35 tangent and arc length in polar coordinatesmath266
The document discusses parametric representations of polar curves. It begins by explaining that a rectangular curve given by y=f(x) can be parametrized as x=t and y=f(t). It then explains that a polar curve given by r=f(θ) can be parametrized as x=f(θ)cos(θ) and y=f(θ)sin(θ). Examples are given of parametrizing the Archimedean spiral r=θ and the cardioid r=1+sin(θ). Formulas are derived for calculating the slope of the tangent line to a polar curve at a given point in terms of r and θ. Examples are worked out for finding the slope
El documento presenta la solución a tres ejercicios sobre fuerzas eléctricas ejercidas por distribuciones de carga. El primer ejercicio encuentra la fuerza total sobre una carga puntual debido a dos cargas puntuales. El segundo calcula la fuerza total sobre una carga puntual proveniente de cuatro cargas iguales en los vértices de un cuadrado. El tercero determina la fuerza sobre una carga en el origen ejercida por ocho cargas en los vértices de un cubo.
Este documento explica la regla de la cadena, que permite derivar funciones compuestas. Presenta la fórmula general de la regla de la cadena y varios ejemplos de su aplicación para derivar funciones que involucran potencias, funciones trigonométricas y funciones implícitas. También cubre cómo usar la regla de la cadena para derivar expresiones que involucran ritmos o velocidades relacionadas.
The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and
The document discusses solving equations that are reducible to quadratic equations. It explains that a quadratic equation is an equation with a maximum power of the variable being squared. There are three methods for solving quadratic equations: factorization, completing the square, and the quadratic formula. Examples are provided of using factorization and completing the square methods to solve equations reducible to quadratic form. The document also covers forming quadratic equations from word problems and solving them.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
The document discusses line integrals in the complex plane. It defines line integrals, shows how complex line integrals are equivalent to two real line integrals, and reviews how to parameterize curves to evaluate line integrals. It also covers Cauchy's theorem, which states that the line integral of an analytic function around a closed curve in its domain is zero. The fundamental theorem of calculus for complex variables and the Cauchy integral formula are also summarized.
Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...jani parth
1) The document discusses ordinary differential equations that model free oscillations of a spring-mass system and electric circuits.
2) It derives the differential equation for simple harmonic motion of a mass attached to a spring as well as cases with damping.
3) Kirchhoff's voltage law is used to derive differential equations for simple R-L and R-C circuits driven by external voltages.
4) As an example, the differential equation for a series R-C circuit is solved analytically to find expressions for charge and current over time.
35 tangent and arc length in polar coordinatesmath266
The document discusses parametric representations of polar curves. It begins by explaining that a rectangular curve given by y=f(x) can be parametrized as x=t and y=f(t). It then explains that a polar curve given by r=f(θ) can be parametrized as x=f(θ)cos(θ) and y=f(θ)sin(θ). Examples are given of parametrizing the Archimedean spiral r=θ and the cardioid r=1+sin(θ). Formulas are derived for calculating the slope of the tangent line to a polar curve at a given point in terms of r and θ. Examples are worked out for finding the slope
El documento presenta la solución a tres ejercicios sobre fuerzas eléctricas ejercidas por distribuciones de carga. El primer ejercicio encuentra la fuerza total sobre una carga puntual debido a dos cargas puntuales. El segundo calcula la fuerza total sobre una carga puntual proveniente de cuatro cargas iguales en los vértices de un cuadrado. El tercero determina la fuerza sobre una carga en el origen ejercida por ocho cargas en los vértices de un cubo.
Este documento explica la regla de la cadena, que permite derivar funciones compuestas. Presenta la fórmula general de la regla de la cadena y varios ejemplos de su aplicación para derivar funciones que involucran potencias, funciones trigonométricas y funciones implícitas. También cubre cómo usar la regla de la cadena para derivar expresiones que involucran ritmos o velocidades relacionadas.
The document defines a homogeneous linear differential equation as an equation of the form:
a0(dx/dy)n + a1(dx/dy)n-1 + ... + an-1(dx/dy) + any = X, where a0, a1, ..., an are constants and X is a function of x.
It provides the method of solving such equations by first reducing it to a linear equation with constant coefficients, then taking a trial solution of the form y = emz, and finally solving the resulting auxiliary equation.
