Pub Date : 2009-12-04DOI: 10.1088/1751-8113/42/48/485001
A Annibale, Acc Coolen, Lp Fernandes, F Fraternali, J Kleinjung
We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.
{"title":"Tailored graph ensembles as proxies or null models for real networks I: tools for quantifying structure.","authors":"A Annibale, Acc Coolen, Lp Fernandes, F Fraternali, J Kleinjung","doi":"10.1088/1751-8113/42/48/485001","DOIUrl":"10.1088/1751-8113/42/48/485001","url":null,"abstract":"<p><p>We study the tailoring of structured random graph ensembles to real networks, with the objective of generating precise and practical mathematical tools for quantifying and comparing network topologies macroscopically, beyond the level of degree statistics. Our family of ensembles can produce graphs with any prescribed degree distribution and any degree-degree correlation function, its control parameters can be calculated fully analytically, and as a result we can calculate (asymptotically) formulae for entropies and complexities, and for information-theoretic distances between networks, expressed directly and explicitly in terms of their measured degree distribution and degree correlations.</p>","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1751-8113/42/48/485001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"40072537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2008-09-19DOI: 10.1088/0305-4470/33/23/307
N. Chuprikov
On the basis of an exact formalism, a system of functional equations for the tunnelling parameters of self-similar fractal potentials (SSFPs) is obtained. Three different families of solutions are found for these equations, two of them having one parameter and one being free of parameters. Both one-parameter solutions are shown to be described, in the long-wave limit, by a fractal dimension. At the same time, the third solution yields transfer matrices which are analytical in this region, similar to the case of structures with the `Euclidean geometry'. We have revealed some manifestations of scale invariance in the physical properties of SSFPs. Nevertheless, in the common case these potentials do not possess, strictly speaking, this symmetry. The point is that SSFPs in the common case are specified, in contrast to the Cantor set, by two length scales but not one. A particular case when SSFPs are exactly scale invariant to an electron with well defined energy is found.
{"title":"The transfer matrices of the self-similar fractal potentials on the Cantor set","authors":"N. Chuprikov","doi":"10.1088/0305-4470/33/23/307","DOIUrl":"https://doi.org/10.1088/0305-4470/33/23/307","url":null,"abstract":"On the basis of an exact formalism, a system of functional equations for the tunnelling parameters of self-similar fractal potentials (SSFPs) is obtained. Three different families of solutions are found for these equations, two of them having one parameter and one being free of parameters. Both one-parameter solutions are shown to be described, in the long-wave limit, by a fractal dimension. At the same time, the third solution yields transfer matrices which are analytical in this region, similar to the case of structures with the `Euclidean geometry'. We have revealed some manifestations of scale invariance in the physical properties of SSFPs. Nevertheless, in the common case these potentials do not possess, strictly speaking, this symmetry. The point is that SSFPs in the common case are specified, in contrast to the Cantor set, by two length scales but not one. A particular case when SSFPs are exactly scale invariant to an electron with well defined energy is found.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2008-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86465303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-07-20DOI: 10.1088/0305-4470/39/29/B02
J. Robbin
The hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose--Einstein condensates, and laser cooling and trapping of atoms, to name a few. Unlike many collections, in which problems are designed around a particular mathematical method, here each problem is devoted to a small group of phenomena or experiments. Most problems contain experimental data from the literature, and readers are asked to estimate parameters from the data, or compare theory to experiment, or both. Standard techniques (e.g., degenerate perturbation theory, addition of angular momentum, asymptotics of special functions) are introduced only as they are needed. The style is closer to a non-specialist seminar rather than an undergraduate lecture. The physical models are kept simple; the emphasis is on cultivating conceptual and qualitative understanding (although in many of the problems, the simple models fit the data quite well). Some less familiar theoretical techniques are introduced, e.g. a variational method for lower (not upper) bounds on ground-state energies for many-body systems with two-body interactions, which is then used to derive a surprisingly accurate relation between baryon and meson masses. The exposition is succinct but clear; the solutions can be read as worked examples if you don't want to do the problems yourself. Many problems have additional discussion on limitations and extensions of the theory, or further applications outside physics (e.g., the accuracy of GPS positioning in connection with atomic clocks; proton and ion tumor therapies in connection with the Bethe--Bloch formula for charged particles in solids). The problems use mainly non-relativistic quantum mechanics and are organised into three sections: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. The coverage is not comprehensive; there is little on scattering theory, for example, and some areas of recent interest, such as topological aspects of quantum mechanics and semiclassics, are not included. The problems are based on examination questions given at the École Polytechnique in the last 15 years. The book is accessible to undergraduates, but working physicists should find it a delight.
