[ { "id": "authors:r402j-n4d30", "collection": "authors", "collection_id": "r402j-n4d30", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151123-095554817", "type": "article", "title": "Time-dependent 2-stream particle transport", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "We consider time-dependent transport in the 2-stream or \"rod\" model via an attractive matrix formalism. After reviewing some classical problems in homogeneous media we discuss transport in materials whose density may vary. There we achieve a significant contraction of the underlying Telegrapher's equation. We conclude with a discussion of stochastics, treated by the \"first-order smoothing approximation.\"", "doi": "10.1016/j.anucene.2015.03.037", "issn": "0306-4549", "publisher": "Elsevier", "publication": "Annals of Nuclear Energy", "publication_date": "2015-12", "volume": "86", "pages": "35-44" }, { "id": "authors:st1mh-ak804", "collection": "authors", "collection_id": "st1mh-ak804", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20121107-143620438", "type": "article", "title": "Radiative Transport Reconsidered", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "We describe situations where coherent and incoherent effects take place in a disordered medium illuminated by a coherent source. We illustrate the transition from coherence to incoherence by considering the propagation of a scalar wave in a medium of point, isotropic scatterers. We note how a traditional transport equation evolves and that it is enriched by a boundary layer in which coherence decays and the intensity is of damped oscillatory nature.", "doi": "10.1080/00411450.2012.671208", "issn": "1532-2424", "publisher": "Taylor and Francis Group LLC", "publication": "Transport Theory and Statistical Physics", "publication_date": "2012-09-10", "series_number": "3-4", "volume": "41", "issue": "3-4", "pages": "200-213" }, { "id": "authors:rw4jy-n9s44", "collection": "authors", "collection_id": "rw4jy-n9s44", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20110615-154004607", "type": "teaching_resource", "title": "A Minimum of Stochastics for Scientists : Ten Lectures", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "These pages contain material I have tried to convey, in a course given occasionally, to a Caltech audience composed mostly of graduate students. The idea behind the course was to introduce students to the ideas and attitudes that underlie the statistical modeling of physical, chemical, biological systems. To provide a sufficient minimum to begin the repair of total ignorance, to get one started, to avoid embarrassing moments at an oral qualifying examination, perhaps. This little book might be titled \"An Introduction to an Introduction to . . .\" The student who wishes to go deeper will find much that is rich in the classic texts and essays listed under References.", "publisher": "California Institute of Technology", "publication_date": "2009" }, { "id": "authors:8z9b3-ydf82", "collection": "authors", "collection_id": "8z9b3-ydf82", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORjmp03", "type": "article", "title": "Classical transport of charged particles in a magnetic field", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "We examine the traditional transport equation for classical, charged particles diffusing in a cold, absorbing medium subject to a uniform magnetic field and in which scattering is isotropic. Steady-state solutions in plane geometry are examined in some detail; we make no expansion about an isotropic angular distribution. Restricting the motion to two dimensions captures most of the interesting features; there is some discussion of the three-dimensional case.", "doi": "10.1063/1.1591994", "issn": "0022-2488", "publisher": "Journal of Mathematical Physics", "publication": "Journal of Mathematical Physics", "publication_date": "2003-09-01", "series_number": "9", "volume": "44", "issue": "9", "pages": "4057-4077" }, { "id": "authors:14f4s-xtm57", "collection": "authors", "collection_id": "14f4s-xtm57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-090753862", "type": "article", "title": "On the collision probability for the infinite cylinder", "author": [ { "family_name": "Corngold", "given_name": "Noel R.", "clpid": "Corngold-N" } ], "abstract": "The derivation of a compact expression for the collision probability for the infinite cylinder involves the reduction of a complicated integral, a reduction attributed to the late D.R. Inglis in a Los Alamos report that is unavailable. We present an