It proves identities relating derivatives of y with respect to x and z, then uses these identities to solve two sample homogeneous linear differential equations of orders 2 and
The document discusses solving equations that are reducible to quadratic equations. It explains that a quadratic equation is an equation with a maximum power of the variable being squared. There are three methods for solving quadratic equations: factorization, completing the square, and the quadratic formula. Examples are provided of using factorization and completing the square methods to solve equations reducible to quadratic form. The document also covers forming quadratic equations from word problems and solving them.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
The document discusses line integrals in the complex plane. It defines line integrals, shows how complex line integrals are equivalent to two real line integrals, and reviews how to parameterize curves to evaluate line integrals. It also covers Cauchy's theorem, which states that the line integral of an analytic function around a closed curve in its domain is zero. The fundamental theorem of calculus for complex variables and the Cauchy integral formula are also summarized.
Ordinary Differential Equations And Their Application: Modeling: Free Oscilla...jani parth
1) The document discusses ordinary differential equations that model free oscillations of a spring-mass system and electric circuits.
2) It derives the differential equation for simple harmonic motion of a mass attached to a spring as well as cases with damping.
3) Kirchhoff's voltage law is used to derive differential equations for simple R-L and R-C circuits driven by external voltages.
4) As an example, the differential equation for a series R-C circuit is solved analytically to find expressions for charge and current over time.
The document discusses continuity of functions and graphs. It defines a continuous function as one where the graph is unbroken within its domain. A function is discontinuous if its graph is broken. Continuity at a point x=a can be determined by comparing the left and right limits of the function at a to the actual value of the function at a. If the limits are equal to the function value, it is continuous from that side. The document provides examples of functions that are right continuous, left continuous, or discontinuous at various points to illustrate these concepts.
Limits are a mathematical concept used to determine the behavior of a function as the input values get closer to a certain value. They allow analysis of what happens to a function as it approaches a particular value of the variable. Weierstrass formally introduced the concept of limits in the early 19th century by defining the limit notation, although others like Newton and Leibniz had earlier conceived of limiting processes. Examples show how to calculate specific limits, and when the limit results in an indeterminate form of 0/0, derivatives can be used to determine the limit through simplification and applying limit rules.
This document provides formulas for integrals of common functions. It includes integrals involving roots, rational functions, exponentials, logarithms, trigonometric functions, hyperbolic functions, and combinations of these functions with exponents. Some example integrals listed are the integral of x from 1 to n, the integral of secant cubed x, and the integral of sine of ax times cosine of bx. Over 30 integrals are listed in the document.
This document discusses exponential functions and equations. It explores the properties of exponential functions by examining their graphs and understanding exponential growth and decay. It also covers how to solve problems leading to exponential equations by learning about bases, exponents, powers, and index rules. The document teaches how to evaluate, write in different bases, identify exponential equations, and solve exponential equations. It includes exercises to solve from the attached document on exponential equations and functions.
This project was created by four students - Ananya Gupta, Priya Srivastava, Manisha Negi, and Muskan Sharma from Class IX C at KV OFD Raipur in Dehradun, Uttarakhand. The project discusses linear equations and systems of linear equations, explaining concepts such as slope, y-intercept, dependent and independent equations, and methods for solving systems of linear equations graphically, by substitution, and by elimination.
This document discusses functions, limits, and continuity. It begins by defining functions, domains, ranges, and some standard real functions like constant, identity, modulus, and greatest integer functions. It then covers limits of functions including one-sided limits and properties of limits. Examples are provided to illustrate evaluating limits using substitution and factorization methods. The overall objectives are to understand functions, domains, ranges, limits of functions and methods to evaluate limits.
1) El documento presenta los conceptos básicos de las estructuras algebraicas, incluyendo semi-grupos, grupos y anillos.
2) Se analizan tres ejemplos de conjuntos (G1, G2 y G3) para verificar si cumplen las propiedades de grupo. G1 y G3 cumplen las propiedades y son grupos, mientras que G2 no tiene elemento neutro y no es grupo.
3) También se verifica que el conjunto A, formado por números reales de la forma a + b√2, es un anillo conmutativo y
1) El documento presenta problemas de mecánica clásica extraídos de un libro de texto.
2) El problema 5 trata sobre dos rines montados en extremos de un eje común que ruedan independientemente sobre una superficie. Se demuestra que hay dos ecuaciones de restricción no holonómicas y una ecuación de restricción holonómica.
