Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains

We study the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam chains at zero and non-zero temperatures. While such breathers are essentially stationary and very long-lived at zero temperature, thermal fluctuations tend to lead to breather motion and more rapid decay

Energy Relaxation in Nonlinear One-Dimensional Lattices

We study energy relaxation in thermalized one-dimensional nonlinear arrays of the Fermi-Pasta-Ulam type. The ends of the thermalized systems are placed in contact with a zero-temperature reservoir via damping forces. Harmonic arrays relax by sequential phonon decay into the cold reservoir, the lower frequency modes relaxing first. The relaxation pathway for purely anharmonic arrays involves the degradation of higher-energy nonlinear modes into lower energy ones. The lowest energy modes are absorbed by the cold reservoir, but a small amount of energy is persistently left behind in the array in the form of almost stationary low-frequency localized modes. Arrays with interactions that contain both a harmonic and an anharmonic contribution exhibit behavior that involves the interplay of phonon modes and breather modes. At long times relaxation is extremely slow due to the spontaneous appearance and persistence of energetic high-frequency stationary breathers. Breather behavior is further ascertained by explicitly injecting a localized excitation into the thermalized array and observing the relaxation behavior

Antifungal And Cytotoxic 2-acylcyclohexane-1,3-diones From Peperomia Alata And P. Trineura

Bioactivity-guided fractionation of the separate CH2Cl 2 extracts from the aerial parts of Peperomia alata and P. trineura yielded seven polyketides: alatanone A [3-hydroxy-2-(5′-phenylpent- 4′E-enoyl)cyclohex-2-en-1-one, 1a] and alatanone B [3-hydroxy-2-(3′- phenyl-6′-methylenedioxypropanoyl)cyclohex-2-en-1-one, 2a] from P. alata and trineurone A [3-hydroxy-2-(11′-phenylundec-10′E-enoyl)cyclohex- 2-en-1-one, 1b], trineurone B [3-hydroxy-2-(15′-phenyl-18′- methylenedioxypentadecanoyl)cyclohex-2-en-1-one, 2b], trineurone C [3-hydroxy-2-(17′-phenyl-20′-methylenedioxyheptadecanoyl) cyclohex-2-en-1-one, 2c], trineurone D [3-hydroxy-2-(hexadec-10′Z-enoyl) cyclohex-2-en-1-one, 3a], and trineurone E [(6R)-(+)-3,6-dihydroxy-2-(hexadec- 10′Z-enoyl)cyclohex-2-en-1-one, 3b] from P. trineura. The isolated compounds were evaluated for antifungal activity against Cladosporium cladosporioides and C. sphaeospermum and for cytotoxicity against the K562 and Nalm-6 leukemia cell lines. © 2014 The American Chemical Society and American Society of Pharmacognosy.77613771382Jaramillo, M.A., Manos, P.S., Zimmer, E.A., (2004) Int. J. Plant Sci., 165, pp. 403-416Wanke, S., Samain, M.S., Vanderschaeve, L., Mathieu, G., Goetghebeur, P., Neinhuis, C., (2006) Plant Biol., 8, pp. 93-102Salazar, K.J.M., Delgado, P.G.E., Luncor, L.R., Young, M.C.M., Kato, M.J., (2005) Phytochemistry, 66, pp. 573-579Seeram, N.P., Jacobs, H., McLean, S., Reynolds, W.F., (1998) Phytochemistry, 49, pp. 1389-1391Tanaka, T., Asai, F., Linuma, M., (1998) Phytochemistry, 49, pp. 229-232Mbah, J.A., Tchuendem, M.H.K., Tane, P., Sterner, O., (2002) Phytochemistry, 60, pp. 799-801Bayma, J.C., Arruda, M.S.P., Müller, A.H., Arruda, A.C., Canto, W.C., (2000) Phytochemistry, 55, pp. 779-782Govindachari, T.R., Kumari, G.N.K., Partho, P.D., (1998) Phytochemistry, 49, pp. 2129-2131Monache, F.D., Compagnone, R.S., (1996) Phytochemistry, 43, pp. 1097-1098Xu, S., Li, N., Ning, M.M., Zhou, C.H., Yang, Q.R., Wang, M.W., (2006) J. Nat. Prod., 69, pp. 247-250Wu, J., Li, N., Hasegawa, T., Sakai, J., Kakuta, S., Tang, W., Oka, S., Ando, M., (2005) J. Nat. Prod., 68, pp. 1656-1660Mahiou, V., Roblot, F., Hocquemiller, R., Cave, A., Rojas Arias, A., Inchausti, A., Yaluff, G., Fournet, A., (1996) J. Nat. Prod., 59, pp. 694-697Soares, M.G., Felippe, A.P.V., Guimarães, E.F., Kato, M.J., Ellena, J., Doriguetto, A.C., (2006) J. Braz. Chem. Soc., 17, pp. 1205-1210Li, N., Wu, J.L., Hasegawa, T., Sakai, J., Bai, L.M., Wang, L.Y., Kakuta, S., Ando, M., (2007) J. Nat. Prod., 70, pp. 998-1001Lago, J.H.G., Oliveira, A., Guimarães, E.F., Kato, M.J., (2007) J. Braz. Chem. Soc., 18, pp. 638-642Kato, M.J., Yoshida, M., Gottlieb, O.R., (1990) Phytochemistry, 29, pp. 1799-1810Nemoto, T., Masao, S., Kuwahara, Y., Takahisa, S., (1987) Agric. Biol. Chem., 51, pp. 1805-1810Mudd, A., (1983) J. Chem. Soc., 1, pp. 2161-2164Kuwahara, Y., Nemoto, T., Shibuya, M., Matsura, H., Shiraiwa, Y., (1983) Agric. Biol. Chem., 47, pp. 1929-1931Li, N., Hasegawa, T., Sakai, J.-I., Kakuta, S., Tang, W., Oka, S., Kiuchi, M., Ando, M., (2005) J. Nat. Prod., 68, pp. 1656-1660Denny, C., Zacharias, M.E., Ruiz, A.L.T.G., Amaral, M.C.E., Bittrich, V., Kohn, L.K., Sousa, I.M.O., Foglio, M.A., (2008) Phytother. Res., 22, pp. 127-130Wang, Q.-W., Yu, D.-H., Lin, M.-G., Zhao, M., Zhu, W.-J., Lu, Q., Li, G.-X., Yang, G.-H., (2012) Molecules, 17, pp. 4474-4483Moreira, D.L., Souza, P.O., Kaplan, M.A.C., Guimarães, E.F., (1999) Acta Hortic., 500, pp. 65-69Haan, J.W.D., Vendeven, L.J., (1973) Org. Magn. Reson., 5, pp. 147-153Azevedo, N.R., Santos, S.C., Miranda, E.G., Ferri, P.H., (1997) Phytochemistry, 46, pp. 1375-1377Cheng, M.J., Lee, S.J., Chang, Y.Y., Wu, S.H., Tsai, I.L., Jayaprakasam, B., Chen, I.S., (2003) Phytochemistry, 63, pp. 603-608Zaitsev, V.G., Mikhal'Chuk, A.L., (2001) Chirality, 13, pp. 488-492Homans, A.L., Fuchs, A., (1970) J. Chromatogr. A, 51, pp. 327-329Koeffler, H.P., Golde, D.W., (1980) Blood, 56, pp. 344-350Hurwitz, R., Hozier, J., Lebien, T., Minowada, J., Gajlpeczalska, K., Kubonishi, I., Kersey, J., (1979) Int. J. Cancer, 23, pp. 174-18

