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Calculus


Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.

 
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Empirical Correction Techniques: Analysis and Applications to Chao...

By: L. Kocarev; D. Smilkov; L. Basnarkov; I. Trpevski

Description: Macedonian Academy of Sciences and Arts, Skopje, Macedonia. Contemporary tools for reducing model error in weather and climate forecasting models include empirical correction techniques. In this paper we explore the use of such techniques on low-order atmospheric models. We first present an iterative linear regression method for model correction that works efficiently when the reference truth is sampled at large time intervals, which is typical for real...

Allgaier, N., Harris, K., and Danforth, C.: Empirical correction of a toy climate model, Phys. Rev. E, 85, 026201, doi:10.1103/PhysRevE.85.026201, 2012.; Anderson, J. L.: An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129, 2884–2903, 2001.; Bishop, C.: Pattern recognition and machine learning, Springer New York, 2006.; Basnarkov, L. and Kocarev, L.: Forecast improvement in Lorenz 96 ...

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Ion Motion in the Current Sheet with Sheared Magnetic Field – Part...

By: A. I. Neishtadt; L. M. Zelenyi; A. V. Artemyev

Description: Space Research Institute RAS, Profsouznaya st., 84/32, GSP-7, 117997 Moscow, Russia. We investigate dynamics of charged particles in current sheets with the sheared magnetic field. In our previouspaper (Artemyev et al., 2013) we studied the particle motion in such magnetic field configurations on the basis of the quasi-adiabatic theory and conservation of the quasi-adiabatic invariant. In this paper we concentrate on violation of the adiabaticity due to ...

Anastasiadis, A., Gontikakis, C., and Efthymiopoulos, C.: Particle Interactions with single or multiple 3D solar reconnecting current sheets, Solar Phys., 253, 199–214, doi:10.1007/s11207-008-9234-4, 2008.; Arnold, V. I.: Geometrical methods in the theory of ordinary differential equations, Springer-Verlag, New York, 1988.; Angelopoulos, V., Kennel, C. F., Coroniti, F. V., Pellat, R., Spence, H. E., Kivelson, M. G.,...

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Regional and Inter-regional Effects in Evolving Climate Networks :...

By: J. Hlinka; N. Marwan; R. Donner; N. Jajcay; M. Vejmelka; D. Hartman; J. Kurths; M. Paluš

Description: Department of Nonlinear Dynamics and Complex Systems, Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodarenskou vezi 2, 182 07 Prague 8, Czech Republic. Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges ...

Albert, R., Jeong, H., and Barabasi, A. L.: Internet – Diameter of the World Wide Web, Nature, 401, 130–131, 1999.; Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., and Zhou, C.: Synchronization in complex networks, Phys. Reports, 469, 93–153, 2008.; Barabási, A.-L. and Albert, R.: Emergence of scaling in random network, Science, 286, 509–512, 1999.; Bialonski, S. and Lehnertz, K.: Assortative mixing in functional brain networks during epileptic seizures, Chaos, 23,...

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Stochastic Electron Motion Driven by Space Plasma Waves : Volume 2...

By: A. A. Tel’nikhin; T. K. Kronberg; G. V. Khazanov

Description: NASA Goddard Space FlightCenter, Greenbelt, MD, USA. Stochastic motion of relativistic electrons under conditions of the nonlinear resonance interaction of particles with space plasma waves is studied. Particular attention is given to the problem of the stability and variability of the Earth's radiation belts. It is found that the interaction between whistler-mode waves and radiation-belt electrons is likely to involve the same mechanism that is respons...

Albert, J. M.: Nonlinear interaction of outer zone electrons with VLF waves, Geopys. Res. Lett., 29, 116-1–116-3, doi:10.1029/2001GL013941, 2002.; Arnold, V.: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer-Verlag, New York, 1988.; Abdo, A. A., Ackermann, M., Ajello, M., Asano, K., Atwood, W. B., Axelsson, M., Baldini, L., Ballet, J., Barbiellini, G., Baring, M. G., Bastieri, D., Bechtol, K...