3) El problema 6 trata sobre una partícula que se mueve en el plano xy bajo la restricción de que su velocidad apunte siempre hacia un punto en el eje x cu
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Simple harmonic motion (SHM) describes the motion of an object undergoing displacement from an equilibrium position due to a restoring force proportional to the displacement. The motion is periodic and sinusoidal, with the displacement following the equation x=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase. Examples of SHM include a mass attached to a spring and the pendular motion of a mass hanging from a fixed point by a string.
The document discusses different methods for calculating the volume of a solid of revolution: disk method, washer method, and shell method. It provides examples of applying each method to find the volume generated when an area bounded by curves is revolved around an axis. The disk method calculates volume by summing the volumes of thin circular disks. The washer method accounts for holes by subtracting the inner circular area from the outer. The shell method imagines the solid as nested cylindrical shells and sums their individual volumes.
Polar coordinates provide an alternative way to specify the location of a point P in a plane using two numbers: r, the distance from P to the origin O, and θ, the angle between the x-axis and a line from O to P. θ is measured counter-clockwise from the x-axis and can be either positive or negative. A point P's polar coordinates (r, θ) uniquely identify its location. Polar and rectangular coordinates can be converted between each using the relationships x=r*cos(θ), y=r*sin(θ), and r=√(x2+y2).
This document defines rational expressions as expressions that can be written in the form P/Q, where P and Q are polynomials and Q ≠ 0. It provides examples of rational expressions and explains the steps to simplify rational expressions: 1) factor the numerator and denominator, 2) divide out common factors, and 3) write the expression in simplified form. Three examples demonstrating these steps are included.
1) Se describen las ecuaciones de Poisson y Laplace, obtenidas a partir de la ley de Gauss, la definición de flujo eléctrico y la relación del gradiente.
2) Se presentan las ecuaciones en coordenadas cartesianas, cilíndricas y esféricas.
3) Se plantean tres problemas para calcular valores numéricos de V y ρv en diferentes puntos.
The document discusses calculating the area swept out by a polar function r=f(θ) between two angles θ=A and θ=B. It introduces the integral formula for finding this area, which is ∫f(θ)2dθ from A to B. It then provides examples of using this formula to calculate the areas of different polar curves, such as a circle, a cardioid, and a curve tracing a circle twice.
The document discusses integration by parts, which is a technique for finding antiderivatives of products. It involves rewriting the integral as the product of two functions minus the integral of their derivatives multiplied. Several examples are provided to demonstrate how to apply the technique by matching the integrand to the form "udv", taking the derivative of u and antiderivative of dv, and rewriting the integral accordingly.
The document discusses Fourier series and their applications. It provides the general forms of the Fourier series for even and odd functions over a periodic interval. The key points are:
- Fourier series can be used to represent functions as an infinite sum of sines and cosines, known as harmonic analysis.
- They have wide applications in fields like signal processing, vibrations, and heat transfer.
- The Fourier series for an even function contains only cosine terms, while an odd function contains only sine terms.
- The Fourier coefficients are found using the orthogonal properties of sines and cosines and integrating the function over the period.
This document discusses functional training in sports. It provides a history of functional training dating back to the 1950s and its use for injury treatment in soldiers and later for fitness and sports training. It defines key terms like core, proprioception, biomotor capabilities. It describes exercises like closed kinetic chain, multi-joint, multi-planar exercises and different planes and directions. It discusses proprioception and the role of the core region and different muscles. It also outlines different tests and how functional training has been applied to improve performance in sports like soccer, basketball, golf, taekwondo and prevent injuries.
In each class we focus on a particular peak posture such as Super Splits, Dancer Pose (Scorpion) or Middle Splits. We will go through exercises and apply techniques designed to release muscular and fascial tension in the muscles that oppose the peak posture.
The document discusses continuity of functions and graphs. It defines a continuous function as one where the graph is unbroken within its domain. A function is discontinuous if its graph is broken. Continuity at a point x=a can be determined by comparing the left and right limits of the function at a to the actual value of the function at a. If the limits are equal to the function value, it is continuous from that side. The document provides examples of functions that are right continuous, left continuous, or discontinuous at various points to illustrate these concepts.
Limits are a mathematical concept used to determine the behavior of a function as the input values get closer to a certain value. They allow analysis of what happens to a function as it approaches a particular value of the variable. Weierstrass formally introduced the concept of limits in the early 19th century by defining the limit notation, although others like Newton and Leibniz had earlier conceived of limiting processes. Examples show how to calculate specific limits, and when the limit results in an indeterminate form of 0/0, derivatives can be used to determine the limit through simplification and applying limit rules.