Dynamical properties of discrete breathers in curved chains with first and second neighbor interaction

We present the study of discrete breather dynamics in curved polymerlike chains consisting of masses connected via nonlinear springs. The polymer chains are one dimensional but not rectilinear and their motion takes place on a plane. After constructing breathers following numerically accurate procedures, we launch them in the chains and investigate properties of their propagation dynamics. We find that breather motion is strongly affected by the presence of curved regions of polymers, while the breathers themselves show a very strong resilience and remarkable stability in the presence of geometrical changes. For chains with strong angular rigidity we find that breathers either pass through bent regions or get reflected while retaining their frequency. Their motion is practically lossless and seems to be determined through local energy conservation. For less rigid chains modeled via second neighbor interactions, we find similarly that chain geometry typically does not destroy the localized breather states but, contrary to the angularly rigid chains, it induces some small but constant energy loss. Furthermore, we find that a curved segment acts as an active gate reflecting or refracting the incident breather and transforming its velocity to a value that depends on the discrete breathers frequency. We analyze the physical reasoning behind these seemingly general breather properties

Interaction of a discrete breather with a lattice junction

We study the scattering of a moving discrete breather (DB) on a junction in a Fermi-Pasta-Ulam chain consisting of two segments with different masses of the particles. We consider four distinct cases: (i) a light-heavy (abrupt) junction in which the DB impinges on the junction from the segment with lighter mass, (ii) a heavy-light junction, (iii) an up mass ramp in which the mass in the heavier segment increases continuously as one moves away from the junction point, and (iv) a down mass ramp. Depending on the mass difference and DB characteristics (frequency and velocity), the DB can either reflect from, or transmit through, or get trapped at the junction or on the ramp. For the heavy-light junction, the DB can even split at the junction into a reflected and a transmitted DB. The latter is found to subsequently split into two or more DBs. For the down mass ramp the DB gets accelerated in several stages, with accompanying radiation (phonons). These results are rationalized by calculating the Peierls-Nabarro barrier for the various cases. We also point out implications of our results in realistic situations such as electron-phonon coupled chains

Investigation of energy relaxation in 1-D nonlinear lattices by wavelets

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes