensions of various operators from finite quantum chains with different boundary conditions the method is illustrated in the case of the three and four state potts models where the anomalous dimensions of the para fermionic operators are found

exact solution and interfacial tension of the six vertex model with anti periodic boundary conditions we consider the six vertex model with anti periodic boundary conditions across a finite strip the row to row transfer matrix is diagonalized by the commuting transfer matrices method from the exact solution we obtain an independent derivation of the interfacial tension of the six vertex model in the anti ferroelectric phase the nature of the corresponding integrable boundary condition on the xxz spin chain is also discussed

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

similarity analysis of inelastic contact analysis of mechanical contact of solids is of interest not only regarding a variety of mechanical assemblies but also on a smaller scale such as roughness properties of surfaces and compaction of powder particles indentation testing is another prominent problem in the context to analyse the phenomena involved is inherently difficult at application essentially due to the presence of large strains nonlinear material behaviour time dependence and moving contact boundaries recently progress has been made however to explicitly solve basic boundary value problems especially due to advances in computational techniques a substantial ingredient which facilitates solution procedures is self similarity and it is the present purpose to explore in detail the advantages in a general setting when this feature prevails a viscoplastic framework is laid down for a wide class of constitutive properties where strain hardening plasticity creep and also nonlinear elasticity arise as special cases it is then shown that when surface shapes and material properties are modelled by homogeneous functions associated boundary value problems posed may be reduced to stationary ones as a consequence within hertzian kinematics relations between contact impression and regions become independent of loading and time and the connection to loading characteristics does not usually require a full solution of the problem in particular it is shown that for general head shapes it proves efficient to use an approach where an intermediate flat die solution serves as a basic tool also for hereditary materials an invariant computational procedure based on the intermediate problem is arrived at and decisive results shown to be found by simple cumulative superposition illustrations are given analytically for ellipsoidal contact of newtonian fluids and by detailed computations for spherical indentation of viscoplastic solids for which also universal hardness formulae are proposed for several bodies in contact it is shown how general results may be extracted from fundamental solutions for a half space

the ashkin teller quantum chain and conformal invariance the authors study the finite size effects for the fourth state one dimensional quantum chain introduced by kohmoto et al 1981 using different boundary conditions from the corrections to the ground state energy for periodic boundary conditions they verify that the central charge of the virasoro algebra is equal to one in the whole domain of criticality their numerical study suggests a new relation between the corrections to the ground state energy with free boundary conditions and with periodic boundary conditions various critical exponents including the surface ones and those corresponding to the para fermions are determined

integrable impurities for an open fermion chain employing the graded versions of the yang baxter equation and the reflection equations we construct two kinds of integrable impurities for a small polaron model with general open boundary conditions a we shift the spectral parameter of the local lax operator at arbitrary sites in the bulk and b we embed the impurity fermion vertex at each boundary of the chain the hamiltonians with different types of impurity terms are given explicitly the bethe ansatz equations as well as the eigenvalues of the hamiltonians are constructed by means of the quantum inverse scattering method in addition we discuss the ground state properties in the thermodynamic limit

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

operator content of the xxz chain the finite size scaling spectra of the xxz heisenberg chain are presented for even and odd numbers of sites respectively the operator content is given for free as well as for toroidal boundary conditions

subsectional polynomial e pulse synthesis and application to radar target discrimination a new family of extinction pulses e pulses called subsectional polynomial e pulses is presented this new type of e pulse is constructed by choosing polynomials of degree q as subsectional basis functions in the e pulse expansion the main feature of this family of e pulses is that the waveforms are continuous and smooth several topics concerning the e pulse technique are investigated such as insensitivity to the exact number of natural modes present in the target response aspect angle independence and effects of additive white gaussian noise numerical results using the response of a thin cylinder and a sphere show that the subsectional polynomial e pulses improve the results obtained using subsectional rectangular e pulses

an asymptotically unbiased e pulse based scheme for radar target discrimination this communication proposes an e pulse based scheme for radar target discrimination that provides asymptotically correct results for any level of additive white noise contaminating the radar signal after multiple sampling of the signal dispersed by the target it is analytically shown that the cross correlation between the output signals of the e pulse designed for the standard target corresponding to two different sampling periods is asymptotically null regardless of the amount of contaminating noise the results obtained by simulation have allowed us to propose a discrimination criterion that produces better results than the original e pulse technique at very low signal to noise ratio snr levels

spectrum of a duality twisted ising quantum chain the ising quantum chain with a peculiar twisted boundary condition is considered this boundary condition first introduced in the framework of the spin 1 2 xxz heisenberg quantum chain is related to the duality transformation which becomes a symmetry of the model at the critical point thus at the critical point the ising quantum chain with the duality twisted boundary is translationally invariant as in the case of the usual periodic or antiperiodic boundary conditions the complete energy spectrum of the ising quantum chain is calculated analytically for finite systems and the conformal properties of the scaling limit are investigated this provides an explicit example of a conformal twisted boundary condition and a corresponding generalized twisted partition function