{"title":"The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics, edition 2nd","authors":"J. Robbin","doi":"10.1088/0305-4470/39/29/B02","DOIUrl":"https://doi.org/10.1088/0305-4470/39/29/B02","url":null,"abstract":"The hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose--Einstein condensates, and laser cooling and trapping of atoms, to name a few. Unlike many collections, in which problems are designed around a particular mathematical method, here each problem is devoted to a small group of phenomena or experiments. Most problems contain experimental data from the literature, and readers are asked to estimate parameters from the data, or compare theory to experiment, or both. Standard techniques (e.g., degenerate perturbation theory, addition of angular momentum, asymptotics of special functions) are introduced only as they are needed. The style is closer to a non-specialist seminar rather than an undergraduate lecture. The physical models are kept simple; the emphasis is on cultivating conceptual and qualitative understanding (although in many of the problems, the simple models fit the data quite well). Some less familiar theoretical techniques are introduced, e.g. a variational method for lower (not upper) bounds on ground-state energies for many-body systems with two-body interactions, which is then used to derive a surprisingly accurate relation between baryon and meson masses. The exposition is succinct but clear; the solutions can be read as worked examples if you don't want to do the problems yourself. Many problems have additional discussion on limitations and extensions of the theory, or further applications outside physics (e.g., the accuracy of GPS positioning in connection with atomic clocks; proton and ion tumor therapies in connection with the Bethe--Bloch formula for charged particles in solids). The problems use mainly non-relativistic quantum mechanics and are organised into three sections: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. The coverage is not comprehensive; there is little on scattering theory, for example, and some areas of recent interest, such as topological aspects of quantum mechanics and semiclassics, are not included. The problems are based on examination questions given at the École Polytechnique in the last 15 years. The book is accessible to undergraduates, but working physicists should find it a delight.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84802321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-05-25DOI: 10.1088/1751-8113/40/21/009
Maria R D'Orsogna, Tom Chou, Tibor Antal
We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratcheted motion. We also define and compare the relative efficiencies of ratcheting by deposition of particles with different sizes and we describe an associated "zone-refinement" process.
{"title":"Exact steady-state velocity of ratchets driven by random sequential adsorption.","authors":"Maria R D'Orsogna, Tom Chou, Tibor Antal","doi":"10.1088/1751-8113/40/21/009","DOIUrl":"https://doi.org/10.1088/1751-8113/40/21/009","url":null,"abstract":"<p><p>We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratcheted motion. We also define and compare the relative efficiencies of ratcheting by deposition of particles with different sizes and we describe an associated \"zone-refinement\" process.</p>","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1751-8113/40/21/009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"27899161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-04-06DOI: 10.1088/0305-4470/39/4/017
H. A. Attia
This paper studies the effect of a porous medium and temperature-dependent viscosity on the unsteady flow and heat transfer for a viscous laminar incompressible fluid due to an impulsively started rotating infinite disc. The unsteady axi-symmetric boundary layer equations are solved using three methods, namely, (i) perturbation solution for small time, (ii) asymptotic analysis for large time and (iii) the finite difference method together with the Keller box elimination technique for intermediate times. The solutions are obtained in terms of local radial skin friction, local tangential skin friction and local rate of heat transfer at the surface of the disc, for different values of the pertinent parameters: the Prandtl number Pr, the viscosity variation parameter ε and porosity parameter m. The computed dimensionless velocity and temperature profiles for Pr = 0.72 are shown graphically for different values of ε and m.
{"title":"Unsteady flow and heat transfer of viscous incompressible fluid with temperature-dependent viscosity due to a rotating disc in a porous medium","authors":"H. A. Attia","doi":"10.1088/0305-4470/39/4/017","DOIUrl":"https://doi.org/10.1088/0305-4470/39/4/017","url":null,"abstract":"This paper studies the effect of a porous medium and temperature-dependent viscosity on the unsteady flow and heat transfer for a viscous laminar incompressible fluid due to an impulsively started rotating infinite disc. The unsteady axi-symmetric boundary layer equations are solved using three methods, namely, (i) perturbation solution for small time, (ii) asymptotic analysis for large time and (iii) the finite difference method together with the Keller box elimination technique for intermediate times. The solutions are obtained in terms of local radial skin friction, local tangential skin friction and local rate of heat transfer at the surface of the disc, for different values of the pertinent parameters: the Prandtl number Pr, the viscosity variation parameter ε and porosity parameter m. The computed dimensionless velocity and temperature profiles for Pr = 0.72 are shown graphically for different values of ε and m.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81635168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-15DOI: 10.1088/0305-4470/39/50/L01
K. Thas
In a paper by M Kac (1966 Am. Math. Mon. 73 1–23), Kac asked his famous question ‘Can one hear the shape of a drum?’, which was answered negatively in Gordon et al (1992 Invent. Math. 110 1–22) by construction of planar isospectral pairs. In Buser et al (1994 Int. Math. Res. Not. 9), it is observed that all operator groups associated with the known counter examples are isomorphic to one of PSL3(2), PSL3(3), PSL4(2) and PSL3(4). We show that if (D1, D2) is a pair of non-congruent planar isospectral domains constructed from unfolding a polygonal base-tile and with associated operator group PSLn(q), then (n, q) belongs to this very restricted list.