alternative evaluation here.", "doi": "10.1016/S0306-4549(01)00102-5", "issn": "0306-4549", "publisher": "Elsevier", "publication": "Annals of Nuclear Energy", "publication_date": "2002-07", "series_number": "10", "volume": "29", "issue": "10", "pages": "1151-1155" }, { "id": "authors:s87j7-f9910", "collection": "authors", "collection_id": "s87j7-f9910", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:AROjosaa99", "type": "article", "title": "Photon diffusion coefficient in an absorbing medium", "author": [ { "family_name": "Aronson", "given_name": "Raphael", "clpid": "Aronson-R" }, { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "A number of investigators have recently claimed, based on both analysis from transport theory and transport theory-based Monte Carlo calculations, that the diffusion coefficient for photon migration should be taken to be independent of absorption. We show that these analyses are flawed and that the correct way of extracting diffusion theory from transport theory gives an absorption-dependent diffusion coefficient. Experiments by two different sets of investigators give conflicting results concerning whether the diffusion coefficient depends on absorption. The discrepancy between theory and the earlier set of experiments poses an interesting challenge.", "issn": "1084-7529", "publisher": "Optical Society of America", "publication": "Journal of the Optical Society of America A", "publication_date": "1999-05", "series_number": "5", "volume": "16", "issue": "5", "pages": "1066-1071" }, { "id": "authors:4nt7k-1x529", "collection": "authors", "collection_id": "4nt7k-1x529", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORpop96", "type": "article", "title": "The nonlinear diocotron mode in a pure electron plasma", "author": [ { "family_name": "Corngold", "given_name": "Noel R.", "clpid": "Corngold-N" } ], "abstract": "The nonlinear diocotron mode, discussed by Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] is characterized by two equations, one describing the frequency of orbiting, the other giving the quadrupole moment, as functions of size and offset. A new analysis, based on the method of moments, which yields equations more general in their content, is presented here. For example, the new equations describe columns whose shapes are not elliptical and whose densities are not constant.", "doi": "10.1063/1.871601", "issn": "1070-664X", "publisher": "Physics of Plasmas", "publication": "Physics of Plasmas", "publication_date": "1996-09-01", "series_number": "9", "volume": "3", "issue": "9", "pages": "3324-3330" }, { "id": "authors:2a76z-zky54", "collection": "authors", "collection_id": "2a76z-zky54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-094517591", "type": "article", "title": "A contribution to the problem of runaway electrons", "author": [ { "family_name": "Christianson", "given_name": "Kent", "clpid": "Christianson-K" }, { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "After giving a short sketch of the status of the field we treat two models of runaway in some detail. One is a Fokker-Planck equation, the other a kinetic equation with compact kernel. Both are 1-d models; both deal with the marginal case of (1v) relaxation of diffusion coefficient or reaction-rate. We also give a description - in 1-d - of the Gaussian shape of the runaway pulse following an initial burst.", "doi": "10.1016/0306-4549(95)00098-4", "issn": "0306-4549", "publisher": "Elsevier", "publication": "Annals of Nuclear Energy", "publication_date": "1996-03", "series_number": "4-5", "volume": "23", "issue": "4-5", "pages": "271-283" }, { "id": "authors:g961q-7af20", "collection": "authors", "collection_id": "g961q-7af20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORpop95", "type": "article", "title": "Linear response of the two-dimensional pure electron plasma: Quasimodes for some model profiles", "author": [ { "family_name": "Corngold", "given_name": "Noel R.", "clpid": "Corngold-N" } ], "abstract": "After examining the initial value problem for the linear, diocotron response of a long cylinder of pure-electron plasma, the \"quasimodes\" associated with convex, power-law density profiles are studied. For these profiles, exact, analytic results are available. The \"quasimodes,\" which are damped by phase mixing, may be characterized by their angular variation, flatness, and the magnitude of the gap separating the plasma from the containing wall.", "doi": "10.1063/1.871413", "issn": "1070-664X", "publisher": "Physics of Plasmas", "publication": "Physics of