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Limits on Fundamental Limits to Computation  [PDF]
Igor L. Markov
Computer Science , 2014, DOI: 10.1038/nature13570
Abstract: An indispensable part of our lives, computing has also become essential to industries and governments. Steady improvements in computer hardware have been supported by periodic doubling of transistor densities in integrated circuits over the last fifty years. Such Moore scaling now requires increasingly heroic efforts, stimulating research in alternative hardware and stirring controversy. To help evaluate emerging technologies and enrich our understanding of integrated-circuit scaling, we review fundamental limits to computation: in manufacturing, energy, physical space, design and verification effort, and algorithms. To outline what is achievable in principle and in practice, we recall how some limits were circumvented, compare loose and tight limits. We also point out that engineering difficulties encountered by emerging technologies may indicate yet-unknown limits.
Fundamental Limits of Ultrathin Metasurfaces  [PDF]
Amir Arbabi,Andrei Faraon
Physics , 2014,
Abstract: We present universal theoretical limits on the operation and performance of non-magnetic passive ultrathin metasurfaces. In particular, we prove that their local transmission, reflection, and polarization conversion coefficients are confined to limited regions of the complex plane. As a result, full control over the phase of the light transmitted through such metasurfaces cannot be achieved if the polarization of the light is not to be affected at the same time. We also establish fundamental limits on the maximum polarization conversion efficiency of these metasurfaces, and show that they cannot achieve more than 25% polarization conversion efficiency in transmission.
Thermodynamic limits of dynamic cooling  [PDF]
Armen E. Allahverdyan,Karen V. Hovhannisyan,Dominik Janzing,Guenter Mahler
Physics , 2011, DOI: 10.1103/PhysRevE.84.041109
Abstract: We study dynamic cooling, where an externally driven two-level system is cooled via reservoir, a quantum system with initial canonical equilibrium state. We obtain explicitly the minimal possible temperature $T_{\rm min}>0$ reachable for the two-level system. The minimization goes over all unitary dynamic processes operating on the system and reservoir, and over the reservoir energy spectrum. The minimal work needed to reach $T_{\rm min}$ grows as $1/T_{\rm min}$. This work cost can be significantly reduced, though, if one is satisfied by temperatures slightly above $T_{\rm min}$. Our results on $T_{\rm min}>0$ prove unattainability of the absolute zero temperature without ambiguities that surround its derivation from the entropic version of the third law. The unattainability can be recovered, albeit via a different mechanism, for cooling by a reservoir with an initially microcanonic state. We also study cooling via a reservoir consisting of $N\gg 1$ identical spins. Here we show that $T_{\rm min}\propto\frac{1}{N}$ and find the maximal cooling compatible with the minimal work determined by the free energy.
Local fluctuation dissipation relation  [PDF]
Giorgio Parisi
Physics , 2002,
Abstract: In this letter I show that the recently proposed local version of the fluctuation dissipation relations follows from the general principle of stochastic stability in a way that is very similar to the usual proof of the fluctuation dissipation theorem for intensive quantities. Similar arguments can be used to prove that all sites in an aging experiment stay at the same effective temperature at the same time.
Fundamental limits to nanoparticle extinction  [PDF]
Owen D. Miller,Chia W. Hsu,M. T. Homer Reid,Wenjun Qiu,Brendan G. DeLacy,John D. Joannopoulos,Marin Solja?i?,Steven G. Johnson
Physics , 2013, DOI: 10.1103/PhysRevLett.112.123903
Abstract: We show that there are shape-independent upper bounds to the extinction cross section per unit volume of randomly oriented nanoparticles, given only material permittivity. Underlying the limits are restrictive sum rules that constrain the distribution of quasistatic eigenvalues. Surprisingly, optimally-designed spheroids, with only a single quasistatic degree of freedom, reach the upper bounds for four permittivity values. Away from these permittivities, we demonstrate computationally-optimized structures that surpass spheroids and approach the fundamental limits.
Fundamental Limits of Caching  [PDF]
Mohammad Ali Maddah-Ali,Urs Niesen
Mathematics , 2012,
Abstract: Caching is a technique to reduce peak traffic rates by prefetching popular content into memories at the end users. Conventionally, these memories are used to deliver requested content in part from a locally cached copy rather than through the network. The gain offered by this approach, which we term local caching gain, depends on the local cache size (i.e, the memory available at each individual user). In this paper, we introduce and exploit a second, global, caching gain not utilized by conventional caching schemes. This gain depends on the aggregate global cache size (i.e., the cumulative memory available at all users), even though there is no cooperation among the users. To evaluate and isolate these two gains, we introduce an information-theoretic formulation of the caching problem focusing on its basic structure. For this setting, we propose a novel coded caching scheme that exploits both local and global caching gains, leading to a multiplicative improvement in the peak rate compared to previously known schemes. In particular, the improvement can be on the order of the number of users in the network. Moreover, we argue that the performance of the proposed scheme is within a constant factor of the information-theoretic optimum for all values of the problem parameters.
Local overlaps, heterogeneities and the local fluctuation dissipation relations  [PDF]
Giorgio Parisi
Physics , 2002, DOI: 10.1088/0305-4470/36/43/007
Abstract: In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation dissipation relations: using the general principle of stochastic stability these local fluctuation dissipation relations can be proved in a way that is very similar to the usual proof of the fluctuation dissipation relations for intensive quantities. The local overlap and its probability distribution play a crucial role in this proof. Similar arguments can be used to prove that all sites in an aging experiment stay at the same effective temperature at the same time.
Quantum Limits of Stochastic Cooling of a Bosonic Gas  [PDF]
D. Ivanov,S. Wallentowitz,I. A. Walmsley
Physics , 2003, DOI: 10.1103/PhysRevA.67.061401
Abstract: The quantum limits of stochastic cooling of trapped atoms are studied. The energy subtraction due to the applied feedback is shown to contain an additional noise term due to atom-number fluctuations in the feedback region. This novel effect is shown to dominate the cooling efficiency near the condensation point. Furthermore, we show first results that indicate that Bose--Einstein condensation could be reached via stochastic cooling.
Penrose Limits and Non-local theories  [PDF]
Veronika E. Hubeny,Mukund Rangamani,Erik Verlinde
Physics , 2002, DOI: 10.1088/1126-6708/2002/10/020
Abstract: We investigate Penrose limits of two classes of non-local theories, little string theories and non-commutative gauge theories. Penrose limits of the near-horizon geometry of NS5-branes help to shed some light on the high energy spectrum of little string theories. We attempt to understand renormalization group flow in these theories by considering Penrose limits wherein the null geodesic also has a radial component. In particular, we demonstrate that it is possible to construct a pp-wave spacetime which interpolates between the linear dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is considered for the holographic dual geometry to non-commutative field theories.
Aerodynamic Losses in Turbines with and without Film Cooling, as Influenced by Mainstream Turbulence, Surface Roughness, Airfoil Shape, and Mach Number  [PDF]
Phil Ligrani
International Journal of Rotating Machinery , 2012, DOI: 10.1155/2012/957421
Abstract: The influences of a variety of different physical phenomena are described as they affect the aerodynamic performance of turbine airfoils in compressible, high-speed flows with either subsonic or transonic Mach number distributions. The presented experimental and numerically predicted results are from a series of investigations which have taken place over the past 32 years. Considered are (i) symmetric airfoils with no film cooling, (ii) symmetric airfoils with film cooling, (iii) cambered vanes with no film cooling, and (iv) cambered vanes with film cooling. When no film cooling is employed on the symmetric airfoils and cambered vanes, experimentally measured and numerically predicted variations of freestream turbulence intensity, surface roughness, exit Mach number, and airfoil camber are considered as they influence local and integrated total pressure losses, deficits of local kinetic energy, Mach number deficits, area-averaged loss coefficients, mass-averaged total pressure loss coefficients, omega loss coefficients, second law loss parameters, and distributions of integrated aerodynamic loss. Similar quantities are measured, and similar parameters are considered when film-cooling is employed on airfoil suction surfaces, along with film cooling density ratio, blowing ratio, Mach number ratio, hole orientation, hole shape, and number of rows of holes. 1. Introduction Numerous investigations consider parameters and phenomena which affect turbine blade and vane aerodynamic losses, such as turbulence intensity, surface roughness, blade row interactions, and blade and vane geometry. Also important are Mach number variations, airfoil camber, and film cooling. A number of these recent studies focus on aerodynamic losses downstream of subsonic turbine airfoils with no film cooling. Of these investigations, Hoheisel et al. [1], Gregory-Smith and Cleak [2], and Ames and Plesniak [3] examine the influences of inlet turbulence on losses across turbine cascades. Hoheisel et al. [1] also consider the effects of blade boundary layers, and Ames and Plesniak [3] demonstrate important connections between wake growth and level of freestream turbulence. Moore et al. [4] indicate that more than one third of total losses develop downstream of airfoil trailing edges. The authors attribute total pressure losses to deformation work and dissipation of secondary kinetic energy. Zhang et al. [5–7], Zhang and Ligrani [8], Xu and Denton [9], Mee et al. [10], Izsak and Chiang [11], Michelassi et al. [12], Joe et al. [13], and Bohn et al. [14] present aerodynamic loss results for
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