Numerical solution of random differential models

This paper deals with the construction of a numerical solution of random initial value problems by means of a random improved Euler method. Conditions for the mean square convergence of the proposed method are established. Finally, an illustrative example is included in which the main statistics properties such as the mean and the variance of the stochastic approximation solution process are given. © 2011 Elsevier Ltd.This work has been partially supported by the Spanish M.C.Y.T. grants MTM2009-08587, DPI2010-20891-C02-01, Universidad Politecnica de Valencia grant PAID06-09-2588 and Mexican Conacyt.Cortés López, JC.; Jódar Sánchez, LA.; Villafuerte Altuzar, L.; Company Rossi, R. (2011). Numerical solution of random differential models. Mathematical and Computer Modelling. 54(7):1846-1851. https://doi.org/10.1016/j.mcm.2010.12.037S1846185154

Relativistic kinematics beyond Special Relativity

In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity that preserves the relativity principle at leading order in 1/M.Comment: Version with minor corrections, to appear in Phys. Rev.

Tachoastrometry: astrometry with radial velocities

Spectra of composite systems (e.g., spectroscopic binaries) contain spatial information that can be retrieved by measuring the radial velocities (i.e., Doppler shifts) of the components in four observations with the slit rotated by 90 degrees in the sky. By using basic concepts of slit spectroscopy we show that the geometry of composite systems can be reliably retrieved by measuring only radial velocity differences taken with different slit angles. The spatial resolution is determined by the precision with which differential radial velocities can be measured. We use the UVES spectrograph at the VLT to observe the known spectroscopic binary star HD 188088 (HIP 97944), which has a maximum expected separation of 23 milli-arcseconds. We measure an astrometric signal in radial velocity of 276 \ms, which corresponds to a separation between the two components at the time of the observations of 18 $\pm2$ milli-arcseconds. The stars were aligned east-west. We describe a simple optical device to simultaneously record pairs of spectra rotated by 180 degrees, thus reducing systematic effects. We compute and provide the function expressing the shift of the centroid of a seeing-limited image in the presence of a narrow slit.The proposed technique is simple to use and our test shows that it is amenable for deriving astrometry with milli-arcsecond accuracy or better, beyond the diffraction limit of the telescope. The technique can be further improved by using simple devices to simultaneously record the spectra with 180 degrees angles.With tachoastrometry, radial velocities and astrometric positions can be measured simultaneously for many double line system binaries in an easy way. The method is not limited to binary stars, but can be applied to any astrophysical configuration in which spectral lines are generated by separate (non-rotational symmetric) regions.Comment: Accepted for publication in A&

Recent advances on simulation and theory of hydrogen storage in metal–organic frameworks and covalent organic frameworks

This critical review covers the application of computer simulations, including quantum calculations (ab initio and DFT), grand canonical Monte-Carlo simulations, and molecular dynamics simulations, to the burgeoning area of the hydrogen storage by metal–organic frameworks and covalent-organic frameworks. This review begins with an overview of the theoretical methods obtained from previous studies. Then strategies for the improvement of hydrogen storage in the porous materials are discussed in detail. The strategies include appropriate pore size, impregnation, catenation, open metal sites in metal oxide parts and within organic linker parts, doping of alkali elements onto organic linkers, substitution of metal oxide with lighter metals, functionalized organic linkers, and hydrogen spillover (186 references)

Design of Covalent Organic Frameworks for Methane Storage

We designed 14 new covalent organic frameworks (COFs), which are expected to adsorb large amounts of methane (CH_4) at 298 K and up to 300 bar. We have calculated their delivery uptake using grand canonical Monte Carlo (GCMC) simulations. We also report their thermodynamic stability based on 7.5 ns molecular dynamics simulations. Two new frameworks, COF-103-Eth-trans and COF-102-Ant, are found to exceed the DOE target of 180 v(STP)/v at 35 bar for methane storage. Their performance is comparable to the best previously reported materials: PCN-14 and Ni-MOF-74. Our results indicate that using thin vinyl bridging groups aid performance by minimizing the interaction methane-COF at low pressure. This is a new feature that can be used to enhance loading in addition to the common practice of adding extra fused benzene rings. Most importantly, this report shows that pure nonbonding interactions, van der Waals (vdW) and electrostatic forces in light elements (C, O, B, H, and Si), can rival the enhancement in uptake obtained for microporous materials derived from early transition metals

High H_2 Uptake in Li-, Na-, K-Metalated Covalent Organic Frameworks and Metal Organic Frameworks at 298 K

The Yaghi laboratory has developed porous covalent organic frameworks (COFs), COF102, COF103, and COF202, and metal–organic frameworks (MOFs), MOF177, MOF180, MOF200, MOF205, and MOF210, with ultrahigh porosity and outstanding H2 storage properties at 77 K. Using grand canonical Monte Carlo (GCMC) simulations with our recently developed first principles based force field (FF) from accurate quantum mechanics (QM), we calculated the molecular hydrogen (H2) uptake at 298 K for these systems, including the uptake for Li-, Na-, and K-metalated systems. We report the total, delivery and excess amount in gravimetric and volumetric units for all these compounds. For the gravimetric delivery amount from 1 to 100 bar, we find that eleven of these compounds reach the 2010 DOE target of 4.5 wt % at 298 K. The best of these compounds are MOF200-Li (6.34) and MOF200-Na (5.94), both reaching the 2015 DOE target of 5.5 wt % at 298 K. Among the undoped systems, we find that MOF200 gives a delivery amount as high as 3.24 wt % while MOF210 gives 2.90 wt % both from 1 to 100 bar and 298 K. However, none of these compounds reach the volumetric 2010 DOE target of 28 g H_2/L. The best volumetric performance is for COF102-Na (24.9), COF102-Li (23.8), COF103-Na (22.8), and COF103-Li (21.7), all using delivery g H_2/L units for 1–100 bar. These are the highest volumetric molecular hydrogen uptakes for a porous material under these thermodynamic conditions. Thus, one can obtain outstanding H_2 uptakes with Li, Na, and K doping of simple frameworks constructed from simple, cheap organic linkers. We present suggestions for strategies for synthesis of alkali metal-doped MOFs or COFs