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1.
We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast
with the Gibbs–Shannon entropy (Bahadoran in J. Stat. Phys. 126(4–5):1069–1082, 2007; Derrida et al. in J. Stat. Phys. 126(4–5):1083–1108, 2007), the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states. 相似文献
2.
3.
4.
C. Bahadoran 《Communications in Mathematical Physics》2012,310(1):1-24
We consider attractive particle systems in
\mathbb Zd{\mathbb {Z}^d} with product invariant measures. We prove that when particles are restricted to a subset of
\mathbb Zd{\mathbb {Z}^d} , with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation
law, with boundary conditions in the sense of Bardos et al. (Comm Part Diff Equ 4:1017–1034, 1979). For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured
in Popkov and Schütz (Europhys Lett 48:257–263, 1999), and show that it is robust with respect to perturbations of the boundaries. 相似文献
5.
The goal of the paper is to prove a perturbative result, concerning the uniqueness of Kerr solutions, a result which we believe
will be useful in the proof of their nonlinear stability. Following the program started in Ionescu and Klainerman (Invent.
Math. 175:35–102, 2009), we attempt to remove the analyticity assumption in the the well known Hawking-Carter-Robinson uniqueness
result for regular stationary vacuum black holes. Unlike (Ionescu and Klainerman in Invent. Math. 175:35–102, 2009), which
was based on a tensorial characterization of the Kerr solutions, due to Mars (Class. Quant. Grav. 16:2507–2523, 1999), we
rely here on Hawking’s original strategy, which is to reduce the case of general stationary space-times to that of stationary
and axi-symmetric spacetimes for which the Carter-Robinson uniqueness result holds. In this reduction Hawking had to appeal
to analyticity. Using a variant of the geometric Carleman estimates developed in Ionescu and Klainerman (Invent. Math. 175:35–102,
2009), in this paper we show how to bypass analyticity in the case when the stationary vacuum space-time is a small perturbation
of a given Kerr solution. Our perturbation assumption is expressed as a uniform smallness condition on the Mars-Simon tensor.
The starting point of our proof is the new local rigidity theorem established in Alexakis et al. (Hawking’s local rigidity
theorem without analyticity. , 2009). 相似文献
6.
Quantum computational logics have recently stirred increasing attention (Cattaneo et al. in Math. Slovaca 54:87–108, 2004; Ledda et al. in Stud. Log. 82(2):245–270, 2006; Giuntini et al. in Stud. Log. 87(1):99–128, 2007). In this paper we outline their motivations and report on the state of the art of the approach to the logic of quantum computation
that has been recently taken up and developed by our research group. 相似文献
7.
A. Faggionato D. Gabrielli M. Ribezzi Crivellari 《Journal of statistical physics》2009,137(2):259-304
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ
d
or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility
and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations
from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601,
2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry
relation with involution map different from time-reversal. 相似文献
8.
Tom M. Evans Elham Doroodchi Behdad Moghtaderi 《Journal of nanoparticle research》2011,13(9):4395-4396
This brief communication provides a response to Murshed et al. (J Nanopart Res 12:2007–2010, 2010). We acknowledge that three of the equations in our original article (Doroodchi et al. J Nanopart Res 11:1501–1507, 2009) contained minor typographical errors. However, we confirm that these misprinted equations have no bearing on the results
presented within that article. In addition, we would like to clarify that we do not challenge the methodology of Leong et
al. (J Nanopart Res 8:245–254, 2006). Instead, we repeated their analysis using a more general form for the temperature field with continuity imposed across
the particle–nanolayer–liquid interfaces and found that the solution reduces to the Renovated-Maxwell model. 相似文献
9.
Dmitry Panchenko 《Journal of statistical physics》2008,130(5):831-842
In Talagrand (J. Stat. Phys. 126(4–5):837–894, 2007) the large deviations limit
for the moments of the partition function Z
N
in the Sherrington-Kirkpatrick model (Sherrington and Kirkpatrick in Phys. Rev. Lett. 35:1792–1796, 1972) was computed for all real a≥0. For a≥1 this result extends the classical physicist’s replica method that corresponds to integer values of a. We give a new proof for a≥1 in the case of the pure p-spin SK model that provides a strong exponential control of the overlap.