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Incidence and Reflection of Internal Waves and Wave-induced Curren...

By: J. P. McHugh

Description: University of New Hampshire, Durham, NH, USA. Weakly nonlinear internal gravity waves are treated in a two-layer fluid with a set of nonlinear Schrodinger equations. The layers have a sharp interface with a jump in buoyance frequency approximately modelling the tropopause. The waves are periodic in the horizontal but modulated in the vertical and Boussinesq flow is assumed. The equation governing the incident wave packet is directly coupled to the equat...

Acheson, D. J.: On over-reflexion, J. Fluid Mech., 77, 433–472, 1976.; Ames, W. F.: Numerical methods for partial differential equations, Academic Press, 1977.; Griffiths, S. D., Grimshaw, R. H. J., and Khusnutdinova, K. R.: Modulational instability of two pairs of counter-propagating waves and energy exchancge in a two-component system, Physica D, 214, 1–24, 2006.; Grimshaw, R. and McHugh, J. P.: Steady and unsteady nonlinear internal waves incident on an interface, Q. ...

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Nonlinear Feedback in a Six-dimensional Lorenz Model: Impact of an...

By: B.-w. Shen

Description: Department of Mathematics and Statistics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-7720, USA. In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred...

Curry, J. H.: Generalized Lorenz systems, Commun. Math. Phys., 60, 193–204, 1978.; Anthes, R.: Turning the tables on chaos: is the atmosphere more predictable than we assume?, UCAR Magazine, available at: https://www2.ucar.edu/atmosnews/opinion/turning-tables-chaos-atmosphere-more-predictable-we-assume-0, 2011.; Bender, C. M. and Orszag, S. A.: Advanced Mathem...

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Reconstructing Bottom Water Temperatures from Measurements of Temp...

By: C. Müller; A. Lechleiter; F. Miesner

Description: Zentrum für Technomathematik, University of Bremen, Bremen, Germany. Continuous monitoring of oceanic bottom water temperatures is a complicated task, even in relatively easy-to-access basins like the North or Baltic seas. Here, a method to determine annual bottom water temperature variations from inverse modeling of instantaneous measurements of temperatures and sediment thermal properties is presented. This concept is similar to climate reconstruction...

Chouinard, C., Fortier, R., and Mareschal, J.-C.: Recent climate variations in the Subarctic inferred from three borehole temperature profiles in Northern Quebec, Canada, Earth Planet. Sc. Lett., 263, 355–369, 2007.; Clauser, C.: Geothermal energy, in: Landolt-Börnstein, Group VIII: Advanced Materials and Technologies, vol. 1: Energy Technologies, Subvol. C: Renewable Energies, edited by: Heinloth, K., Springer Verlag, Heidelberg-Berlin, 493–604, 2006.; Davis, E. E., Wan...

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Mechanisms Controlling Primary and New Production in a Global Ecos...

By: B. De Cuevas; A. C. Coward; G. A. Nurser; T. R. Anderson; M. J. R. Fasham; E. E. Popova

Description: National Oceanographic Centre, Southampton, UK. A global general circulation model coupled to a simple six-compartment ecosystem model is used to study the extent to which global variability in primary and export production can be realistically predicted on the basis of advanced parameterizations of upper mixed layer physics, without recourse to introducing extra complexity in model biology. The K profile parameterization (KPP) scheme employed, combined...

Aksenov, Y.: The sea ice-ocean global coupled model, ARCICE Project Report Part 1: Description of the Dynamical-Thermodynamical Sea Ice Model, Southampton Oceanography Centre, Southampton, UK, 2002.; Anderson, T. R. and Pondaven, P.: Non-redfield carbon and nitrogen cycling in the Sargasso Sea: pelagic imbalances and export flux, Deep-Sea Res. I, 50, 573–591, 2003.; Anderson, T. R.: Plankton functional type modelling: running before we can walk?, J. plankton research, 27...

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Development of Black Sea Nowcasting and Forecasting System : Volum...