Plasmas", "publication_date": "1995-03-01", "series_number": "3", "volume": "2", "issue": "3", "pages": "620-628" }, { "id": "authors:ssgwt-hzg68", "collection": "authors", "collection_id": "ssgwt-hzg68", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-095412484", "type": "article", "title": "On the zero-energy moments of the distribution of fast atoms and cascades", "author": [ { "family_name": "Corngold", "given_name": "Noel R.", "clpid": "Corngold-N" } ], "abstract": "The slowing down of neutrons in capture-free hydrogen is not only a classic problem in transport theory but is a paradigm for several problems in the interaction of energetic ions with matter. Here we are concerned primarily with the distribution of stopped particles. We describe a novel expansion for the transport equation which which gives extremely accurate results for the moments of the distribution and which proves an earlier conjecture made by E.M. Baroody. We discuss additional applications of the expansion, which appears to be an improved \"straight-ahead\" approximation.", "doi": "10.1016/0306-4549(92)90009-Z", "issn": "0306-4549", "publisher": "Elsevier", "publication": "Annals of Nuclear Energy", "publication_date": "1992-10", "series_number": "10-12", "volume": "19", "issue": "10-12", "pages": "655-662" }, { "id": "authors:cwn8k-ghr60", "collection": "authors", "collection_id": "cwn8k-ghr60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORpra89", "type": "article", "title": "Time-dependent collision cascades", "author": [ { "family_name": "Corngold", "given_name": "N. R.", "clpid": "Corngold-N" } ], "abstract": "We use the linearized Boltzmann equation to discuss the time dependence of atomic collision cascades. The atoms are presumed to interact via a power-law potential, the power being denoted (-2/a). We wish to ascertain whether the equation, and/or certain special solutions, show striking changes in behavior at certain special values of a. We find a value of a which distinguishes energy-conserving cascades from anomalous cascades, and another which signals the failure of the linear approximation. Scaling, and also the emergence of similarity solutions, are discussed.", "doi": "10.1103/PhysRevA.39.2126", "issn": "0556-2791", "publisher": "Physical Review A", "publication": "Physical Review A", "publication_date": "1989-02-15", "series_number": "4", "volume": "39", "issue": "4", "pages": "2126-2132" }, { "id": "authors:tragq-jrx10", "collection": "authors", "collection_id": "tragq-jrx10", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180521-163704706", "type": "article", "title": "The mathematical theory of resonances whose widths are exponentially small, II", "author": [ { "family_name": "Harrell", "given_name": "Evans M.", "clpid": "Harrell-E-M" }, { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" }, { "family_name": "Simon", "given_name": "Barry", "orcid": "0000-0003-2561-8539", "clpid": "Simon-B" } ], "abstract": "It is shown how the rigorous justification of resonance widths in Paper I [5] can be simplified by exploiting Langer's trick of expanding the independent variable rather than the dependent variable [9].", "doi": "10.1016/0022-247X(84)90225-7", "issn": "0022-247X", "publisher": "Elsevier", "publication": "Journal of Mathematical Analysis and Applictions", "publication_date": "1984-04-15", "series_number": "2", "volume": "99", "issue": "2", "pages": "447-457" }, { "id": "authors:w2v9b-x0q46", "collection": "authors", "collection_id": "w2v9b-x0q46", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-131023165", "type": "article", "title": "Aspects of Fokker-Planck transport", "author": [ { "family_name": "Corngold", "given_name": "N.", "clpid": "Corngold-N" } ], "abstract": "We apply to a simple example, taken from neutron thermalization, techniques we have been using in the study of Fokker-Planck transport of test particles. The example from neutron physics concerns the divergence of the series expressing diffusion length as a function of absorber concentration. In both cases, analytic continuation, and matched asymptotic expansion play a role.", "doi": "10.1016/0149-1970(81)90010-X", "issn": "0149-1970", "publisher": "Elsevier", "publication": "Progress in Nuclear Energy", "publication_date": "1981", "series_number": "2-3", "volume": "8", "issue": "2-3", "pages": "163-170" }, { "id": "authors:w6xdp-01g54", "collection": "authors", "collection_id": "w6xdp-01g54", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20141017-152754159", "type": "book_section", "title": "Progress in