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

test of modular invariance for finite xxz chains the central charge c of the virasoro algebra is determined using its relation to the set of anomalous dimensions of the scaling fields for the critical anisotropic heisenberg chain the results obtained by exactly solving the bethe ansatz for n or 4 are compared with the standard procedure for calculating c in the whole region of anisotropy for odd n the system is no longer modular invariant and the analogous averaging leads to an anisotropy dependent function which has been calculated

a theoretical study of the brinell hardness test brinell tests have long been the preferred method of assaying the hardness of metals during forming operations the general significance of the test has been codified in empirical laws especially those of meyer o neill and tabor on the other hand the indentation of elastoplastic media by a ball has never been thoroughly analysed in the context of modern mechanics of continua this is the objective here the actual boundary value problem is non steady but can be made steady in terms of reduced variables when the material response is suitably modelled namely the strain should be infinitesimal and expressible as the tensor gradient of a potential function of the stress deviator the function must be homogeneous of degree n 1 2 but is otherwise arbitrary meyer s law is then derivable rigorously ahead of a detailed solution moreover the predicted index is 2n 1 n substantiating o neill s rule for materials whose strain under uniaxial tension varies as some nth power of the stress it is predicted also that the piling up or sinking in around the indenter is correlated with n in the manner observed these immediate implications of the model amount to a priori evidence of its overall ability to simulate elastoplastic response of the kind induced in brinell tests evidence a posteriori was supplied by finite element computations for a standard potential whose level surfaces are of mises type mixed nine node quadrilateral elements were adopted these are known to promote optimal convergence and are well suited to handling incompressibility a carefully graded mesh provided about 24000 degrees of freedom computations were performed for n 1 2 4 and 10 covering the practical range the results include i distributions of the contact pressure and the radial and circumferential in surface stresses ii profiles of the deformed surface and iii contours of representative strain in the main body of material excellent agreement was obtained with tabor s experimental findings that the representative strain at the contact perimeter is y0 4 a d for any n a is the contact radius and d the ball diameter while the average pressure is 2 8 times the flow stress at strain y in a tension test finally strain paths at fixed stations were sampled to check the simulation of elastoplastic response locally as well as overall

operator content of the cyclic solid on solid models the operator content of the cyclic solid on solid models is derived under general boundary conditions by mapping the row to row transfer matrix onto the six vertex model and xxz heisenberg chain for the shift boundary conditions the dimensions and spins of the primary operators are derived analytically from finite size corrections to the scaling spectra the full operator content agrees with results for a quantum chain model having the same local symmetry

indentation of a power law creeping solid the aim of this paper is to establish a rigorous theoretical basis for interpreting the results of hardness tests on creeping specimens we investigate the deformation of a creeping half space with uniaxial stress strain behaviour 0 0 m which is indented by a rigid punch both axisymmetric and plane indenters are considered the shape of the punch is described by a general expression which includes most indenter profiles of practical importance two methods are used to solve the problem the main results are found using a transformation method suggested by r hill it is shown that the creep indentation problem may be reduced to a form which is independent of the geometry of the punch and depends only on the material properties through m the reduced problem consists of a nonlinear elastic half space which is indented to a unit depth by a rigid flat punch of unit radius in the axisymmetric case or unit semi width in the plane case exact solutions are given for m 1 and m for m between these two limits the reduced problem has been solved using the finite element method the results enable the load on the indenter and the contact radius to be calculated in terms of the indentation depth and rate of penetration the stress strain and displacement fields in the half space may also be deduced the accuracy of the solution is demonstrated by comparing the results with full field finite element calculations the predictions of the theory are shown to be consistent with experimental observations of hardness tests on creeping materials reported in the literature

branching rules for unitary representations of virasoro and super virasoro algebras at c 1 the branching rules for unitary highest weight representations of virasoro and super virasoro algebras that contain a subalgebra with central charge c 1 are presented these rules are useful for identifying points of higher symmetry in two dimensional critical systems with c 1 and for the analysis of a defected ising chain

