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The Maxwell Energy-stress tensor: from Electrostatics to Continuum Mechanics
No full textThe Maxwell energy-stress tensor:
from Electrostatics to Continuum Mechanics.
Carmine Trimarco
University of Pisa, Italy
Dipartimento di Matematica Applicata ‘U.Dini’
Via Bonanno 25/B
I-56126 Pisa
e-mail: [email protected]
The Maxwell energy-stress tensor of electrostatics was revisited and re-proposed in elasticity by Eshelby, in 1951. The two tensors share the following feature: both account for the presence of an inhomogeneity. In electrostatics, the inhomogeneity is the electric charge whereas, in elasticity, is the material ‘defect’ of a body. Despite the close similarity of the two tensors, they definitely differ from one another as they describe distinct physical phenomena.
An Eshelby-like tensor is here proposed for electrostatics. This tensor identically vanishes out the body, whereas the Maxwell stress tensor is defined everywhere in the space
Polarisation and Magnetisation in Continua. Some remarks on similarities and differences.
No full textTMR meeting
Paris, 21-23.02.02
Polarisation and Magnetisation.
Carmine Trimarco
University of Pisa, Italy
Dipartimento di Matematica Applicata ‘U.Dini’
Via Bonanno 25/B
I-56126 Pisa
e-mail: [email protected]
Abstract.
Polarisation and magnetisation are material quantities that are currently associated with the electromagnetic fields. However, there are materials that, otherwise purely thermoelastic, may undergo through a phase transition process, at the end of which they possibly exhibit also electromagnetic properties, such as ferro-electricity or ferro-magnetic properties. Typically, the crystalline unit cell suffers a permanent geometrical deformation in the phase transformation process. Such an intrinsic deformation possibly alters the initial distribution of the electric charges or of the atomic spins. As a result, electric or magnetic dipoles may arise in the crystalline cell. These dipoles, in turn, can arrange themselves in domains and possibly develop ferro-electricity or ferro-magnetism, in the absence of external electric or magnetic fields and under suitable thermal or mechanical loading, or both. This is the case of the barium titanate, which becomes anisotropic and ferro-electric below 120°C.
Despite the fact that polarisation and magnetisation are governed by similar phenomenological equations in most of the cases of interest, these two quantities differ deeply from one another. Some of these differences are pointed out hereby, in rigid and in deformable bodies
Ruolo del solvente negli equilibri tautomerici di benzopiranoimidazoli e 2-nitrometil-4-amminopiridine
No full textI fenomeni di tautomeria prototropica dei composti eterociclici possono influenzarne la reattività chimica e il comportamento biologico1. Risulta quindi importante poter usufruire di modelli teorici in grado di descrivere correttamente gli equilibri tautomerici in fase gassosa e in soluzione. Presentiamo i risultati di calcoli quantomeccanici ab-initio e DFT condotti sui tautomeri più significativi di alcuni derivati benzopiranoimidazolici da noi sintetizzati (fig. 1).2 Le differenze energetiche tra i tautomeri alfa e beta si riducono drasticamente utilizzando il modello solvente PCM, confermando i dati spettroscopici ottenuti mediante 1H e 13C NMR. Riportiamo, inoltre, i risultati di calcoli ab-initio condotti sui tautomeri di derivati di 2-nitrometil-4-amminopiridine (fig. 2). Gli spettri 1H e 13C NMR registrati in C6D6 e CD3OD mostrano la presenza univoca dei tautomeri alfa nel primo solvente e beta nel secondo. I calcoli condotti con modello PCM non confermano le osservazioni sperimentali. Una migliore descrizione del fenomeno si ottiene considerando le interazioni esplicite tra il soluto e un numero limitato di molecole di solvente.
(1) Pospisil, P.; Ballmer, P.; Folkers, G.; Scapozza, L.; Tautomerism of nucleobase derivatives and their score in virtual screening to thymidine kinase, Abstract of Papers, 224th ACS National Meeting, Boston, MA, United States, August 18-22, 2002.
(2) Contini, A.; Beccalli, E.M.; Trimarco, P.; Eur. J. Org. Chem., 2003, in stampa
Remarkable Identities in Mechanics and Thermodynamics
No full textREMARKABLE IDENTITIES IN MECHANICS AND ELECTROMAGNETISM
Carmine Trimarco
University of Pisa, Italy
Dipartimento di Matematica Applicata ‘U.Dini’
Via Bonanno 25/B
I-56126 Pisa
e-mail: [email protected]
Abstract.
In homogeneous hyperelastic solids some identities, which are based on the classical balance laws of continua, can be arranged in the form of conservations laws. In the presence of inhomogeneities, singularities or defects, these identities still hold true, though in a slightly modified form, and can be interpreted as balance laws of nonclassical forces that act on the inhomogeneity or on the defect. In this view, novel physical quantities are envisaged through these laws, which in turn address configurational mechanics. These quantities are known as material quantities and can be readily extended to the more general context of nonclassical continua and to continua with microstructure.