在卡茨(1966)的一篇论文中。数学。星期一(73 - 23)，卡茨问了他著名的问题“人能听到鼓的形状吗?”， Gordon et al(1992)对此给出了否定的回答。数学。110 - 22)通过构造平面等谱对。In Buser et al . (1994);数学。Res. Not. 9)，可以观察到与已知反例相关的所有算子群都与PSL3(2)、PSL3(3)、PSL4(2)和PSL3(4)中的一个同构。我们证明了如果(D1, D2)是由展开一个多边形基图构成的一对非全等平面等谱域，并且具有相应的算子群PSLn(q)，则(n, q)属于这个极限表。
{"title":"PSLn(q) as operator group of isospectral drums","authors":"K. Thas","doi":"10.1088/0305-4470/39/50/L01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/50/L01","url":null,"abstract":"In a paper by M Kac (1966 Am. Math. Mon. 73 1–23), Kac asked his famous question ‘Can one hear the shape of a drum?’, which was answered negatively in Gordon et al (1992 Invent. Math. 110 1–22) by construction of planar isospectral pairs. In Buser et al (1994 Int. Math. Res. Not. 9), it is observed that all operator groups associated with the known counter examples are isomorphic to one of PSL3(2), PSL3(3), PSL4(2) and PSL3(4). We show that if (D1, D2) is a pair of non-congruent planar isospectral domains constructed from unfolding a polygonal base-tile and with associated operator group PSLn(q), then (n, q) belongs to this very restricted list.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78388288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-08DOI: 10.1088/0305-4470/39/49/011
G. Livadiotis, N. Voglis
A rotation number in the case of one-dimensional maps is introduced. As is shown, this rotation number is equivalent to the already known rotation number in the case of two-dimensional maps. The definition of the rotation number is given in two steps. First, it is defined for periodic orbits inside a window of organized motion (WOM). We show that in this case our definition coincides with the definition of the over-rotation number. Then, our definition is further generalized for chaotic orbits outside the WOMs. Thus, we obtain a unified definition of the rotation number for the whole area of the chaotic zone of the bifurcation diagram, having a number of useful applications. Namely, it can be used as a tool to distinguish whether an orbit is contained within a WOM or not, as a tool of numerical location of the bifurcation points, of the band mergings, as well as of the boundary points of a WOM. Finally, a method of numerical calculation of the percentage of the cumulative width of the WOMs in every particular segment (chaotic band) of the chaotic zone is given.
{"title":"The rotation number in one-dimensional maps: definition and applications","authors":"G. Livadiotis, N. Voglis","doi":"10.1088/0305-4470/39/49/011","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/011","url":null,"abstract":"A rotation number in the case of one-dimensional maps is introduced. As is shown, this rotation number is equivalent to the already known rotation number in the case of two-dimensional maps. The definition of the rotation number is given in two steps. First, it is defined for periodic orbits inside a window of organized motion (WOM). We show that in this case our definition coincides with the definition of the over-rotation number. Then, our definition is further generalized for chaotic orbits outside the WOMs. Thus, we obtain a unified definition of the rotation number for the whole area of the chaotic zone of the bifurcation diagram, having a number of useful applications. Namely, it can be used as a tool to distinguish whether an orbit is contained within a WOM or not, as a tool of numerical location of the bifurcation points, of the band mergings, as well as of the boundary points of a WOM. Finally, a method of numerical calculation of the percentage of the cumulative width of the WOMs in every particular segment (chaotic band) of the chaotic zone is given.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90974714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-08DOI: 10.1088/0305-4470/39/49/005
S. Meleshko
A new algorithm for linearization of a third-order ordinary differential equation is presented. The algorithm consists of composition of two operations: reducing order of an ordinary differential equation and using the Lie linearization test for the obtained second-order ordinary differential equation. The application of the algorithm to several ordinary differential equations is given.