By: V. L. Dorofeyev; A. I. Kubryakov; G. K. Korotaev; Yu. B. Ratner; T. Oguz; S. G. Demyshev

Description: Marine Hydrophysical Institute National Academy of Sciences, Sevastopol, Ukraine. The paper presents the development of the Black Sea community nowcasting and forecasting system under the Black Sea GOOS initiative and the EU framework projects ARENA, ASCABOS and ECOOP. One of the objectives of the Black Sea Global Ocean Observing System project is a promotion of the nowcasting and forecasting system of the Black Sea, in order to implement the operational...

Agoshkov, V. I., Ipatova, V. M., Zalesny, V. B., Parmuzin, E. I., and Shutyaev V. P.: Problems of variational assimilation of observational data into Ocean general circulation models and methods for their solution, Izvestiya, Atmos. Ocean. Phys., 46, 677–712, 2010.; Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I, J. Comput. Phys., 1, 119–43, 1966.; Blatov, A. S., Bulgakov...

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An Operational Model for the West Iberian Coast: Products and Serv...

By: P. Chambel; L. Fernandes; G. Riflet; M. Juliano; M. Mateus; R. Fernandes; F. Campuzano; R. Neves; H. De Pablo

Description: MARETEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal. This paper presents the structure and application of a regional scale operational modelling tool for the West Iberian coast, and discusses its potential for products and services for both scientific and coastal management activities. The forecasting suite includes nested hydrodynamic models forced with up-to-date meteorological forecast data...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I, Journal of Computational Physics, 1, 119-143, 1966.; Balseiro, C. F., Carracedo, P., Gómez, B., Leitão, P. C., Montero, P., Naranjo, L., Penabad, E., and Pérez-Muñuzuri, V.: Tracking the Prestige oil spill: An operational experience in simulation at MeteoGalicia, Weather, 58, 452-458, 2003.; Beckmann, A., and Haidvogel, D. B...

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High Frequency Fluctuations in the Heat Content of an Ocean Genera...

By: D. J. Webb; A. M. Huerta-casas

Description: National Oceanography Centre, Southampton SO14 3ZH, UK. The transport and storage of heat by the ocean is of crucial importance because of its effect on ocean dynamics and its impact on the atmosphere, climate and climate change. Unfortunately, limits to the amount of data that can be collected and stored mean that many experimental and modelling studies of the heat budget have to make use of mean datasets where the effects of short term fluctuations ar...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two dimensional incompressible flow, Part I, J. Comput. Phys., 1, 119–143, 1966.; Bonjean, F. and Lagerloef, G.: Diagnostic Model and Analysis of the Surface Currents in the Tropical Pacific Ocean, J. Phys. Oceanogr., 32, 2938–2954, 2002.; Bryan, K.: A numerical method for the study of the circulation of the world ocean, J. Comput. Phys., 4, 347–376, 1969.; Bryden, H. ...

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The Effect of Various Vertical Discretization Schemes and Horizont...

By: D. Storkey; J. Pickering; M. Luneva; G. Shapiro

Description: University of Plymouth, School of Marine Science and Engineering, Drake Circus, Plymouth, PL4 8AA, UK. Results of a sensitivity study are presented from various configurations of the NEMO ocean model in the Black Sea. The standard choices of vertical discretization, viz. z levels, s coordinates and enveloped s coordinates, all show their limitations in the areas of complex topography. Two new hybrid vertical coordinate schemes are pr...

Becker, E. and Burkhard, U.: Nonlinear Horizontal Diffusion for GCMs Monthly Weather Review, 135, 1439–1454, 2007.; Berntsen, J., Xing, J., and Davies, A. M.: Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size, Ocean Dynam., 59, 6, 1043–1059, 2010.; Besiktepe, S. T., Ünlüata, Ü., and Bologa, A. S. E.: Environmental Degradation of the Black Sea: Challenges and Remedies. Proceedings of the NATO Advanced Research Workshop, Con...

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On the Shelf Resonances of the English Channel and Irish Sea : Vol...

