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Plot the following functions with energy at different temperatures. a) Maxwell-Boltzmann distribution b) Fermi-Dirac distribution c) Bose-Einstein distribution , . - Scilab Solution

a) Maxwell-Boltzmann distribution b) Fermi-Dirac distribution  c) Bose-Einstein distribution a) Maxwell-Boltzmann distribution // Define the constants and energy range mu = 0.0; tempE1 = 0.1; tempE2 = 0.5; eps = [0.01:0.01:2]'; // Calculate the distribution functions feps1 = exp(-(eps-mu)/tempE1); feps2 = exp(-(eps-mu)/tempE2); // Plot the distribution functions clf(); plot2d(eps, feps1, style = 2); plot2d(eps, feps2, style = 3); xgrid(); xlabel("$\epsilon$", "fontsize", 5, "color", black); ylabel("$f(\epsilon)$", "fontsize", 5); title("Maxwell-Boltzmann distribution at different temperatures"); // Display a legend for the two curves legend(["T = " + string(tempE1), "T = " + string(tempE2)], location = "northwest"); b) Fermi-Dirac distribution  // Define the constants and energy range mu = 2.0; tempE1 = 0.1; tempE2 = 0.5; eps = [0.01:0.01:6]'; // Calculate the distribution functions feps1 ...
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Plot Planck’s law for Black Body radiation and compare it with Raleigh-Jeans Law at high temperature and low temperature -Scilab

experiment - 3 // Define frequency ranges and constants omega = [0.1:0.1:10]; omegar = [0.1:0.1:2]; A = 1.0; B = 1.0; Temp = 1.0; // Calculate energy density using Planck's law and Raleigh-Jeans law enr = A * omega.^3 ./ (exp(B*omega/Temp) - 1); rj = A * omegar.^2; // Plot the two functions clf(); plot2d(omega, enr, style = 1); plot2d(omegar, rj, style = 4); xgrid(); xlabel("$\omega$", "fontsize", 5, "color", black); ylabel("$u(\omega, T)$", "fontsize", 5);

Systems Biology

Systems Biology: Systems Biology is an approach in biology that looks at living organisms as a whole, interconnected system, rather than focusing on individual parts in isolation. It tries to understand how different components of a biological system, such as genes, proteins, and cells, work together to create complex behaviors and functions. Key Concepts: Interconnectedness: In systems biology, we study how various components of an organism interact and communicate with each other. It's like understanding how different parts of a machine work together to make it function. Emergent Properties: Systems biology explores how the combination of individual components can give rise to new and unexpected behaviors or functions. These are called "emergent properties." It's like how a group of musicians playing different instruments can create a beautiful symphony together. Data and Models: Scientists in systems biology collect a lot of data from various biological processes....

Living Systems as Complex Organizations

  Living Systems as Complex Organizations: Living systems, like plants, animals, and humans, are incredibly complex and organized structures. They are made up of many different parts, each with its own function, and they all work together to make the organism function properly. Let's break down this concept into simpler terms: Living Systems: Living systems refer to all the living things around us, from tiny microorganisms to large animals and plants. These living organisms are made up of cells, which are like the building blocks of life. Complex Organizations: A "complex organization" means that living things are structured in a way that involves many parts working together. It's like a well-organized team where every member has a specific role, and together they achieve a common goal. Parts and Functions: In living systems, there are many different parts, such as organs and tissues, each with its own unique function. For example, in a human body, the heart pumps ...

Understanding the Stoichiometric Matrix: A Key Concept in Biological Physics at the Cellular Level

Introduction: In the fascinating world of biological physics, understanding the inner workings of cells is crucial. One important concept that helps us unravel the mysteries of cellular processes is the stoichiometric matrix. In this blog post, we will explore what the stoichiometric matrix is and how it plays a vital role in studying cellular dynamics. Section 1: What is the Stoichiometric Matrix? At its core, the stoichiometric matrix is a mathematical representation that describes the relationships between different chemical species within a biological system. It provides a quantitative understanding of how molecules interact with one another during cellular processes. Imagine a recipe for baking a cake. The stoichiometric matrix would be like a list of ingredients and their respective quantities. It shows us how much of each ingredient is needed to achieve the desired outcome—a delicious cake! Section 2: Unveiling the Components of the Stoichiometric Matrix The stoichiometric matri...

The Stoichiometric Matrix in easy language

The Stoichiometric Matrix: In biological physics, the stoichiometric matrix is a tool used to describe the chemical reactions that happen within living organisms, like cells or metabolic pathways. It helps us understand how different molecules interact and change during these reactions. Breaking it Down: Chemical Reactions: Think of chemical reactions as processes where molecules come together and change into different molecules. For example, in our bodies, food is broken down into smaller molecules, and these molecules react with oxygen to release energy. Stoichiometry: Stoichiometry is just a fancy word that means understanding the quantities of different molecules involved in a chemical reaction. It's like knowing how much of each ingredient you need to make a recipe. Matrix: A matrix is a grid or table where we organize information. Instead of using a recipe, we use a matrix to represent chemical reactions. Putting it Together - Stoichiometric Matrix: The stoichiometric matrix ...

Complex networks of molecular interactions: metabolic, regulatory and signaling networks

Imagine biological systems, like cells and organisms, as cities with many roads and pathways connecting different places. These networks of roads and pathways represent how molecules inside living organisms interact and communicate with each other. There are three types of networks we'll explore: Metabolic Networks: Think of metabolic networks as the pathways that handle energy and building blocks inside a living organism. Just like how roads transport people and goods between different places, metabolic networks transport molecules and chemicals to where they are needed in the cell. These networks help convert food into energy and create the materials the cell needs to survive and grow. Regulatory Networks: Imagine regulatory networks as traffic control systems in a city. These networks control and coordinate the activities inside the cell. They ensure that the right genes are turned on or off at the right times, allowing cells to respond to changes in their environment and perf...