{"title":"On linearization of third-order ordinary differential equations","authors":"S. Meleshko","doi":"10.1088/0305-4470/39/49/005","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/005","url":null,"abstract":"A new algorithm for linearization of a third-order ordinary differential equation is presented. The algorithm consists of composition of two operations: reducing order of an ordinary differential equation and using the Lie linearization test for the obtained second-order ordinary differential equation. The application of the algorithm to several ordinary differential equations is given.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81897771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-08DOI: 10.1088/0305-4470/39/49/B01
S. Heusler
The main focus of the second, enlarged edition of the book Mathematica for Theoretical Physics is on computational examples using the computer program Mathematica in various areas in physics. It is a notebook rather than a textbook. Indeed, the book is just a printout of the Mathematica notebooks included on the CD. The second edition is divided into two volumes, the first covering classical mechanics and nonlinear dynamics, the second dealing with examples in electrodynamics, quantum mechanics, general relativity and fractal geometry. The second volume is not suited for newcomers because basic and simple physical ideas which lead to complex formulas are not explained in detail. Instead, the computer technology makes it possible to write down and manipulate formulas of practically any length. For researchers with experience in computing, the book contains a lot of interesting and non-trivial examples. Most of the examples discussed are standard textbook problems, but the power of Mathematica opens the path to more sophisticated solutions. For example, the exact solution for the perihelion shift of Mercury within general relativity is worked out in detail using elliptic functions. The virial equation of state for molecules' interaction with Lennard-Jones-like potentials is discussed, including both classical and quantum corrections to the second virial coefficient. Interestingly, closed solutions become available using sophisticated computing methods within Mathematica. In my opinion, the textbook should not show formulas in detail which cover three or more pages—these technical data should just be contained on the CD. Instead, the textbook should focus on more detailed explanation of the physical concepts behind the technicalities. The discussion of the virial equation would benefit much from replacing 15 pages of Mathematica output with 15 pages of further explanation and motivation. In this combination, the power of computing merged with physical intuition would be of benefit even for newcomers. In summary, this book shows in a convincing manner how classical problems in physics can be attacked with modern computing technology. The second volume is interesting for experienced users of Mathematica. For students, the textbook can be very useful in combination with a seminar.
{"title":"Mathematica for Theoretical Physics: Electrodynamics, Quantum Mechanics, General Relativity and Fractals","authors":"S. Heusler","doi":"10.1088/0305-4470/39/49/B01","DOIUrl":"https://doi.org/10.1088/0305-4470/39/49/B01","url":null,"abstract":"The main focus of the second, enlarged edition of the book Mathematica for Theoretical Physics is on computational examples using the computer program Mathematica in various areas in physics. It is a notebook rather than a textbook. Indeed, the book is just a printout of the Mathematica notebooks included on the CD. The second edition is divided into two volumes, the first covering classical mechanics and nonlinear dynamics, the second dealing with examples in electrodynamics, quantum mechanics, general relativity and fractal geometry. The second volume is not suited for newcomers because basic and simple physical ideas which lead to complex formulas are not explained in detail. Instead, the computer technology makes it possible to write down and manipulate formulas of practically any length. For researchers with experience in computing, the book contains a lot of interesting and non-trivial examples. Most of the examples discussed are standard textbook problems, but the power of Mathematica opens the path to more sophisticated solutions. For example, the exact solution for the perihelion shift of Mercury within general relativity is worked out in detail using elliptic functions. The virial equation of state for molecules' interaction with Lennard-Jones-like potentials is discussed, including both classical and quantum corrections to the second virial coefficient. Interestingly, closed solutions become available using sophisticated computing methods within Mathematica. In my opinion, the textbook should not show formulas in detail which cover three or more pages—these technical data should just be contained on the CD. Instead, the textbook should focus on more detailed explanation of the physical concepts behind the technicalities. The discussion of the virial equation would benefit much from replacing 15 pages of Mathematica output with 15 pages of further explanation and motivation. In this combination, the power of computing merged with physical intuition would be of benefit even for newcomers. In summary, this book shows in a convincing manner how classical problems in physics can be attacked with modern computing technology. The second volume is interesting for experienced users of Mathematica. For students, the textbook can be very useful in combination with a seminar.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88468733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2006-12-01DOI: 10.1088/0305-4470/39/48/013
J. Shen, Sailing He
This addendum states the relationship between our recent paper and Mackay et al's work on the negative refraction in gyrotropic chiral media, and emphasizes the advantages of their work that we did not mention in our recent paper.
{"title":"Backward waves and negative refractive indices in gyrotropic chiral media","authors":"J. Shen, Sailing He","doi":"10.1088/0305-4470/39/48/013","DOIUrl":"https://doi.org/10.1088/0305-4470/39/48/013","url":null,"abstract":"This addendum states the relationship between our recent paper and Mackay et al's work on the negative refraction in gyrotropic chiral media, and emphasizes the advantages of their work that we did not mention in our recent paper.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2006-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81334922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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