Cosmic microwave background with Brans-Dicke Gravity: I. Covariant Formulation

In the covariant cosmological perturbation theory, a 1+3 decomposition ensures that all variables in the frame-independent equations are covariant, gauge-invariant and have clear physical interpretations. We develop this formalism in the case of Brans-Dicke gravity, and apply this method to the calculation of cosmic microwave background (CMB) anisotropy and large scale structures (LSS). We modify the publicly available Boltzmann code CAMB to calculate numerically the evolution of the background and adiabatic perturbations, and obtain the temperature and polarization spectra of the Brans-Dicke theory for both scalar and tensor mode, the tensor mode result for the Brans-Dicke gravity are obtained numerically for the first time. We first present our theoretical formalism in detail, then explicitly describe the techniques used in modifying the CAMB code. These techniques are also very useful to other gravity models. Next we compare the CMB and LSS spectra in Brans-Dicke theory with those in the standard general relativity theory. At last, we investigate the ISW effect and the CMB lensing effect in the Brans-Dicke theory. Constraints on Brans-Dicke model with current observational data is presented in a companion paper (paper II).Comment: 17 double column pages, 11 figures. Replaced with revised version, tensor modes, ISW effect now include

Credit Mismatch and Breakdown

This paper studies the phenomenon of mismatch in a decentralized credit market where borrowers and lenders must engage in costly search to establish credit relationships. Our dynamic general equilibrium framework integrates incentive based informational frictions with a matching process highlighted by (i) borrowers’ endogenous market entry and exit decision (entry frictions) and (ii) time and resource costs necessary to locate credit opportunities (search frictions). A key feature of the incentive compatible loan contract negotiated between borrowers and lenders is the interaction of informational frictions (in the form of moral hazard) with entry and search frictions. We find that the removal of entry barriers can eliminate information-based equilibrium credit rationing. More generally, entry and incentive frictions are important in understanding the extent of credit rationing, while entry and search frictions are important for understanding credit market breakdown.Entry, Moral Hazard, Credit Rationing, Credit Mismatch, Credit-Market Breakdown

Rank-frequency relation for Chinese characters

We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long Chinese texts (or for mixtures of short Chinese texts), rank-frequency relations for Chinese characters display a two-layer, hierarchic structure that combines a Zipfian power-law regime for frequent characters (first layer) with an exponential-like regime for less frequent characters (second layer). For these two layers we provide different (though related) theoretical descriptions that include the range of low-frequency characters (hapax legomena). The comparative analysis of rank-frequency relations for Chinese characters versus English words illustrates the extent to which the characters play for Chinese writers the same role as the words for those writing within alphabetical systems.Comment: To appear in European Physical Journal B (EPJ B), 2014 (22 pages, 7 figures

Towards Constraining Parity-Violations in Gravity with Satellite Gradiometry

Parity violation in gravity, if existed, could have important implications, and it is meaningful to search and test the possible observational effects. Chern-Simons modified gravity serves as a natural model for gravitational parity-violations. Especially, considering extensions to Einstein-Hilbert action up to second order curvature terms, it is known that theories of gravitational parity-violation will reduce to the dynamical Chern-Simons gravity. In this letter, we outline the theoretical principles of testing the dynamical Chern-Simons gravity with orbiting gravity gradiometers, which could be naturally incorporated into future satellite gravity missions. The secular gravity gradient signals, due to the Mashhoon-Theiss (anomaly) effect, in dynamical Chern-Simons gravity are worked out, which can improve the constraint of the corresponding Chern-Simons length scale $\xi^{\frac{1}{4}}_{cs}$ obtained from such measurement scheme. For orbiting superconducting gradiometers or gradiometers with optical readout, a bound $\xi^{\frac{1}{4}}_{cs}\leq 10^6 \ km$ (or even better) could in principle be obtained, which will be at least 2 orders of magnitude stronger than the current one based on the observations from the GP-B mission and the LAGEOS I, II satellites.Comment: 15 pages, 6 figures. arXiv admin note: text overlap with arXiv:1606.0818

Analytic solution of charge density of single wall carbon nanotube in conditions of field electron emission

We derived the analytic solution of induced electrostatic potential along single wall carbon nanotubes. Under the hypothesis of constant density of states in the charge-neutral level, we are able to obtain the linear density of excess charge in an external field parallel to the tube axis.Comment: 4 pages, 3 figure

Towards quantitative tissue absorption imaging by combining photoacoustics and acousto-optics

We propose a strategy for quantitative photoacoustic mapping of chromophore concentrations that can be performed purely experimentally. We exploit the possibility of acousto-optic modulation using focused ultrasound, and the principle that photons follow trajectories through a turbid medium in two directions with equal probability. A theory is presented that expresses the local absorption coefficient inside a medium in terms of noninvasively measured quantities and experimental parameters. Proof of the validity of the theory is given with Monte Carlo simulations.Comment: 14 pages, 5 figure

Anomalous heat conduction and anomalous diffusion in nonlinear lattices, single walled nanotubes, and billiard gas channels

We study anomalous heat conduction and anomalous diffusion in low dimensional systems ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels. We find that in all discussed systems, the anomalous heat conductivity can be connected with the anomalous diffusion, namely, if energy diffusion is $\sigma^2(t)\equiv =2Dt^{\alpha} (0<\alpha\le 2)$, then the thermal conductivity can be expressed in terms of the system size $L$ as $\kappa = cL^{\beta}$ with $\beta=2-2/\alpha$. This result predicts that a normal diffusion ($\alpha =1$) implies a normal heat conduction obeying the Fourier law ($\beta=0$), a superdiffusion ($\alpha>1$) implies an anomalous heat conduction with a divergent thermal conductivity ($\beta>0$), and more interestingly, a subdiffusion ($\alpha <1$) implies an anomalous heat conduction with a convergent thermal conductivity ($\beta<0$), consequently, the system is a thermal insulator in the thermodynamic limit. Existing numerical data support our theoretical prediction.Comment: 15 Revtex pages, 16 figures. Invited article for CHAOS focus issue commemorating the 50th anniversary of the Fermi-Pasta-Ulam (FPU) mode

Decentralized Exchange and Factor Payments: A Multiple-Matching Approach

The emergence of fiat money is studied in an environment in which exchange is organized around trading posts where many producers and shoppers are matched in a dynamic monopolistically competitive framework. Each household consumes a bundle of commodities and has a preference for consumption variety. Within this multiple matching structure we determine the endogenous organization of exchange between firms and shoppers and the means of factor payment (remuneration) as well as the price at which these trades occur. Although each household contacts many sellers, the specialization of tastes implies that the variety of the consumption basket under barter mediated exchange is sparser than that obtained under monetary exchange. We verify that the endogenous linkage of factor payments with the medium of exchange can lead to a monetary equilibrium outcome where only fiat money trades for goods, an ex-ante feature of cash-in-advance models. We also examine the long-run effects of money growth on the equilibrium pattern of exchange. A primary finding, consistent with documented hyperinflationary episodes, is that a sufficiently rapid expansion of money supply and inflation leads to the gradual emergence of barter. Under these circumstances sellers will accept both goods and cash payments whereas workers receive part of their remuneration in goods.Variety Preference, Search, Trading Post, Monetary vs. Barter Equilibrium