In electromagnetic materials similar identities can be established. They hold true along the solutions of the mechanical equations, which are now coupled with the Maxwell equations of electromagnetism.
A different standpoint may be adopted however and, by reversing the reasoning, the aforementioned conservation laws can be viewed as primary equations rather than identities. This view is supported by a nonclassical variational approach, which addresses interesting remarks in the case of electromagnetic materials
Tautomeric equilibria of benzopyranoimidazoles: useful insights from quantum chemical calculation and NMR
No full textThe development of novel syntetic strategies for achieving compounds containing the coumarin nucleus condensed to several heterocycles has been the subject of our research for the latter few years. [1] Such heterocycles are pharmacologically relevant as CNS depressants, [2] growth inhibitors of mammalian cancer [3] and also phosphodiesterase VII inhibitors for treatment of immunity-associated diseases. [4]
Recently we reported the synthesis of some substituted benzopyranoimidazolones, and we pointed out the possibility of such heterocycles to exist in solution in at least two tautomeric forms, the N3-H and the N1-H tautomers (Fig. 1). [5] The study and quantitative evaluation of prototropic tautomerism in heterocyclic compounds is of primary interest, influencing both reactivity and biological behavior, for example the ability of a drug to bind the active site of a target enzyme [6]. Unfortunately literature does not report any reliable structural information and neither experimental data concerning tautomerism on pyranoimidazolone nucleus. Furthermore RT NMR experiments conducted by us so far were able to evidence the presence of at least two tautomers only for compound 4d and the attempts previously reported by us to unequivocally assign the preferred tautomeric structure by NMR were unsuccessful. The only result was obtained by N-methylation of compound 4d, were just the N3-CH3 product was isolated both at high and low reaction temperatures. However the reaction condition adopted could have influenced the tautomeric equilibrium. On the other hand tautomerism has been successfully described on various substituted imidazoles by ab-initio and DFT calculations in both gas-phase and solution within the continuum solvent model or evaluating explicit solvent interactions. [7]
In our previous work, where the main object was the development of a synthetic strategy for benzopiranoimidazoles, preliminary quantum chemical calculations explained only in part the tautomeric behavior observed, thus the need of a throughout theoretical and experimental investigation. The relative stability of all the possible tautomers for [1]benzopyrano[3,4-d]imidazol-4(3H)-ones, namely the N3-H (alpha tautomer), N1-H (beta tautomer), coumarin O-H (gamma tautomer) and C2-H (delta tautomer), has been evaluated by mean of HF and B3LYP calculations, including the solvent contribution by the SCRF PCM model. Furthermore the 13C and 1H chemical shifts were calculated by GIAO technique at the HF/6-311+G(2d,p) and B3LYP/TZVP levels of theory both in gas phase and in solution by using the PCM model for DMSO. The calculation of 13C chemical shifts by GIAO technique and the comparison with the experimental has been reported as one of the most reliable methods for the investigation of tautomeric equilibria in solution [8]. Finally, 1H NMR spectra were recorded in CD3COCD3 at 500 Mhz at variable temperature in a range from RT to –60°C in order to evidence the presence of the most probable tautomers by progressively lowering their interconversion rates.
The combination of the above mentioned theoretical techniques and experimental NMR allowed us to demonstrate that:
1.The only relevant tautomeric equilibrium for benzopyranoimidazolones is between alpha and beta forms.
2.All compounds 4a-e are able to exhibit tautomeric equilibrium in polar solvents.
3.The interconversion rate between alpha and beta tautomers is fast, thus by NMR is possibile to detect the presence of both tautomers only at low temperatures, otherwise averaged signals are recorded.
Bibliography
1.[a] E.M. Beccalli, A. Contini and P. Trimarco, Eur. J. Org. Chem., 2003, 3976-3984, [b] E.M. Beccalli, A. Contini and P. Trimarco, Tetrahedron Letters, 2004, 45, 3447-3449.
2.V. L. Savel’ev, N. T. Pryanishnikova, V. A. Zagorevskii, I. V. Chernyakova, O.S. Artamonova, V. V. Shavyrina, L. I. Malysheva, Khim. Farm. Zh. 1983, 17, 697-700; see Chem. Abstr. 1983, 99, 158325.
3.M. Trkovnik, V. Kalaj, D. Kitan, Org. Prep. Proced. Int., 1987, 19, 450-455
4.M. Eggenweiler, J. Rochus, M. Wolf, M. Gassen, O. Poeschke, Merck Patent Gmbh, Germany, PCT Int. Appl. 2001; see Chem. Abstr. 2001, 134, 331619.
