Antieigenvalue theory: Difference between revisions

Latest revision as of 13:56, 16 February 2013

The sea level equation (SLE) is the linear, integral equation that describes the sea–level variations associated with the Glacial Isostatic Adjustement (GIA).

The basic idea of the SLE dates back to 1888, when Woodward published his pioneering work on the form and position of mean sea level,^[1] and only later has been refined by Platzman ^[2] and Farrell ^[3] in the context of the study of the ocean tides. In the words of Wu and Peltier,^[4] the solution of the SLE yields the space– and time–dependent change of ocean bathymetry which is required to keep the gravitational potential of the sea surface constant for a specific deglaciation chronology and viscoelastic earth model. The SLE theory was then developed by other authors as Mitrovica & Peltier,^[5] Mitrovica et al.^[6] and Spada & Stocchi.^[7] In its simplest form, the SLE reads

S=N-U,

where $S$ is the sea–level change, $N$ is the sea surface variation as seen from Earth's center of mass, and $U$ is vertical displacement.

In a more explicit form the SLE can be written as follow:

S(\theta ,\lambda ,t)={\frac {\rho _{i}}{\gamma }}G_{s}\otimes _{i}I+{\frac {\rho _{w}}{\gamma }}G_{s}\otimes _{o}S+S^{E}-{\frac {\rho _{i}}{\gamma }}{\overline {G_{s}\otimes _{i}I}}-{\frac {\rho _{w}}{\gamma }}{\overline {G_{o}\otimes _{o}S}},

where $\theta$ is colatitude and $\lambda$ is longitude, $t$ is time, $\rho _{i}$ and $\rho _{w}$ are the densities of ice and water, respectively, $\gamma$ is the reference surface gravity, $G_{s}=G_{s}(h,k)$ is the sea–level Green’s function (dependent upon the $h$ and $k$ viscoelastic load–deformation coefficients - LDCs), $I=I(\theta ,\lambda ,t)$ is the ice thickness variation, $S^{E}=S^{E}(t)$ represents the eustatic term (i.e. the ocean–averaged value of $S$ ), $\otimes _{i}$ and $\otimes _{o}$ denote spatio–temporal convolutions over the ice– and ocean–covered regions, and the overbar indicates an average over the surface of the oceans that ensures mass conservation.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

↑ Woodward, R. S., 1988. On the form and position of mean sea level. United States Geol. Survey Bull., 48, 87170.
↑ Platzman , G. W., 1971. Ocean tides. In Lectures in Applied Mathematics, 14, part 2, pp. 239292, American Mathematical Society, Providence, RI.
↑ Farrell, W. E., 1973. Earth tides, ocean tides and tidal loading. Phil. Trans. R. Soc. Lond. A, 274, 253259.
↑ Wu, P., and W. R. Peltier. Glacial isostatic adjustment and the free–air gravity anomaly as a constraint on deep mantle viscosity. Geophys. J. R. Astron. Soc., 74, 377449, 1983.
↑ Mitrovica, J. X. & Peltier, W. R., 1991. On postglacial geoid subsidence over the equatorial ocean. J. geophys. Res., 96, 20,05320,071.
↑ Mitrovica, J. X., Davis, J. L. & Shapiro, I. I., 1994. A spectral formal- ism for computing three–dimensional deformations due to surface loads. J. geophys. Res., 99, 70577073.
↑ Spada G. & Stocchi, P., 2006. The Sea Level Equation, Theory and Numerical Examples. ISBN 88-548-0384-7, 96 pp., Aracne, Roma.

[Woodward-1] Woodward, R. S., 1988. On the form and position of mean sea level. United States Geol. Survey Bull., 48, 87170.

[Platzman-2] Platzman , G. W., 1971. Ocean tides. In Lectures in Applied Mathematics, 14, part 2, pp. 239292, American Mathematical Society, Providence, RI.

[Farrell-3] Farrell, W. E., 1973. Earth tides, ocean tides and tidal loading. Phil. Trans. R. Soc. Lond. A, 274, 253259.

