35,120 research outputs found

    Multiple solutions and periodic oscillations in nonlinear diffusion processes

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    We study the oscillatory stationary states in the temperature and concentration fields occurring in tubular chemical reactors. Singular perturbation and multitime scale procedures are combined formally to clearly and simply reveal the mechanism controlling these oscillatory states. Their stability is also studied, and when coupled with previously obtained results on multiple steady states, this information completes the response (bifurcation) diagram in one-parameter range of the tubular reactor. The results apply also to more general nonlinear parabolic problems of which the first order tubular reactor is a special case

    Response to Comments on Early Quaker Ecclesiology

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    The Genotype of the Endosperm and Embryo as It Influences Vivipary in Maize

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    The development of the maize seed is dependent on the orderly unfolding of events in which each component of the developing caryopsis has a particular role to play. The ultimate control of these events must depend upon numerous genes, which if altered will interfere with normal development. Many mutants of this type have been described, ranging from those which produce relatively slight alteration in the caryopsis to those which prevent practically all development. Among those producing relatively slight changes are mutants which give rise to premature germination. The seeds of these mutants develop normally until late in ontogeny. During the early dough stage the plumule begins to elongate, and the seeds germinate while still attached to the ear. Such mutants have been called viviparous

    The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts (Rutherford Aris)

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    [Book review

    New Eigenfunction Expansions and Alternative Representations for the Reduced Wave Equation

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    It has long been known that certain integral transforms and Fourier-type series can be used methodically for the resolution of certain kinds of classical boundary and initial value problems in separable coordinate systems. More recently, it has been shown that these classical transforms and series are spectral representations associated with an ordinary differential system which results on applying separation of variables to the given boundary value problem. This has been the basis for recent work concerned with systematically generating the proper spectral representation needed to solve a given problem. See [1] and [2] for a list of references

    Multiple Solutions of Singular Perturbation Problems

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    Under certain conditions on g(x, u) we establish the existence and asymptotic behavior for small ε > 0 of multiple asymptotic solutions of the nonlinear boundary value problem εu" + u’ - g(x,u) = 0, 0 < x < 1, u’(0) - au(0)= A ≥ 0, a > 0, u’(1) + bu(1) = B > 0, b > 0. Formal techniques of singular perturbation theory clearly reveal the mechanism which controls the appearance of multiple solutions. Their existence is then established rigorously by iteration schemes and the so-called "shooting method" for ordinary differential equations

    New Synonymies and Combinations for New World Pselaphinae (Coleoptera: Staphylinidae)

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    The following new synonymies and new combinations for Pselaphinae of North and Central America are documented: Anarmodius aequinoctialis (Motschulsky) (Trichonyx), New Comb.; Anthylarthron cornutum (Brendel) (= Anthylarthron curtipenne Casey, New Syn.); Aporhexius robustus (Motschulsky) (Euplectus), New Comb.; Batrisodespunctlfrons Casey (= Batrisodes appalachianus Casey, New Syn.); Batrisodes ionae (LeConte) (= Batrisodes caseyt Blatchley, New Syn.); Batrisodes clypeonotus (Brendel) (= Batrisodes kahli Bowman, New Syn.); Batrisodes lineaticollis (Aube) (= Batrisus globosus LeConte, New Syn.); Brachygluta corniventris (Motschulsky) (Bryaxts), New Comb., (= Bryaxts illinoiensis Brendel, New Syn.); Cedius ziegleri LeConte (= Cedius robustus Casey, New Syn.); Conoplectus simplex (Motschulsky) (Rhexius), New Comb., jun. syn. of Conoplectus canaliculatus (LeConte), New Syn.; Ctenisodes Raffray (= Pilopius Casey, New Syn.); Cylindrarctus ludovicianus (Brendel) (= Cylindrarctus comes Casey, New Syn.; Dalmosanus Park (= Pygmactium Grigarick and Schuster, New Syn.); Decarthron consanguineum (Motschulsky) (Bryaxis), New Comb.; Decarthron formiceti (LeConte) (= Decarthron rayi Park, = Decarthron seriepunctatum Brendel, New Syns.); Decarthron velutinum (LeConte), New Status (= D. formiceti, Park, 1958); Decarthron marinum Brendel (= Decarthron diversum Park, New Syn.); Decarthron robustum (Motschulsky) (Metaxis), New Comb.; Euphalepsus Reitter (= Barada Raffray, = Tetrasemus Jeannel, New Syns.), in subtribe Baradina; Eupsentus dilatatus Motschulsky (= Eupsenius rufus LeConte, New Syn.); Eurhexius canaliculatus (Motschulsky) (Trichonyx), New Comb. (= Eurhexius zonalis Park, New Syn.); Harmophola adusta (Motschulsky) (Euplectus), New Comb.; Iteticus cylindricus (Motschulsky) (Batrisus), New Comb.; Nisaxis Casey (=Dranisaxa Park, New Syn.); Oropus strtatus (LeConte) (=Oropus keeni Casey and O. brevipennis Casey, New Syns.); Panaramecia tropicalis (Motschulsky) (Euplectus), New Comb. (= Panaramecia zvilliamsi Park, New Syn.); Phamisus Aube, (= Canthoderus Motschulsky, New Syn.); Pselaptus oedipus (Sharp) (Bryaxis, Cryptorhinula), New Comb.; Pselaphus bellax Casey (= Pselaphus ulkei Bowman, New Syn); Reichenbachia intacta (Sharp) (= Bryaxis sarcinaria Schaufuss, New Syn.); Reichenbachia pruinosa (Motschulsky) (Bryaxis), New Comb., (= Bryaxis macrura Motschulsky, = Reichenbachia bterigi Park, New Syns.); Reichenbachia rubricunda (Aube) (= Bryaxis gemmifer LeConte, New Syn.); Trimicerus Motschulsky, (= Batrybraxis Reitter, New Syn.); Trimicerus corn?gera (Motschulsky) (Bryaxis), New Comb. (= Batrybraxis panamensis Park, New Syn.); Trimicerus pacificus Motschulsky (= Batrybraxis bowmani Park, New Syn.); Trimiomelba dubia (LeConte) (= Trimium americanum Motschulsky, = Trimium convexulum LeConte, = Trimiomelba laevis Casey, New Syns.); Tyrus humeralis (Aube) (= Tyrus consimilis Casey, New Syn.); Tyrus semiruber Casey (= Tyrus humeralis of authors); Tyrus cortidnus Casey (= Tyrus carinifer Casey, New Syn.); Xybarida trimioides (Sharp) (Bryaxis, Cryptorhinula), New Comb. Lectotype designations: Batrisus ionae LeConte; Batrisus globosus LeConte; Bryaxis consangu?nea Motschulsky; Bryaxis corniventris Motschulsky; Bryaxis pruinosa Motschulsky; Metaxis robusta Motschulsky; Rhextus simplex Motschulsky; Trimium americanum LeConte; Tyrus consimilis Casey. New species and genera: Cylindrarctus semin?le Chandler, New Species (= Cylindrarctus comes, Chandler, 1988); Motschtyrus pilosus (Motschulsky) (Tychus), Panama, New Genus, New Comb