This work is partially supported by NSF grant. 相似文献
10.
We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced
in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced
by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat.
Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which
these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative
models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed
for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state. 相似文献
11.
We establish comparison theorems for eigenvalues between higher order elliptic equations on compact manifolds with boundary.
As an application, it follows that if the Pólya conjecture is true then so is the generalized Pólya conjecture proposed by
Ku et al. (J Differ Equ 97:127–139, 1992). We also obtain new lower bound for the eigenvalues of higher order elliptic equations on bounded domains in a Euclidean
space. 相似文献
12.
As Bleher (J. Stat. Phys. 66(1):315–373, 1992) observed the free flight vector of the planar, infinite horizon, periodic Lorentz process {S n ∣n=0,1,2,…} belongs to the non-standard domain of attraction of the Gaussian law—actually with the $\sqrt{n\log n}As Bleher (J. Stat. Phys. 66(1):315–373, 1992) observed the free flight vector of the planar, infinite horizon, periodic Lorentz process {S
n
∣n=0,1,2,…} belongs to the non-standard domain of attraction of the Gaussian law—actually with the
scaling. Our first aim is to establish his conjecture that, indeed,
converges in distribution to the Gaussian law (a Global Limit Theorem). Here the recent method of Bálint and Gou?zel (Commun.
Math. Phys. 263:461–512, 2006), helped us to essentially simplify the ideas of our earlier sketchy proof (Szász, D., Varjú, T. in Modern dynamical systems
and applications, pp. 433–445, 2004). Moreover, we can also derive (a) the local version of the Global Limit Theorem, (b) the recurrence of the planar, infinite
horizon, periodic Lorentz process, and finally (c) the ergodicity of its infinite invariant measure.
Dedicated to Ya.G. Sinai on the occasion of his seventieth birthday.
Research supported by the Hungarian National Foundation for Scientific Research grants No. T046187, NK 63066 and TS 049835,
further by Hungarian Science and Technology Foundation grant No. A-9/03. 相似文献
13.
In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov
(Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic,
Norwell, 2004; Fuzzy Sets Syst. 155:4–17, 2005; Biosystems 84:225–241, 2006; Found. Phys. 35(10):1655–1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105–117, 2009), it was pointed out that statistics collected in such the experiments have “quantum-like” properties, which can not be explained
in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process
in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical
frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33–59, 1999). 相似文献
14.
Yaacov Kopeliovich 《Letters in Mathematical Physics》2010,94(3):313-333
Let X be a general cyclic cover of
\mathbbCP1{\mathbb{CP}^{1}} ramified at m points, λ1... λ
m
. we define a class of non-positive divisors on X of degree g −1 supported in the pre images of the branch points on X, such that the Riemann theta function does not vanish on their image in J(X). We generalize the results of Bershadsky and Radul (Commun Math Phys 116:689–700, 1988), Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) and Enolskii and Grava (Lett Math Phys 76(2–3):187–214, 2006) and prove that up to a certain determinant of the non-standard periods of X, the value of the Riemann theta function at these divisors raised to a high enough power is a polynomial in the branch point
of the curve X. Our approach is based on a refinement of Accola’s results for 3 cyclic sheeted cover (Accola, in Trans Am Math Soc 283:423–449,
1984) and a generalization of Nakayashiki’s approach explained in Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) for general cyclic covers. 相似文献
15.
We apply a PDE-based method to deduce the critical time and the size of the giant component of the “triangle percolation”
on the Erdős-Rényi random graph process investigated by Derényi, Palla and Vicsek in (Phys. Rev. Lett. 94:160202, [2005]; J. Stat. Phys. 128:219–227, [2007]). 相似文献
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We study the limit of quasilocal energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) for a family of spacelike 2-surfaces approaching null infinity of an asymptotically flat spacetime. It is shown that Lorentzian
symmetry is recovered and an energy-momentum 4-vector is obtained. In particular, the result is consistent with the Bondi–Sachs
energy-momentum at a retarded time. The quasilocal mass in Wang and Yau (Phys Rev Lett 102(2):021101, 2009; Commun Math Phys 288(3):919–942, 2009) is defined by minimizing quasilocal energy among admissible isometric embeddings and observers. The solvability of the Euler-Lagrange
equation for this variational problem is also discussed in both the asymptotically flat and asymptotically null cases. Assuming
analyticity, the equation can be solved and the solution is locally minimizing in all orders. In particular, this produces
an optimal reference hypersurface in the Minkowski space for the spatial or null exterior region of an asymptotically flat
spacetime. 相似文献
18.