[Wu-Peltier-4] Wu, P., and W. R. Peltier. Glacial isostatic adjustment and the free–air gravity anomaly as a constraint on deep mantle viscosity. Geophys. J. R. Astron. Soc., 74, 377449, 1983.

[Mitrovica-Peltier-5] Mitrovica, J. X. & Peltier, W. R., 1991. On postglacial geoid subsidence over the equatorial ocean. J. geophys. Res., 96, 20,05320,071.

[Mitrovica-etal-6] Mitrovica, J. X., Davis, J. L. & Shapiro, I. I., 1994. A spectral formal- ism for computing three–dimensional deformations due to surface loads. J. geophys. Res., 99, 70577073.

[Spada-Stocchi-7] Spada G. & Stocchi, P., 2006. The Sea Level Equation, Theory and Numerical Examples. ISBN 88-548-0384-7, 96 pp., Aracne, Roma.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

@@ Line 1: / Line 1: @@
-A civil rights organization on Thursday demanded a meeting with the CEO of Barneys New York and threatened to picket the luxury department store in Manhattan after two black customers said they were stopped by police after making expensive purchases.<br><br>
+{{Orphan|date=March 2013}}
-Trayon Christian, 19, of Queens said after he bought a $349 Ferragamo belt on April 29 he was handcuffed and detained for two hours before being released with no charges. He filed a discrimination lawsuit against Barneys and the New York City Police Department on Monday.<br><br>Undercover police swarmed Kayla Phillips, 21, of Brooklyn at a subway station and demanded to see her credit card after she left Barneys with her purchase of a $2,500 [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine Bags Outlet] purse on Feb. 28, said her lawyer Kareem Vessup.<br>Phillips, a nursing student, had received a tax return and decided to splurge on the designer purse, Vessup said.<br><br>She filed notice of an upcoming lawsuit against the NYPD and plans to sue Barneys, he said.<br>In his lawsuit, Christian, a mechanical engineering student, said when he bought the belt, Barneys telephoned police to report a criminal act. When he stepped out of the store with his shopping bag, he was handcuffed on the sidewalk and brought to the 19th Precinct, the lawsuit said.<br><br>Police interrogated him "as to how a young black man such as himself could afford to purchase such an expensive belt and that the debit card he had in his possession had to be fake," the lawsuit said.<br>Michael Palillo, a lawyer representing Christian, said his client had saved up earnings from a work-study program at New York City College of Technology and was excited to treat himself to a trendy belt he'd admired on some of the rappers he follows on television.<br><br>"He enjoys fashion," Palillo said.<br>The racial profiling [http://search.un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=incident&Submit=Go incident] violated his civil rights, said the lawsuit, which was filed in state Supreme Court in Manhattan and seeks unspecified damages.<br>Barneys on its Facebook page said "no employee of Barneys" was involved and it "has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights."<br><br>The NYPD did not immediately respond to a request for comment.<br>National Action Network, a civil rights group led by Reverend Al Sharpton, said it was mobilizing activists to take direct action against the store and the NYPD.<br>"National Action Network will immediately demand a meeting with the Barneys New York CEO," NAN spokeswoman Rachel Noerdlinger said in a statement.<br><br>The group is "planning to picket the store if the pattern of racial profiling is not immediately rectified after numerous incidents of discrimination have come to light," Noerdlinger said.<br>The incidents came to light little more than two months after a judge ruled the NYPD discriminated against black and Hispanic youths in its controversial stop-and-frisk crime fighting tactic.<br><br>On its website, Barneys describes itself as "... a mecca for discerning fashionistas and clothing connoisseurs since 1923" and quotes "Sex and the City" actress Sarah Jessica Parker as telling Vanity Fair, "If you're a nice person and you work hard, you get to go shopping at Barneys. It's the decadent reward."<br><br>(Additional reporting by Luke Swiderski; editing by Gunna Dickson)