    An Integral Transform Associated with Boundary Conditions Containing an Eigenvalue Parameter

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    It has long been known that certain integral transforms and Fourier-type series can be used to solve many classical boundary and initial value problems in separable coordinate systems. More recently, it has been shown that these classical transforms and series are spectral representations associated with an ordinary differential system which results on applying separation of variables to the given boundary value problem. This has been the basis for recent work concerned with systematically generating the proper spectral representation needed to solve a given problem. See [1]-[4] for a list of references. We shall consider the problem of finding the associated spectral representation when the resulting ordinary differential system has the eigenvalue parameter occurring in both the equation and one boundary condition. Moreover, the differential equation is to be satisfied on a semi-infinite interval, thus leading to a singular problem which does not seem to have been studied before. In §2 by using a transformation due to B. Friedman (which we modify appropriately for our singular case), we first give a formal derivation of the spectral representation, and then we rigorously prove the result. In §3 our representation is applied to solve an initial-boundary value problem arising in the theory of diffusion and heat flow in one dimension. We should bear in mind that even in cases where solutions are already known, our method systematically yields alternative representations which are often more rapidly convergent and from which asymptotic expansions of solutions with respect to parameters can often be found. In the problem to be considered a representation of the solution can also be found easily by a straight-forward application of the Laplace transform in time t, while the new transform derived in §2 yields the solution when applied in space x. The new transform, however, can be applied when the coefficients in the boundary value problem are time dependent, a situation which, in general, precludes the use of the Laplace transform.. As a general rule [1] there should be a spectral representation associated with each ordinary differential system resulting from applying separation of variables to the original boundary value problem, and each spectral representation should lead to a different representation of the solution of the original problem

    Instabilities in chemically reacting mixtures

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    We shall study two different types of instability which arise in the theory of chemical and biochemical reactions [1], [2] and in the study of heat and mass transfer in porous catalysts [3], [4]. Peculiar physical effects involving local regions of oscillation and local instability (in a sense to be explained below) are observed experimentally. For each of the two different types of phenomena we believe that we have identified one possible mechanism for such occurrences. In § 2 we shall show that the sudden transition to localized temporal oscillation is reflected in a special situation first observed by N. Levinson [5]. The underlying chemistry and mathematics is introduced via a very simple initial value problem for a model system of reaction equations. A singular perturbation analysis clearly reveals the structure of the solution and also the mechanism which governs the occurrence of the oscillatory instabilities. In § 3 we consider the phenomenon of localized steady spatial oscillation for general reaction-diffusion equations. By combining singular perturbation and generalized WKB type methods we present a general technique for studying this type of phenomenon
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