G. F. Iriarte 《Journal of nanoparticle research》2011,13(4):1737-1745
Artificial nanostructures (Samuelson et al., Physica E 21:560–567, 2004; Xia et al., Adv Mater 15:353–389, 2003) show promise for the organization of functional materials (Huck and Samuelson, Nanotechnology 14:NIL_5–NIL_8, 2003) to create nanoelectronic (Mizuta and Oda, Science 279:208–211, 2008) or nano-optical devices (Mazur et al.; Tanemura et al., Synthesis, Optical Properties and Functional Applications of ZnO
Nano-materials: A Review, 1–3:58–63, 2008). However, in most manufacturing recipes described so far, nanostructures are synthesized in solution and/or uncontrolled
deposition results in random arrangements; this makes it difficult to measure the properties of attached nanodevices or to
integrate them with conventionally fabricated microcircuitry. Here, we describe a fully CMOS compatible process technology
for mass manufacture of polysilicon nanowires by the CVD (chemical vapor deposition) method. The large scale production of
nanowires could successfully be synthesized on silicon (100) substrates. However, the method presented here can successfully
be employed with all technologically useful substrates with good adhesion for silicon such as SiO2, diamond-like carbon or III–V semiconductors. This opens up the possibility for the fabrication of strain-sensitive and defect-sensitive
optoelectronic devices on the optimum III–V substrate (Fonstad et al.). Finally, scanning electron microscopy (SEM) was used
to characterize the as-synthesized nanowires and energy-filtered transmission electron microscopy (EFTEM) and scanning transmission
electron microscopy (STEM) analysis were used to determine the nanowire composition. 相似文献
19.
In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination
of the Vicsek alignment model (Vicsek et al. in Phys. Rev. Lett. 75(6):1226–1229, 1995) and the Persistent Turning Walker (PTW) model of motion by curvature control (Degond and Motsch in J. Stat. Phys. 131(6):989–1021,
2008; Gautrais et al. in J. Math. Biol. 58(3):429–445, 2009). The PTW model was designed to fit measured trajectories of individual fish (Gautrais et al. in J. Math. Biol. 58(3):429–445,
2009). The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature
in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized
collisional invariant introduced in (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215, 2008). The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals.
It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the
same form as the macroscopic limit of the Vicsek model (Degond and Motsch in Math. Models Methods Appl. Sci. 18(1):1193–1215,
2008) (the ‘Vicsek hydrodynamics’) but for the expression of the model coefficients. The numerical computations show that the
numerical values of the coefficients are very close. The ‘Vicsek Hydrodynamic model’ appears in this way as a more generic
macroscopic model of swarming behavior as originally anticipated. 相似文献
20.
The regularized determinant of the Paneitz operator arises in quantum gravity [see Connes in (Noncommutative geometry, 1994), IV.4.γ]. An explicit formula for the relative determinant of two conformally related metrics was computed by Branson in (Commun Math Phys 178:301–309, 1996). A similar formula holds for Cheeger’s half-torsion, which plays a role in self-dual field theory [see Juhl in (Families of conformally covariant differential operators, q-curvature and holography. Progress in Mathematics, vol 275, 2009)], and is defined in terms of regularized determinants of the Hodge laplacian on p-forms (p < n/2). In this article we show that the corresponding actions are unbounded (above and below) on any conformal four-manifold. We also show that the conformal class of the round sphere admits a second solution which is not given by the pull-back of the round metric by a conformal map, thus violating uniqueness up to gauge equivalence. These results differ from the properties of the determinant of the conformal Laplacian established in (Commun Math Phys 149:241–262, 1992), (Ann Math 142:171–212, 1995), (Commun Math Phys 189:655–665, 1997). 相似文献