This document provides formulas for integrals of common functions. It includes integrals involving roots, rational functions, exponentials, logarithms, trigonometric functions, hyperbolic functions, and combinations of these functions with exponents. Some example integrals listed are the integral of x from 1 to n, the integral of secant cubed x, and the integral of sine of ax times cosine of bx. Over 30 integrals are listed in the document.
This document discusses exponential functions and equations. It explores the properties of exponential functions by examining their graphs and understanding exponential growth and decay. It also covers how to solve problems leading to exponential equations by learning about bases, exponents, powers, and index rules. The document teaches how to evaluate, write in different bases, identify exponential equations, and solve exponential equations. It includes exercises to solve from the attached document on exponential equations and functions.
This project was created by four students - Ananya Gupta, Priya Srivastava, Manisha Negi, and Muskan Sharma from Class IX C at KV OFD Raipur in Dehradun, Uttarakhand. The project discusses linear equations and systems of linear equations, explaining concepts such as slope, y-intercept, dependent and independent equations, and methods for solving systems of linear equations graphically, by substitution, and by elimination.
This document discusses functions, limits, and continuity. It begins by defining functions, domains, ranges, and some standard real functions like constant, identity, modulus, and greatest integer functions. It then covers limits of functions including one-sided limits and properties of limits. Examples are provided to illustrate evaluating limits using substitution and factorization methods. The overall objectives are to understand functions, domains, ranges, limits of functions and methods to evaluate limits.
1) El documento presenta los conceptos básicos de las estructuras algebraicas, incluyendo semi-grupos, grupos y anillos.
2) Se analizan tres ejemplos de conjuntos (G1, G2 y G3) para verificar si cumplen las propiedades de grupo. G1 y G3 cumplen las propiedades y son grupos, mientras que G2 no tiene elemento neutro y no es grupo.
3) También se verifica que el conjunto A, formado por números reales de la forma a + b√2, es un anillo conmutativo y
1) El documento presenta problemas de mecánica clásica extraídos de un libro de texto.
2) El problema 5 trata sobre dos rines montados en extremos de un eje común que ruedan independientemente sobre una superficie. Se demuestra que hay dos ecuaciones de restricción no holonómicas y una ecuación de restricción holonómica.
3) El problema 6 trata sobre una partícula que se mueve en el plano xy bajo la restricción de que su velocidad apunte siempre hacia un punto en el eje x cu
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Simple harmonic motion (SHM) describes the motion of an object undergoing displacement from an equilibrium position due to a restoring force proportional to the displacement. The motion is periodic and sinusoidal, with the displacement following the equation x=A sin(ωt+φ), where A is the amplitude, ω is the angular frequency, t is time, and φ is the phase. Examples of SHM include a mass attached to a spring and the pendular motion of a mass hanging from a fixed point by a string.
The document discusses different methods for calculating the volume of a solid of revolution: disk method, washer method, and shell method. It provides examples of applying each method to find the volume generated when an area bounded by curves is revolved around an axis. The disk method calculates volume by summing the volumes of thin circular disks. The washer method accounts for holes by subtracting the inner circular area from the outer. The shell method imagines the solid as nested cylindrical shells and sums their individual volumes.
Polar coordinates provide an alternative way to specify the location of a point P in a plane using two numbers: r, the distance from P to the origin O, and θ, the angle between the x-axis and a line from O to P. θ is measured counter-clockwise from the x-axis and can be either positive or negative. A point P's polar coordinates (r, θ) uniquely identify its location. Polar and rectangular coordinates can be converted between each using the relationships x=r*cos(θ), y=r*sin(θ), and r=√(x2+y2).
This document defines rational expressions as expressions that can be written in the form P/Q, where P and Q are polynomials and Q ≠ 0. It provides examples of rational expressions and explains the steps to simplify rational expressions: 1) factor the numerator and denominator, 2) divide out common factors, and 3) write the expression in simplified form. Three examples demonstrating these steps are included.
1) Se describen las ecuaciones de Poisson y Laplace, obtenidas a partir de la ley de Gauss, la definición de flujo eléctrico y la relación del gradiente.
2) Se presentan las ecuaciones en coordenadas cartesianas, cilíndricas y esféricas.
3) Se plantean tres problemas para calcular valores numéricos de V y ρv en diferentes puntos.
The document discusses calculating the area swept out by a polar function r=f(θ) between two angles θ=A and θ=B. It introduces the integral formula for finding this area, which is ∫f(θ)2dθ from A to B. It then provides examples of using this formula to calculate the areas of different polar curves, such as a circle, a cardioid, and a curve tracing a circle twice.