By: D. J. Webb

Description: National Oceanography Centre, Southampton SO14 3ZH, UK. The resonances of the English Channel and Irish Sea are investigated using the methods of Webb (2012a) together with an Arakawa C-grid model of the region under study. In the semi-diurnal tidal band, the high tides of the Bristol Channel and Gulf of St. Malo are shown to be due to two shelf resonances which strongly couple the two regions. In the diurnal band, the response is complicated by the pre...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, J. Computat. Phys., 1, 119–143, 1966.; Arakawa, A. and Lamb, V. R.: A Potential Enstrophy and Energy Conserving Scheme for the Shallow Water Equations, Monthly Weather Rev., 109, 19–36, 1981.; Arbic, B. K., St-Laurent, P., Sutherland, G., and Garrett, C.: On the resonance and influence of the tides in Ungava Bay and Hudson Strait, G...

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On the Shelf Resonances of the English Channel and Irish Sea : Vol...

By: D. J. Webb

Description: National Oceanography Centre, Southampton SO14 3ZH, UK. The resonances of the English Channel and Irish Sea are investigated using the methods of Webb (2012) together with an Arakawa C-grid model of the region under study. In the semi-diurnal tidal band, the high tides of the Bristol Channel and Gulf of St. Malo are shown to be due to two shelf resonances which strongly couple the two regions. In the diurnal band, the response is complica...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow, J. Comput. Phys., 1, 119–143, 1966.; Arbic, B. K., St-Laurent, P., Sutherland, G., and Garrett, C.: On the resonance and influence of the tides in Ungava Bay and Hudson Strait, Geophys. Res. Lett, 34, L17606, doi:10.1029/2007GL030845, 2007.; Arbic, B. K., Karsten, R. H., and Garrett, C.: On tidal resonance in the global ocean and th...

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Reconstructing Bottom Water Temperatures from Measurements of Temp...

By: C. Müller; F. Miesner; A. Lechleiter

Description: Zentrum für Technomathematik, University of Bremen, Bremen, Germany. Temperature fields in marine sediments are studied for various purposes. Often, the target of research is the steady state heat flow as a (possible) source of energy but there are also studies attempting to reconstruct bottom water temperature variations to understand more about climate history. The bottom water temperature propagates into the sediment to different depths, dependi...

Clauser, C.: Geothermal energy, in: Landolt-Börnstein, Group VIII: Advanced Materials and Technologies, vol. 1: Energy Technologies, Subvol. C: Renewable Energies, edited by: Heinloth, K., Springer Verlag, Heidelberg-Berlin, 493–604, 2006.; Davis, E. E., Wang, K., Becker, K., and Yashayaev, I.: Deep-ocean temperature variations and implications for errors in sea floor heat flow determinations, J. Geophys. Res., 108, 2034, do...

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On the Indonesian Throughflow in the Occam 1/4 Degree Ocean Model ...

By: D. J. Webb; U. W. Humphries

Description: King Monghut's Institute of Technology, Thailand. The Indonesian Throughflow is analysed in two runs of the OCCAM 1/4 degree global ocean model, one using monthly climatological winds and one using ECMWF analysed six-hourly winds for the period 1993 to 1998. The long-term model throughflow agrees with observations and the value predicted by Godfrey's Island Rule. The Island Rule has some skill in predicting the annual signal each year but is poor at pre...

Molcard, R., Ilahude, A. G., Fieux, M., Swallow, J. C., and Banjarnahor, J.: Low frequency variability of the currents in Indonesian Channels (Savu-Roti M1 and Roti-Ashmore Reef M2), Deep Sea Res., 41, 1643–1662, 1994.; Murray, S. P. and Arief, D.: Throughflow into the Indian Ocean through the Lombok Strait, January 1985–January 1986. Nature 333, 444–447, 1988.; Murray, S. P., Arief, D., Kindle, J. C., and Hurlburt, H. E.: Characteristics of circulation in an Indonesian ...

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On the Time to Tracer Equilibrium in the Global Ocean : Volume 5, ...

