Hirsch model

Evaluation of the Hirsch model has shown a slight improvement over Witczak s predictive model (Christensen et al. 2003 Dongre et al. 2005). 

A more simplified predictive model has been developed by Al-Khateeb et al. (2006), which, for the determination of dynamic modulus, uses only two parameters the voids in the mineral aggregate and the dynamic shear modulus of the binder. As concluded, the model is capable of predicting the dynamic modulus of an asphalt concrete at a broader range of temperatures and loading frequencies than the Hirsch model. It also has the advantage of estimating the dynamic modulus of an asphalt concrete with modified bitumen (Al-Khateeb et al. 2006). The mathematical formulation of the model developed is as follows ... 

Mohammad et al. (2007) evaluated the original Witczak and Hirsch models and found that the reliability of the Witczak model increases for higher nominal maximum aggregate size, whereas the reliability of the Hirsch model increases for lower nominal maximum aggregate size. 

Christensen D.W.,T.K. Pellinen, and R.E Bonaquist. 2003. Hirsch model for estimating the modulus of asphalt concrete. Journal of the Association of Asphalt Paving Technologists, Vol. 72, pp. 97-121. 

HIRSCH MODEL COUNTO MODEL HASHIN MODEL... 

Homer JB, Hirsch GB (2006) System dynamics modelling for pubhc health background and opportunities, Am J Public Heith 96 452-458... 

The use of various in vitro models in studying renal toxicology is well documented in the literature (Ware et al., 1979 Kacew and Hirsch, 1981 Hassall et al., 1983 Hook and Hewitt, 1986 Smith et al., 1987 Tay et al., 1988 Williams, 1989). A listing of the available in vitro models is provided in Table 17.6. Each model system possesses its own advantages and disadvantages, and all have demonstrated their usefulness and application in renal toxicology. 

Beuerle F, Witte P, Hartnagel U, Lebovitz R, Parng C, Hirsch A (2007) Cytoprotective activities of water-soluble fullerenes in zebrafish models. J. Exp. Nanosci. 2 147-170. 

Foley S, Curtis ADM, Hirsch A, Brettreich M, Pelegrin A, Seta P, Larroque C (2002b) Interaction of a water soluble fullerene derivative with reactive oxygen species and model enzymatic systems. Fullerenes Nanotubes and Carbon Nanostructures 10 49-67. 

Hirsch-Reinshagen, V., Maia, L.F., Burgess, B.L., et al. (2005) The absence of ABCAl decreases soluble APOE levels but does not diminish amyloid deposition in two murine models of Alzheimer s disease. J. Biol. Chem., 280, 43243 3256. 

Hirsch A, Vostrowsky O (2001) Dendrimers with Carbon Rich-Cores. 217 51 -93 HiyamaT,ShirakawaE(2002)Organosihcon Compounds. 219 61-85 Houseman BT, Mrksich M (2002) Model Systems for Studying Polyvalent Carbohydrate Binding Interactions. 218 1-44 Hricovmiova Z, see Petrus L (2001) 2J5 15-41... 

Lattice gas (Molt and Davis, 1971, 1979 Gill, 1972 Pfister, 1977 Hirsch, 1979) and percolation (Silver et al., 1979 Ries et al., 1986) models describe the concentration dependencies of the mobility. The lattice gas model is based on... 

Santos-Lemus and Hirsch (1986) measured hole mobilities of NIPC doped PC. Over a range of concentrations, fields, and temperatures, the transport was nondispersive. The field and temperature dependencies followed logn / El/2 and -(T0IT)2 relationships. For concentrations of less than 40%, a power-law concentration dependence was reported. The concentration dependence was described by a wavefunction decay constant of 1.6 A. To explain a mobility that shows features expected for trap-free transport with a field dependence predicted from the Poole-Frenkel effect, the authors proposed a model based on field-enhanced polaron tunneling. The model is based on an earlier argument of Mott (1971). 

Santos-Lemus and Yartsev (1995) analyzed earlier data on NIPC doped PC by Santos-Lemus (1983) and Santos-Lemus and Hirsch (1986). The temperature dependence was analyzed by a Poole-Frenkel model. From plots of the activation energy versus E /2, zero-field energies were determined for different NIPC concentrations. The values were in the range of 0.60 to 0.73 eV. From a plot of the zero-field activation energy versus p K a value of 0.98 eV was derived for the potential barrier of an isolated NIPC molecule. 

Bai, X. S., and Fuchs, L., Numerical model for turbulent diffusion flames with applications. In Computational Fluid Dynamics (C. Hirsch, J. Periaux and W. Kordulla, eds.). Elsevier, Amsterdam, 1992, vol. l,p. 169. 

Hirsch, A. 1., Michalak, A. M., Bmhwiler, L. M., Peters, W., Dlugokencky, E. J., and Tans, P. P. (2006). Inverse modeling estimates of the global nitrous oxide surface flux from 1998—2001. Global Biochem. Cycles 20, doi 10.1029/2004GB002443. 

The study of mathematical models of competition has led to the discovery of some very beautiful mathematics. This mathematics, often referred to as monotone dynamical systems theory, was largely developed by M. W. Hirsch [Hil Hi3], although others have made substantial contributions as well. In this section we describe a result that was first obtained in a now classical paper of DeMottoni and Schiaffino [DS] for the special case of periodic Lotka-Volterra systems. Later, it was recognized by Hale and Somolinos [HaS] and Smith [S4 S5] that the arguments in [DS] hold for general competitive and cooperative planar periodic systems. The result says that every bounded solution of such a system converges to a periodic solution that has the same period as the differential equation. 

Hunot S, Vila M, Teismaim P, Davis RJ, Hirsch EC, Przedborski S, Rakic P, Flavell RA (2004) JNK-mediated iiiduction of cyclooxygenase 2 is required for iieurodegeiieratioii in a mouse model of Parkinson s disease. Proc Natl Acad Sci USA 101 665-670. 

Breidert T, Callebert J, Heneka MT, Landi edi G, Launay JM, Hirsch EC (2002) Protecdve acdon of die peroxisome proliferator-acd-vated receptor-gamma agonist pioglitazone in a mouse model of Pai kinson s disease. J Neurochem 82 615-624. 

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