The document discusses integration by parts, which is a technique for finding antiderivatives of products. It involves rewriting the integral as the product of two functions minus the integral of their derivatives multiplied. Several examples are provided to demonstrate how to apply the technique by matching the integrand to the form "udv", taking the derivative of u and antiderivative of dv, and rewriting the integral accordingly.
The document discusses Fourier series and their applications. It provides the general forms of the Fourier series for even and odd functions over a periodic interval. The key points are:
- Fourier series can be used to represent functions as an infinite sum of sines and cosines, known as harmonic analysis.
- They have wide applications in fields like signal processing, vibrations, and heat transfer.
- The Fourier series for an even function contains only cosine terms, while an odd function contains only sine terms.
- The Fourier coefficients are found using the orthogonal properties of sines and cosines and integrating the function over the period.
This document discusses functional training in sports. It provides a history of functional training dating back to the 1950s and its use for injury treatment in soldiers and later for fitness and sports training. It defines key terms like core, proprioception, biomotor capabilities. It describes exercises like closed kinetic chain, multi-joint, multi-planar exercises and different planes and directions. It discusses proprioception and the role of the core region and different muscles. It also outlines different tests and how functional training has been applied to improve performance in sports like soccer, basketball, golf, taekwondo and prevent injuries.
In each class we focus on a particular peak posture such as Super Splits, Dancer Pose (Scorpion) or Middle Splits. We will go through exercises and apply techniques designed to release muscular and fascial tension in the muscles that oppose the peak posture.
This course consists of 15 contact hours. That time will be spent diving into the anatomy of the spine, hips and shoulder girdle. Breaking down movement to gain an understanding of what is really happening in the body. And how joint position and the surrounding musculature and fascia either moves you forward or holds you back.
The document contains repeated instances of the word "Instructions" with no other content. It appears to be providing instructions but contains no actual instructions or informative text.
This course focuses on flexibility training for athletes through yoga. It covers anatomy, stretching techniques, and five signature flexibility plans. Students will learn how to safely move into peak postures and teach these to others. Topics include the nervous system, various stretches, and anatomy of the spine, hips, and shoulders. Upon completion, students receive flexibility plans, straps, and 15 contact hours for a cost of $649.
Our mUvmethod Flexibility Training is intended for those already working in the field of yoga, pilates, dance, fitness and/or movement. It is for trained professionals looking to add flexibility plans to their programs and classes.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
ESA/ACT Science Coffee: Diego Blas - Gravitational wave detection with orbita...Advanced-Concepts-Team
Presentation in the Science Coffee of the Advanced Concepts Team of the European Space Agency on the 07.06.2024.
Speaker: Diego Blas (IFAE/ICREA)
Title: Gravitational wave detection with orbital motion of Moon and artificial
Abstract:
In this talk I will describe some recent ideas to find gravitational waves from supermassive black holes or of primordial origin by studying their secular effect on the orbital motion of the Moon or satellites that are laser ranged.
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
When I was asked to give a companion lecture in support of ‘The Philosophy of Science’ (https://shorturl.at/4pUXz) I decided not to walk through the detail of the many methodologies in order of use. Instead, I chose to employ a long standing, and ongoing, scientific development as an exemplar. And so, I chose the ever evolving story of Thermodynamics as a scientific investigation at its best.
Conducted over a period of >200 years, Thermodynamics R&D, and application, benefitted from the highest levels of professionalism, collaboration, and technical thoroughness. New layers of application, methodology, and practice were made possible by the progressive advance of technology. In turn, this has seen measurement and modelling accuracy continually improved at a micro and macro level.
Perhaps most importantly, Thermodynamics rapidly became a primary tool in the advance of applied science/engineering/technology, spanning micro-tech, to aerospace and cosmology. I can think of no better a story to illustrate the breadth of scientific methodologies and applications at their best.
The cost of acquiring information by natural selectionCarl Bergstrom
This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.
It's based on the first part of this research paper:
The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
Mending Clothing to Support Sustainable Fashion_CIMaR 2024.pdfSelcen Ozturkcan
Ozturkcan, S., Berndt, A., & Angelakis, A. (2024). Mending clothing to support sustainable fashion. Presented at the 31st Annual Conference by the Consortium for International Marketing Research (CIMaR), 10-13 Jun 2024, University of Gävle, Sweden.