By: E. Deleersnijder; F. Primeau

Description: Department of Earth System Science, University of California at Irvine, Rowland Hall, Irvine, CA 92697, USA. An important issue for the interpretation of data from deep-sea cores is the time for tracers to be transported from the sea surface to the deep ocean. Global ocean circulation models can help shed light on the timescales over which a tracer comes to equilibrium in different regions of the ocean. In this note, we discuss how the most slowly ...

Delhez, E. J. M., Campin, J.-M., Hirst, A. C., and Deleersnijder, E.: Toward a general theory of the age in ocean modelling, Ocean Model., 1, 17–27, 1999.; Campin, J.-M., Fichefet, T., and Duplessy, J.-C.: Problems with using radiocarbon to infer ocean ventilation rates for past and present climates, Earth Planet. Sci. Lett., 165, 17–24, 1999.; Deleersnijder, E., Mouchet, A., Delhez, E. J. M., and Beckers, J.-M.: Transient behaviour of water ages in the World Ocean, Math...

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Development of Black Sea Nowcasting and Forecasting System : Volum...

By: Y. B. Ratner; A. I. Kubryakov; G. K. Korotaev; V. L. Dorofeyev; T. Oguz; S. G. Demyshev

Description: Marine Hydrophysical Institute, National Academy of Sciences, Sevastopol, Ukraine. The paper presents the development of the Black Sea community nowcasting and forecasting system under the Black Sea GOOS initiative and the EU framework projects ARENA, ASCABOS and ECOOP. One of the objectives of the Black Sea Global Ocean Observing System project is a promotion of the nowcasting and forecasting system of the Black Sea, in order to implement the operationa...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I, J. Comput. Phys., 1, 119–43, 1966.; Demyshev, S. G. and Korotaev, G. K.: Numerical energy-balanced model of baroclinic currents in the ocean with bottom topography on the C-grid, in: Numerical models and results of intercalibration simulations in the Atlantic ocean, Moscow, 163–231, 1992 (in Russian).; Demyshev, S. G., Dovga...

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An Operational Model for the West Iberian Coast: Products and Serv...

By: G. Riflet; L. Fernandes; P. Chambel; M. Juliano; R. Neves; F. Campuzano; R. Fernandes; M. Mateus; H. De Pablo

Description: MARETEC, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal. The paper presents the structure and application of a regional scale operational modelling tool for the West Iberian coast. The forecasting suite includes nested hydrodynamic models forced with up-to-date meteorological forecast data and large scale model results as lateral boundary conditions. The present status of the system and its rece...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I, J. Comput. Phys., 1, 119–143, 1966.; Balseiro, C. F., Carracedo, P., Gómez, B., Leitão, P. C., Montero, P., Naranjo, L., Penabad, E., and Pérez-Muñuzuri, V.: Tracking the Prestige oil spill: an operational experience in simulation at MeteoGalicia, Weather, 58, 452–458, 2003.; Bell, M. J., Lefèbvre, M., Le Traon, P.-Y., Smith...

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High Frequency Fluctuations in the Heat Content of an Ocean Genera...

By: D. J. Webb; A. M. Huerta-casas

Description: National Oceanography Centre, Southampton SO14 3ZH, UK. The transport and storage of heat by the ocean is of crucial importance because of its effect on ocean dynamics and its impact on the atmosphere, climate and climate change. Unfortunately, limits to the amount of data that can be collected and stored means that many experimental and modelling studies of the heat budget have to make use of mean datasets where the effects of short ...

Arakawa, A.: Computational design for long-term numerical integration of the equations of fluid motion: two dimensional incompressible flow. Part I, J. Comput. Phys., 1, 119–143, 1966.; Bryan, K.: A numerical method for the study of the circulation of the world ocean, J. Comput. Phys., 4, 347–376, 1969.; Bryden, H. and Brady, E.: Eddy momentum and heat fluxes and their effects on the circulation of the equatorial Pacific-Ocean, J. Mar. Res., 47, 55–79, 1989.; Cox, M. D.:...

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