conformal invariance in incommensurate phases we study finite size corrections to the free energy of free fermion models on a torus with periodic twisted and fixed boundary conditions inside the critical striped incommensurate phase the free energy densityf n m on ann m square lattice with periodic or twisted boundary conditions scales asf n m f a s nm we derive exactly the finite size scaling fss amplitudesa s as a function of the aspect ratios m n these amplitudes are universal because they do not depend on details of the free fermion hamiltonian we establish an equivalence between the fss amplitudes of the free fermion model and the coulomb gas system with electric and magnetic defect lines the twist angle generates magnetic defect lines while electric defect lines are generated by competition between domain wall separation and system size the fss behavior of the free fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec l for instance the fss amplitude on an infinite cylinder with fixed boundary conditions is found to be one quarter of that with periodic boundary conditions finally we conjecture the exact form of the fss amplitudes for an interacting fermion model on a torus numerical calculations employing the bethe ansatz confirm our conjecture in the infinite cylinder limit

the spin 1 2xxz heisenberg chain the quantum algebra uq sl 2 and duality transformations for minimal models the finite size scaling spectra of the spin 1 2 xxz heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c 1 including the unitary and nonunitary minimal series taking into account the half integer angular momentum sectors which correspond to chains with an odd number of sites in many cases leads to new spinor operators appearing in the projected systems these new sectors in the xxz chain correspond to new types of frustration lines in the projected minimal models the corresponding new boundary conditions in the hamiltonian limit are investigated for the ising model and the 3 state potts model and are shown to be related to duality transformations which are an additional symmetry at their self dual critical point by different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite xxz chain the observed degeneracies in the energy and momentummore spectra are shown to be the consequence of intertwining relations involving u sub q sl 2 quantum algebra transformations 35 refs 3 tabs less

parameter estimation of exponentially damped sinusoids using a higher order correlation based approach a very common problem in signal processing is parameter estimation of exponentially damped sinusoids from a finite subset of noisy observations when the signal is contaminated with colored noise of unknown power spectral density a cumulant based approach provides an appropriate solution to this problem we propose a new class of estimator namely a covariance type estimator which reduces the deterministic errors associated with imperfect estimation of higher order correlations from finite data length this estimator allows a higher order correlation sequence to be modeled as a damped exponential model in certain slices of the moments plane this result shows a useful link with well known linear prediction based methods such as the minimum norm principal eigenvector method of kumaresan and tufts 1982 which can be subsequently applied to extracting frequencies and damping coefficients from the 1 d correlation sequence this paper discusses the slices allowed in the moments plane the uses and limitations of this estimator using multiple realizations and a single record in a noisy environment monte carlo simulations applied to standard examples are also performed and the results are compared with the kt method and the standard biased estimator based approach the comparison shows the effectiveness of the proposed estimator in terms of bias and mean square error when the signals are contaminated with additive gaussian noise and a single data record with short data length is available

some finite size amplitudes and critical exponents for potts and ashkin teller quantum chains analytic expressions are derived for the leading finite size corrections to a class of energy eigenvalues of the potts and ashkin teller quantum chains making use of their equivalences with a modified xxz heisenberg chain assuming conformal invariance exact results are thence obtained for some bulk scaling dimensions and surface exponents in these models

vector coherent state theory in a group with non commuting raising generators vector coherent state theory is used to give an explicit construction of the irreducible representations of a group with non commuting raising generators the simple example of the compact unitary symplectic group usp 4 contains implies usp 2 usp 2

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

similarity analysis of creep indentation tests the general theory of axisymmetric hardness tests on nonlinear media is approached from the standpoint of similarity transformations it is shown how an entire process of indentation can be made to depend on the solution of just one boundary value problem in scaled variables and with a fixed geometry once this single auxiliary solution has been obtained the values of all physical quantities in the original problem can be generated readily at any stage without further numerical error even by themselves the similarity relations provide valuable information about for example an invariant connection between the depth of penetration and the radius of contact or about the variation of penetration with time in a creep test under dead load two kinds of material behaviour are considered a nonlinear elastic modelling strain hardening plasticity and b nonlinear viscous modelling secondary creep in either category the constitutive specification is sufficiently flexible to represent a wide range of actual responses in the context of hardness testing the analysis for case a extends a theory of ball indentation by hill et al to a class of indenters with shapes varying from flat to conical it also prepares the ground for case b which is more difficult and calls for a quite different auxiliary problem