5.See ref 1a
6.P. Pospisil, P. Ballmer, G. Folkers, L. Scapozza, Tautomerism of nucleobase derivatives and their score in virtual screening to thymidine kinase, Abstracts of Papers, 224th ACS National Meeting, Boston, MA, United States, August 18-22, 2002
7.[a] O. V. Shishkin, O. S. Sukhanov, L. Gorb and J. Leszczynski, PCCP, 2002, 4, 5359-5364. [b] G. -S. Li, M. F. Ruiz-Lopez, M. S. Zhang, B. Maigret, J. Mol. Struct. (Theochem), 1998, 422, 197-204. [c] E. D. Raczyńska, Anal. Chim. Acta, 1997, 348, 431-441. [d] G. A. Worth, P. M. King, W. G. Richards, Biochem. Biophys. Acta, 1989, 993, 134-136. [e] G. -S. Li, M. F. Ruiz-Lopez, M. -S. Zhang, B. Maigret, J. Phys. Chem., 1997, 101, 7885-7892. [f] F. J. Luque, J. M. Lopez-Bes, J. Cemeli, M. Aroztegui, M. Orozco, Theor. Chem. Acc., 1997, 96, 105-113.
8.[a] N. E. Campillo, C. Montero, J. A. Páez, J. Mol. Struct. (Theochem), 2004, 678, 83-89. [b] E. Kleinpeter and A. Koch, J. Phys. Org. Chem., 2001, 14, 566-576
2-Pyridineacetamides: a novel class of Tyrosine Kinases Inhibitors
No full textWe developed a new synthesis of 2-pyridineacetamides starting from pyran-2-one N-functionalized amidines. Secondary amines reacted in a sealed tube with the above-mentioned amidines and, by nucleophilic attack on pyran-2-one nucleus and thermal rearrangement, afforded exclusively the desired 2-pyridineacetamide derivatives. Ab-initio electrostatic potential calculations correctly predicted the selectivity of the nucleophilic attack on the pyran-2-one derivatives.
In the context of a blind screening, resulting 2-Pyridineacetamides have been pharmacologically tested on smooth muscular cells proliferation. Some of them resulted active with an IC50 ranging from 40 to 0.7 μM. At this point cheminformatics and bioinformatics tools have been essential for understanding the molecular mechanism of action of our amides. With the aid of Scifinder we searched bioactive molecules presenting substructures similar to our scaffold. Results pointed us toward GF tyrosine kinase receptors. In silico experiments showed us a strong selectivity toward the epidermal derived growth factor receptor kinase (EGFRK) and the platelet derived growth factor receptor kinase (PDGFRK) if compared with the vascular endothelial derived growth factor receptor kinase (VEGFRK) and the fibroblast derived growth factor receptor kinase (FGFRK). We realized that including the water molecule H-bonded to Tyr766 in the EGFR kinase is necessary for reliable docking experiments. Results show that the predicted potency of the 2-pyridineacetamides described in the present study is comparable to that of known EGFRK inhibitor TarcevaTM. Preliminary pharmacological experiments conducted on rat’s aorta smooth muscular cells confirm the observed computational results
Revitalizing culture and ecosystems through environmental education in Samburu, Kenya
No full textPresented at the Spring 2015 Center for Collaborative Conservation (https://collaborativeconservation.org/) Seminar and Discussion Series highlights the work of the Cohort 6 Fellows. Series Spring 2015 presents: Jon Trimarco, February 10th, 2015, Colorado State University, Fort Collins, Colorado.Jon Trimarco is currently pursuing his masters in the department of Human Dimensions of Natural Resources. For his thesis he is investigating the relationship between Kenya's formal education system and the rate of traditional ecological knowledge erosion in Samburu, Kenya, where he has spent the past two field seasons. He recently served as a Peace Corps volunteer in Ghana, working as an agroforestry extensionist and environmental educator. He is an alumni of the Warner College, with a bachelors in Conservation Biology.PowerPoint presentation.Traditional ecological knowledge (TEK) is being lost across the planet and it is feared that, as a consequence, indigenous communities have become less resilient in the face of environmental changes. In this talk, Jon will reflect on his experiences leading a collaborative effort to address such concerns among the pastoralists of Samburu, Kenya. Through a fellowship with the CCC, Jon and his team investigated the nature of TEK loss in Samburu, created TEK-centered environmental education programs and mobilized hundreds of community members in afforestation efforts using both traditional and western techniques. This talk will focus on the importance of collaboration in developing environmental education programs and the surprising 'innovations' that can be discovered while working with TEK
Tolerability of long-term treatment with lercanidipine versus amlodipine and lacidipine in elderly hypertensives
No full text
Tolerability of long-term treatment with lercanidipine versus amlodipine and lacidipine in elderly hypertensives
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