More is different.
04 Aug 1972-Science (American Association for the Advancement of Science)-Vol. 177, Iss: 4047, pp 393-396
About: This article is published in Science.The article was published on 1972-08-04. It has received 3150 citations till now. The article focuses on the topics: MEDLINE & Scientific enterprise.
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TL;DR: General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints.
Abstract: Cellular functions, such as signal transmission, are carried out by 'modules' made up of many species of interacting molecules Understanding how modules work has depended on combining phenomenological analysis with molecular studies General principles that govern the structure and behaviour of modules may be discovered with help from synthetic sciences such as engineering and computer science, from stronger interactions between experiment and theory in cell biology, and from an appreciation of evolutionary constraints
3,604 citations
TL;DR: The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses.
Abstract: Over the past 20 years, neuroimaging has become a predominant technique in systems neuroscience. One might envisage that over the next 20 years the neuroimaging of distributed processing and connectivity will play a major role in disclosing the brain's functional architecture and operational principles. The inception of this journal has been foreshadowed by an ever-increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. I accepted the invitation to write this review with great pleasure and hope to celebrate and critique the achievements to date, while addressing the challenges ahead.
2,822 citations
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01 Jan 2004TL;DR: In this paper, the Kohn-Sham ansatz is used to solve the problem of determining the electronic structure of atoms, and the three basic methods for determining electronic structure are presented.
Abstract: Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.
2,690 citations
TL;DR: Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces, with characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale.
Abstract: Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.
2,037 citations
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...1 ) that appear only through the collective behaviour of electrons and cannot be expected from individual electron...
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TL;DR: In this article, the authors proposed a method for automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula, without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation.
Abstract: For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We propose a principle for the identification of nontriviality. We demonstrated this approach by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.
1,946 citations
References
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TL;DR: In this paper, it was shown that the Meissner effect can be maintained in the quasi-particle picture by taking into account a certain class of corrections to the chargecurrent operator due to the phonon and Coulomb interaction.
Abstract: Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogoliubov'sThe gauge invariance, to the first order in the external electromagnetic field, can be maintained in the quasi-particle picture by taking into account a certain class of corrections to the chargecurrent operator due to the phonon and Coulomb interaction In fact, generalized forms of the Ward identity are obtained between certain vertex parts and the self-energy The Meissner effect calculation is thus rendered strictly gauge invariant, but essentially keeping the BCS result unaltered for transverse fieldsIt is shown also that the integral equation for vertex parts allows homogeneous solutions which describe collective excitations of quasi-particle pairs, and the nature and effects of such collective states are discussed
1,125 citations
TL;DR: In this paper, a generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the superconductivity theory, and it is shown that most elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but there are collective excitations also.
Abstract: A generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the theory of superconductivity. With no further approximations it is shown that most of the elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but that there are collective excitations also. The most important of these are the longitudinal waves which have a velocity ${v}_{F}{{\frac{1}{3}[1\ensuremath{-}4N(0)|V|]}}^{\frac{1}{2}}$ in the neutral Fermi gas, and are essentially unperturbed plasma oscillations in the charged case. Other collective excitations resembling higher bound pair states may or may not exist but do not seriously affect the energy gap. The theory obeys the sum rules and is gauge invariant to an adequate degree throughout.
943 citations
TL;DR: In this paper, the ground state energy of the Kramers-Heller theory of ferromagnetic ground states has been investigated and its properties were shown to lie within limits found elsewhere on rigorous grounds.
Abstract: A careful treatment of the zero-point energy of the spin-waves in the Kramers-Heller semiclassical theory of ferromagnetics leads to surprisingly exact results for the properties of the ground state, as shown by Klein and Smith. An analogous treatment of the antiferromagnetic ground state, whose properties were unknown, is here carried out and justified. The results are expected to be valid to order $\frac{1}{S}$ or better, where $S$ is the spin quantum number of the separate atoms.The energy of the ground state is computed and found to lie within limits found elsewhere on rigorous grounds. For the linear chain, there is no long-range order in the ground state; for the simple cubic and plane square lattices, a finite long-range order in the ground state is found. The fact that this order can be observed experimentally, somewhat puzzling since one knows the ground state to be a singlet, is explained.
769 citations
TL;DR: In this article, it was shown that the non-gauge-invariant terms in the Hamiltonian of Bardeen, Cooper, and Schrieffer have an effect on these states which vanishes in the weak coupling limit.
Abstract: We discuss the coherent states generated in the Bardeen, Cooper, and Schrieffer theory of superconductivity by the momentum displacement operator ${\ensuremath{\rho}}_{\mathrm{Q}}=\ensuremath{\Sigma}{n}^{}\mathrm{exp}(i\mathrm{Q}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{r}}_{n})$. Without taking into account plasma effects, these states are like bound Cooper pairs with momentum $\ensuremath{\hbar}\mathrm{Q}$ and energies lying in the gap, and they play a central role in the explanation of the gauge invariance of the Meissner effect. Long-range Coulomb forces recombine them into plasmons with equations of motion unaffected by the gap. Central to the argument is the proof that the non-gauge-invariant terms in the Hamiltonian of Bardeen, Cooper, and Schrieffer have an effect on these states which vanishes in the weak-coupling limit.
285 citations
TL;DR: A detailed theory of the velocity of propagation of the acrasin pulse responsible for the aggregation of some of the cellular slime molds is presented and it is shown that there is a critical density of amebae below which the waves cannot propagate.
154 citations