critical behaviour of mixed heisenberg chains the critical behaviour of anisotropic heisenberg models with two kinds of antiferromagnetically exchange coupled centres are studied numerically by using finite size calculations and conformal invariance these models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism most of our results are centred in the mixed heisenberg chain where we have at even odd sites a spin su 2 operator interacting with a xxz like interaction anisotropy our results indicate universal properties for all these chains the whole phase where the models change from ferromagnetic to ferrimagnetic behaviour is critical along this phase the critical fluctuations are ruled by a c 1 conformal field theory of gaussian type the conformal dimensions and critical exponents along this phase are calculated by studying these models with several boundary conditions

toroidal boundary conditions in n state quantum chains the author considers one dimensional n state quantum chains having as symmetry an abelian group a of order n generalised ising chain these hamiltonians depend on 2 n 1 coupling constants for special values of the coupling constants the symmetry of the quantum chains is larger than a corresponding to a in general non abelian group g with m elements m n for each element of g he finds explicitly a boundary condition which leaves the hamiltonian translationally invariant this problem is relevant in finite size scaling studies at the critical point of a second order phase transition

the phase boundary in dilute and random ising and potts ferromagnets the authors present an approach to dilute ising and potts models based on the fortuin kasteleyn random cluster representation which is simultaneously rigorous intuitive and surprisingly simple their analysis yields with no dimensional restrictions or other caveats the following asymptotic form of the phase boundary for the regular dilute model in which bonds have constant ferromagnetic coupling j with probability p and are vacant with probability 1 p the critical temperature scales as exp j ktc p approximately mod p pc mod implying that the crossover exponent is phi 1 if the constant couplings are replaced by a distribution f j with mass near j 0 quite different crossover behaviour is observed for example if f j approximately jalpha then for p near pc tc p approximately mod p pc mod 1 alpha

extinction pulses synthesis for radar target discrimination using spl beta splines new e pulse conditions the extinction pulse method has been proven to be a suitable method for radar target discrimination using the natural resonance annihilation concept the standard procedure for extinction pulse e pulse construction is based on an expansion on subsectional polynomials in this paper it is proposed a new formalism for e pulse construction using beta splines this formalism allows the e pulse polynomial basis expansion to be treated in a unified theoretical framework and leads to a simplification of the original problem due to the linear nature of all the involved parameters this new formulation has been also used to impose new conditions over the spectral contents of the e pulses these e pulses constructed using the new conditions annihilate better the natural modes in the late time radar target response and provide a better discrimination rates than the classical scheme

walks trials and polymers with loops lattice models interpolating between free and self avoiding random walks are investigated generating functions are constructed for k tolerant walks various trail problems etc for trail problems the effective field theory describing the global behaviour is analysed in the vicinity of the upper critical dimension dc 4 their asymptotic large scale behaviours are the same as those of the self avoiding walk arguments are presented to support the same conclusion for much more general classes of walks including k tolerant walks one of the models exhibits a new tricritical point of order epsilon 1 2 if the fugacity for crossing is increased

spectra of non hermitian quantum spin chains describing boundary induced phase transitions the spectrum of the non hermitian asymmetric xxz chain with additional non diagonal boundary terms is studied the lowest lying eigenvalues are determined numerically for the ferromagnetic chain the temporal correlation length shows the same properties as the spatial correlation length for the antiferromagnetic chain we find a conformal invariant spectrum where the partition function corresponds to the one of a coulomb gas with only magnetic charges this is in contrast to the case of diagonal boundary terms where one finds only electric charges similar results are obtained in a toy model that can be diagonalized analytically in terms of free fermions

conformal invariance and the operator content of the xxz model with arbitrary spin the authors are concerned with the critical properties of the anisotropic heisenberg chain or xxz model with arbitrary integer or half integer spin the eigenspectra of these hamiltonians with periodic boundaries are calculated for finite chains by solving numerically their associated bethe ansatz equations the resulting spectra are found to be in accord with the predictions of conformal invariance and the operator content is identified for lattices with an even and odd number of sites the results for spin 1 and spin 3 2 indicate that the conformal anomaly c for these models in the gapless regime has the value c 3s 1 s independent of the anisotropy and the exponents vary continuously with the anisotropy as in the eight vertex model the operator content of these models indicate that the underlying field theory governing these critical spin s models is described by composite fields formed by the product of gaussian and z n fields with n 2s finally some of the irrelevant operators which produce the leading finite size corrections of the eigenenergies are identified

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum