991 resultados para heat equations


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Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds N r r. In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt’00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure. The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in N r> , with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.

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In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

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With nine examples, we seek to illustrate the utility of the Renormalization Group approach as a unification of other asymptotic and perturbation methods.

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This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

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This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

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We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

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This article presents the results on the diagnostics and numerical modeling of low-frequency (∼460 KHz) inductively coupled plasmas generated in a cylindrical metal chamber by an external flat spiral coil. Experimental data on the electron number densities and temperatures, electron energy distribution functions, and optical emission intensities of the abundant plasma species in low/intermediate pressure argon discharges are included. The spatial profiles of the plasma density, electron temperature, and excited argon species are computed, for different rf powers and working gas pressures, using the two-dimensional fluid approach. The model allows one to achieve a reasonable agreement between the computed and experimental data. The effect of the neutral gas temperature on the plasma parameters is also investigated. It is shown that neutral gas heating (at rf powers≥0.55kW) is one of the key factors that control the electron number density and temperature. The dependence of the average rf power loss, per electron-ion pair created, on the working gas pressure shows that the electron heat flux to the walls appears to be a critical factor in the total power loss in the discharge.

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The ionization energy theory is used to calculate the evolution of the resistivity and specific heat curves with respect to different doping elements in the recently discovered superconducting pnictide materials. Electron-conduction mechanism in the pnictides above the structural transition temperature is explained unambiguously, which is also consistent with other strongly correlated materials, such as cuprates, manganites, titanates and magnetic semiconductors.

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The present study explores reproducing the closest geometry of a high pressure ratio single stage radial-inflow turbine applied in the Sundstrans Power Systems T-100 Multipurpose Small Power Unit. The commercial software ANSYS-Vista RTD along with a built in module, BladeGen, is used to conduct a meanline design and create 3D geometry of one flow passage. Carefully examining the proposed design against the geometrical and experimental data, ANSYS-TurboGrid is applied to generate computational mesh. CFD simulations are performed with ANSYS-CFX in which three-dimensional Reynolds-Averaged Navier-Stokes equations are solved subject to appropriate boundary conditions. Results are compared with numerical and experimental data published in the literature in order to generate the exact geometry of the existing turbine and validate the numerical results against the experimental ones.

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This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

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A solar assisted heat pump is used for different applications, such as, water heating, drying and air conditioning. The unglazed evaporator-collector enables to absorb both solar energy and ambient energy due to low operating temperature. Three different systems are described: solar assisted heat pump system for hot water using an unglazed evaporator collector; solar assisted heat pump for hot water and drying, where evaporator collector and air collector are used; an integrated solar heat pump system making use of solar and ambient energy, and air-con waste heat. Unlike conventional collector, evaporator collector was found to have higher efficiency, 80% to 90%, and the coefficient of performance attained a value as high as 8.0. The integrated system leads to a reduction of global warming, as it uses solar energy, ambient energy and air-con waste heat.

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The solar-assisted heat pump (SAHP) desalination, based on the Rankin cycle, operates in low temperature and utilizes both solar and ambient energy. An experimental SAHP desalination system has been constructed at the National University of Singapore, Singapore. The system consisted of two main sections: an SAHP and a water distillation section. Experiments were carried out under the different meteorological condition of Singapore and results showed that the system had a performance ratio close to 1.3. The heat pump has a coefficient of performance of about 8, with solar collector efficiencies of 80% and 60% for evaporator and liquid collectors, respectively. Economic analysis showed that at a production rate of 900 L/day and an evaporator collector area of around 70m2 will have a payback period of about 3.5 years.

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Desalination is considered one of the most suitable areas for the utilization of solar energy, as there are many places in the world where abundant supply of solar energy is available and also there is a great demand for fresh water. An integrated solar heat pump desalination system has been developed at the National University of Singapore. The system also offers the opportunity of water heating and drying utilizing solar, ambient energy and waste heat from air conditioning system, which is conventionally dumped into the environment causing global warming. Desalination is carried out by making use of a single effect of Multi-Effect Distillation (MED) system. Within the desalination chamber, both fl ashing and evaporation of saline water take place. The maximum Coefficient of Performance (COP) of the heat pump system was around 5.8. In the integrated system, the maximum fresh water production rate was 9.6 l h−1 and a Performance Ratio (PR) of 1.2. For only desalination, the system has the potential to produce a maximum of 30 l h−1 of fresh water.

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Singapore is located at the equator, with abundant supply of solar radiation, relatively high ambient temperature and relative humidity throughout the year. The meteorological conditions of Singapore are favourable for efficient operation of solar energy based systems. Solar assisted heat pump systems are built on the roof-top of National University of Singapore’s Faculty of Engineering. The objectives of this study include the design and performance evaluation of a solar assisted heat-pump system for water desalination, water heating and drying of clothes. Using MATLAB programming language, a 2-dimensional simulation model has been developed to conduct parametric studies on the system. The system shows good prospect to be implemented in both industrial and residential applications and would give new opportunities in replacing conventional energy sources with green renewable energy.

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In view of the growing global demand for energy and concern expressed for environmental degradation, a clean and "free" energy source, such as solar energy, has been receiving greater attention in recent years for various applications using different techniques. The Direct Expansion Solar Assisted Heat Pump (DX-SAHP) principle is one of the most promising techniques as it makes use of both solar and ambient energy. As the system has capability to function at low temperatures, it has the potential to operate at night in the tropics. The system utilizes multi-effect distillation (MED) principle for the conversion of seawater to fresh water. An experimental setup of the DX-SAHP desalination system has been built at the Department of Mechanical Engineering, National University of Singapore (NUS). This system uses two types of flat-plate solar collectors. One is called evaporator-collector, where no glazing is used, and the efficiency varies between 80 and 90%. The other type of collector is single-glazed, where the maximum efficiency is about 60%, and it is used for feed water heating. For the heat pump cycle, refrigerant R134a is used. The present study provides a comprehensive analyses and performance evaluation of this system under different operating and meteorological conditions of Singapore. The Coefficient of Performance (COP) of the heat pump system reached a maximum value of 10. For a single effect of desalination, the system shows a Performance Ratio (PR) of around 1.3.