Leonard stresses

The above equations describe the large-scale motion. Lij represents the interactions among the large scales. The effect of small scales appears through the residual stress tensors (i.e., Cij and Rij). In particular, Cij represents the interactions between the large and small scales, and Rij reflects the interactions between subgrid scales. The tensors Lij, Cij and Rij are known as the Leonard stress, cross-term stress and the residual Reynolds stress, respectively. 

In practice, the Leonard stress is often dominated by the numerical errors inherent in the finite difference (and finite volume) representation and is thus neglected or lumped into the deviatoric stress tensor (e.g., [97] [106] [186], p. 325). Consequently, as the box filter is applied to the Navier-Stokes equation, the residual stresses assume the form of sub-grid scale stresses ... 

Leonard stress tensor in LES Pa) residual stress tensor in LES Pa)... 

The Leonard stress term can be computed directly and does not need to be modeled. However, as shown by Shaanan et al. [50], the Leonard stresses are of the same order as the truncation errors of a second-order discretization scheme, and therefore, L can be implicitly accounted for. Consequently, a computed solution may depend on the numerical scheme that is used. 

Reduction of aromatic nitro compounds may give products sensitive to air. Moder and Leonard (d5) stressed the importance of rigid exclusion of air during reduction of a nitro compound to a complex air-sensitive diamine in order to maximize the yield. It is quite likely that in these cases the oxidation products will have an adverse influence on catalyst life. 

Kramer, T., Lindy, J., Green, B., Grace, M. and Leonard, A., The lombordity of post traumatic stress disorder and suicidality in Vietnam veterans. Suicide and Life Threatening Behaviors 24(1), 58, 1994. 

Bayer KU, De Koninck P, Leonard AS, et al (2001) Interaction with the NMDA receptor locks CaMKll in an active conformation. Nature 411 801-805 Beal MF (1995) Aging, energy, and oxidative stress in neurodegenerative diseases. Ann Neurol 38 357-366... 

Natural rubber exhibits unique physical and chemical properties. Rubbers stress-strain behavior exhibits the Mullins effect and the Payne effect. It strain crystallizes. Under repeated tensile strain, many filler reinforced rubbers exhibit a reduction in stress after the initial extension, and this is the so-called Mullins Effect which is technically understood as stress decay or relaxation. The phenomenon is named after the British rubber scientist Leonard Mullins, working at MBL Group in Leyland, and can be applied for many purposes as an instantaneous and irreversible softening of the stress-strain curve that occurs whenever the load increases beyond... 

Leonard, B. E. Brain cytokines and the psychopathology of depression. In Antidepressants, Leonard, B. E. (Ed.). Basel Birkhauser-Verlag, 2000, pp. 109-122. Leonard, B. E. and Miller, K. (Eds) Stress, the Immune System and Psychiatry. Chichester John Wiley Sons, 1995. 

Elliott MD, Holly TA, Leonard SM, Hendel RC. Impact of an abbreviated adenosine protocol incorporating adjunctive treadmill exercise on adverse effects and image quality in patients undergoing stress myocardial perfusion imaging. J Nucl Cardiol 2000 7(6) 584-9. 

Cassidy J, Merrick MV, Smyth JF, Leonard RC. Cardiotoxicity of mitozantrone assessed by stress and resting nuclear ventriculography. Eur J Cancer Chn Oncol 1988 24(5) 935-8. 

Wilmes A, Crean D, Aydin S, Pfaller W, Jennings P, Leonard MO (2011) Identification and dissection of the Nrf2 mediated oxidative stress pathway in human renal proximal tubule toxicity. Toxicol In Vitro 25(3) 613-622. doi 10.1016/j.tiv.2010.12.009... 

Limonciel A, Aschauer L, Wilmes A, Prajczer S, Leonard MO, Pfaller W, Jennings P (2011) Lactate is an ideal non-invasive marker for evaluating temporal alterations in cell stress and toxicity in repeat dose testing regimes. Toxicol In Vitro 25(8) 1855-1862. doi 10.1016/j. tiv.2011.05.018... 

The Euler s formula developed by Leonard Euler (Swiss mathematician, 1707 to 1783) is used in product designs and also in designs using columns in molds and dies that process plastic. Euler s formula assumes that the failure of a column is due solely to the stresses induced by sidewise bending. This assumption is not true for short columns that fidl mainly by direct compression, nor is it true for columns of medium length. The failure in such cases is by a combination of direct compression and bending. 

---