+The '''sea level equation''' (SLE) is the linear, integral equation that describes the sea–level variations associated with the [[Post-glacial rebound|Glacial Isostatic Adjustement]] (GIA).
+The basic idea of the SLE dates back to 1888, when Woodward published his pioneering work on the form and position of mean [[sea level]],<ref name="Woodward">Woodward, R. S., 1988. On the form and position of mean sea level. United States Geol. Survey Bull., 48, 87170.</ref> and only later has been refined by Platzman <ref name="Platzman">Platzman , G. W., 1971. Ocean tides. In Lectures in Applied Mathematics, 14, part 2, pp. 239292, American Mathematical Society, Providence, RI.</ref> and Farrell <ref name="Farrell">Farrell, W. E., 1973. Earth tides, ocean tides and tidal loading. Phil. Trans. R. Soc. Lond. A, 274, 253259.</ref> in the context of the study of the ocean tides. In the words of Wu and Peltier,<ref name="Wu-Peltier">Wu, P., and W. R. Peltier. Glacial isostatic adjustment and the free–air gravity anomaly as a constraint on deep mantle viscosity. Geophys. J. R. Astron. Soc., 74, 377449, 1983.</ref> the solution of the SLE yields the space– and time–dependent change of ocean [[bathymetry]] which is required to keep the [[geoid|gravitational potential of the sea surface]] constant for a specific [[deglaciation]] chronology and [[Viscoelasticity|viscoelastic]] earth model. The SLE theory was then developed by other authors as Mitrovica & Peltier,<ref name="Mitrovica-Peltier">Mitrovica, J. X. & Peltier, W. R., 1991. On postglacial geoid subsidence over the equatorial ocean. J. geophys. Res., 96, 20,05320,071.</ref> Mitrovica et al.<ref name="Mitrovica-etal">Mitrovica, J. X., Davis, J. L. & Shapiro, I. I., 1994. A spectral formal- ism for computing three–dimensional deformations due to surface loads. J. geophys. Res., 99, 70577073.</ref> and Spada & Stocchi.<ref name="Spada-Stocchi">Spada G. & Stocchi, P., 2006. The Sea Level Equation, Theory and Numerical Examples. ISBN 88-548-0384-7, 96 pp., [[Aracne (publisher)|Aracne]], Roma.</ref> In its simplest form, the SLE reads
+:<math> S=N-U, </math>
+where <math>S</math>  is the sea–level change, <math>N</math> is the sea surface variation as seen from Earth's center of mass, and <math>U</math> is vertical displacement.
+In a more explicit form the SLE can be written as follow:
+: <math>S (\theta, \lambda, t) = \frac{\rho_i}{\gamma}  G_s \otimes_i I + \frac{\rho_w}{\gamma} G_s \otimes_o S + S^E - \frac{\rho_i}{\gamma}\overline{G_s \otimes_i I } - \frac{\rho_w}{\gamma}\overline{G_o \otimes_o S }, </math>
+where <math>\theta</math> is [[colatitude]] and <math>\lambda</math> is [[longitude]], <math>t</math> is time, <math>\rho_i</math> and <math>\rho_w</math> are the densities of ice and water, respectively, <math>\gamma</math> is the reference surface gravity, <math>G_s=G_s(h,k)</math> is the sea–level Green’s function (dependent upon the  <math>h</math> and  <math>k</math> viscoelastic load–deformation coefficients - LDCs), <math> I= I(\theta, \lambda, t)</math> is the ice thickness variation, <math>S^E=S^E(t)</math> represents the [[eustatic]] term (i.e. the ocean–averaged value of <math>S</math>),   <math>\otimes_i</math> and <math>\otimes_o</math> denote spatio–temporal convolutions over the ice– and ocean–covered regions, and the overbar indicates an average over the surface of the oceans that ensures mass conservation.
+==References==
+{{Reflist}}
+{{DEFAULTSORT:Sea level equation}}
+[[Category:Geodynamics| ]]

Antieigenvalue theory: Difference between revisions

Latest revision as of 13:56, 16 February 2013

References

Navigation menu

Search