Kinetic Theory: Generalization of Boltzmann's Equation", "book_title": "Rarefied gas dynamics; International Symposium, 10th, Aspen, Colo., July 18-23, 1976, Technical Papers", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "contributor": [ { "family_name": "Potter", "given_name": "J. Leigh", "clpid": "Potter-J-L" } ], "abstract": "We have recently celebrated the hundredth birthday of Boltzmann's kinetic equation, an equation that has been enormously fruitful in physics and engineering. However, Boltzmann's model of transport processes has\nits limitations. It is based upon a view of Nature that is 'coarse-grained' in time and space, the intervals of coarse-graining being the duration of a collision, and the range of intermolecular force. In the coarse-grained\nworld of rarefied systems, Boltzmann' s Stosszahlansatz works well. As more data on transport processes in liquids and dense gases accumulate, the need for systematic generalization of Boltzmann's equation (and the\nChapman-Enskog analysis) grows. Computer experiments, neutron scattering experiments, and the scattering of laser beams have been particularly stimulating here, for they probe extremely short intervals of space\nand time in the dynamics of the target system. Coarse-graining, and the Stosszahlansatz are no longer acceptable. It is not widely appreciated that for the past decade, scientists have had a compact and elegant formalism\nat their disposal, for the construction of generalized kinetic equations. The new equations describe the response of the N-body system in the full frequency\nand wave-number domain. They are characterized by kernels that exhibit both spatial and temporal 'memory' and are, necessarily, very complicated. We shall review recent progress in the analysis, commenting\non 1) the generalization of Boltzmann's equation to higher densities . . . the cluster expansion and the Bogoljubov Ansatz, revisited. 2) the generalized\nkinetic equations of Zwanzig and Mori 3) progress in analysis and solution.", "doi": "10.2514/4.865251", "isbn": "978-0-915928-15-6", "publisher": "American Institute of Aeronautics and Astronautics", "place_of_publication": "New York, NY", "publication_date": "1977", "pages": "651-678" }, { "id": "authors:h1zmc-fqa52", "collection": "authors", "collection_id": "h1zmc-fqa52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-135447143", "type": "article", "title": "Kinetic theory of diffusion in liquids: A hydrodynamic approximation", "author": [ { "family_name": "Ku\u0161\u010der", "given_name": "I.", "clpid": "Ku\u0161\u010der-I" }, { "family_name": "Corngold", "given_name": "N.", "clpid": "Corngold-N" } ], "abstract": "Diffusion in simple classical liquids is analyzed in terms of the test-particle phase-space density, with emphasis upon its long-time behavior. The Green's function of the generalized Fokker-Planck equation is used to define auxiliary quantities, in particular the transport mean path that enters solutions of the Chapman-Enskog type. Approximations for the lowest eigenvalues and eigenfunctions of the Fourier- and Laplace-transformed F.-P. operator \u03c3_(ks) are constructed, and an expansion for the resolvent operator (s + ik \u00b7 v \u2013 \u03c3_(ks))^(-1) proposed. With the additional assumption that branch-points on the negative real axis of s are the only singularities of the transformed F.-P. operator, a Laplace inversion is tentatively carried out, so that the general form of the solution is obtained. This is found to agree with the solution derived by hydrodynamic arguments. Only in a limited sense is the latter method equivalent to that of mode-mode coupling.", "doi": "10.1016/0378-4371(75)90045-X", "issn": "0378-4371", "publisher": "Elsevier", "publication": "Physica A", "publication_date": "1976", "series_number": "2", "volume": "82", "issue": "2", "pages": "195-220" }, { "id": "authors:3yet2-kky10", "collection": "authors", "collection_id": "3yet2-kky10", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-131643421", "type": "book_section", "title": "Quasi-Exponential Decay of Neutron Fields", "book_title": "Advances in Nuclear Science and Technology", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "contributor": [ { "family_name": "Henley", "given_name": "Ernest J.", "clpid": "Henley-E-J" }, { "family_name": "Lewins", "given_name": "Jeffery", "clpid": "Lewins-J" } ], "abstract": "This chapter discusses the phenomenon of quasi-exponential behavior. The neutron field often behaves in an exponential manner. In a pulsed neutron experiment, the behavior may be exponential in time. In a diffusion length experiment or its generalization, the wave experiment, the field may be exponential in space. The decay constants that characterize these exponentials are natural data for the description of the system. The decay constants are eigenvalues. They depend upon the nature of the material in which the neutron field is established and upon the shape of the assembly. Sometimes, the effects can be separated, though never completely. More precisely, the observed decay constants are discrete eigenvalues. The operators associated with these eigenvalues have a continuous and a discrete spectrum. The number of eigenvalues in the point spectrum is often quite small; in some systems, the point spectrum is empty.", "doi": "10.1016/B978-0-12-029308-7.50008-7", "isbn": "978-0-12-029308-7", "publisher": "Academic Press", "place_of_publication": "New York, NY", "publication_date": "1975-01-01", "pages": "1-46" }, { "id": "authors:pje8e-ack13", "collection": "authors", "collection_id": "pje8e-ack13", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-140055203", "type": "article", "title": "Some abalytical methods in neutron transport theory", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "In this paper, whose purpose is pedagogic, we discuss some distinctive features of neutron transport theory. The linearized transport equation is similar to those met in theories of gas dynamics and radiative transfer. We describe the analytical techniques that have been most successful in analyzing the neutron equation. Among these are: The method of separated solutions (in space and angle co-ordinates), and the construction of velocity-dependent collision models.", "doi": "10.1016/0022-4073(71)90060-4", "issn": "0022-4073", "publisher": "Elsevier", "publication": "Journal of Quantitative Spectroscopy and Radiative Transfer", "publication_date": "1971-06", "series_number": "6", "volume": "11", "issue": "6", "pages": "851-868" }, { "id": "authors:1n817-jz231", "collection": "authors", "collection_id": "1n817-jz231", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-140705439", "type": "article", "title": "Nuclear structure study with neutrons [Book review]", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "The physicist who, like many of us, gets his nuclear physics from the New York Times, will be delightfully surprised by Nuclear Structure Study with Neutrons.", "doi": "10.1016/0016-0032(67)90049-X", "issn": "0016-0032", "publisher": "Elsevier", "publication": "Journal of the Franklin Institute", "publication_date": "1967-04", "series_number": "4", "volume": "283", "issue": "4", "pages": "345" }, { "id": "authors:r78cq-5pt17", "collection": "authors", "collection_id": "r78cq-5pt17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-133338347", "type": "article", "title": "Chemical binding effects in the thermalization of neutrons", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "In an earlier paper we extracted an asymptotic series solution in half-integral powers of (kTE) from the Boltzmann transport equation for neutrons coming into thermal equilibrium with a moderating material. In this paper we consider the series in detail for moderators having simple crystalline structure, or in which vibrational modes predominate, and give the coefficients of the series explicitly in terms of moments of the frequency spectrum of crystal vibrations. Our calculations indicate that the neutron density in the asymptotic region increases as one hardens the spectrum of crystal vibrations, whence the \"hardness\" of the neutron spectrum increases, too. We also discuss some aspects of the mass-expansion for these systems, and compare our calculations with those of other workers, and with typical experimental data for thermalization in water. Finally, we discuss the asymptotic expansion for moments of the scattering kernel and for \u03be\u03c3_s, the slowing down power.", "doi": "10.1016/0003-4916(60)90114-7", "issn": "0003-4916", "publisher": "Elsevier", "publication": "Annals of Physics", "publication_date": "1960-11", "series_number": "3", "volume": "11", "issue": "3", "pages": "338-358" }, { "id": "authors:sk40k-zv335", "collection": "authors", "collection_id": "sk40k-zv335", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:SCHpps59", "type": "article", "title": "Resonance capture of neutrons in infinite homogeneous media", "author": [ { "family_name": "Schermer", "given_name": "R.", "clpid": "Schermer-R" }, { "family_name": "Corngold", "given_name": "N.", "clpid": "Corngold-N" } ], "abstract": "In a previous paper, a variational principle was introduced for 1 - p, the capture probability for neutrons slowing down in a homogeneous medium of infinite extent. In the present paper, the variational principle is used together with simple but accurate trial functions to obtain expressions for (i) corrections to the commonly used 'narrow resonance' formula for capture and (ii) interference effects in the capture of neutrons by closely spaced resonances.", "doi": "10.1088/0370-1328/73/4/304", "issn": "0370-1328", "publisher": "Proceedings of the Physical Society of London", "publication": "Proceedings of the Physical Society of London", "publication_date": "1959-04-01", "series_number": "4", "volume": "73", "issue": "4", "pages": "561-571" }, { "id": "authors:g9hnb-6t950", "collection": "authors", "collection_id": "g9hnb-6t950", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-095953849", "type": "article", "title": "Thermalization of neutrons in infinite homogeneous systems", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "The Boltzmann transport equation describing the steady state distribution in energy of fast neutrons which have been \"thermalized\" in a moderator, is analyzed. The principal result of the analysis is an asymptotic series solution in terms of powers of (kTE) whose coefficients depend upon the important physical parameters characterizing the system. In this first paper the general solution is elucidated by application to thermalization by a monatomic gas.", "doi": "10.1016/0003-4916(59)90070-3", "issn": "0003-4916", "publisher": "Elsevier", "publication": "Annals of Physics", "publication_date": "1959-04", "series_number": "4", "volume": "6", "issue": "4", "pages": "368-398" }, { "id": "authors:atevz-9rh66", "collection": "authors", "collection_id": "atevz-9rh66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:CORppsa57", "type": "article", "title": "Slowing Down of Neutrons in Infinite Homogeneous Media", "author": [ { "family_name": "Corngold", "given_name": "N.", "clpid": "Corngold-N" } ], "abstract": "We have derived from the Boltzmann equation a new integral equation governing the slowing down of neutrons in a homogeneous mixture of atoms. The new equation reflects a view of the neutrons as propagating down the energy scale, whereas the Boltzmann equation expresses a collision balance. Unlike the Boltzmann equation the new equation lends itself to approximate solution by iteration and to the construction of an accurate variational principle for p, the resonance escape probability. Some numerical results are given.", "doi": "10.1088/0370-1298/70/11/302", "issn": "0370-1298", "publisher": "Proceedings of the Physical Society A", "publication": "Proceedings of the Physical Society A", "publication_date": "1957-11-01", "series_number": "11", "volume": "70", "issue": "11", "pages": "793-801" }, { "id": "authors:24hch-ya184", "collection": "authors", "collection_id": "24hch-ya184", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20180522-132226891", "type": "article", "title": "Resonance escape probability in slab lattices", "author": [ { "family_name": "Corngold", "given_name": "Noel", "clpid": "Corngold-N" } ], "abstract": "We have examined the slowing down of neutrons in a lattice consisting of alternate slabs of noncapturing moderator and nonmoderating fuel whose cross-sections vary arbitrarily with energy. The Boltzmann equation is transformed to an integral equation into which appropriate boundary conditions are incorporated. Expansion of the flux functions in terms of orthogonal polynomials in space and angle co-ordinates yields an infinite set of coupled integral equations in energy. In the simplest approximation and for a hydrogen moderator these equations are easily integrated to give an expression for the resonance escape probability identical with the one recently derived\u2014from quite different considerations\u2014by J. Chernick. We show that higher-order terms in our equations should contribute little to neutron absorption in those capture resonances which contribute most to the integrated capture probability. Thus, while our simplest approximation is not a good one for determining flux distributions, it will be quite good for determining resonance escape probabilities. Numerical results will be given.", "doi": "10.1016/0891-3919(57)90204-8", "issn": "0891-3919", "publisher": "Elsevier", "publication": "Journal of Nuclear Energy", "publication_date": "1957-03", "series_number": "3", "volume": "4", "issue": "3", "pages": "293-304" } ]