Pressure-volume Curves
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Pressure-volume Curves
In ecology, pressure-volume curves describe the relationship between total water potential (Ψt) and relative water content (R) of living organisms. These values are widely used in research on plant-water relations, and provide valuable information on the turgor, osmosis, osmotic and Elastic deformation, elastic properties of plant tissues. According to the Boyle–v'ant Hoff Relation, the product of osmotic potential and volume of solution should be a constant for any given amount of osmotically active solutes in an ideal osmotic system. \psi_0\mathit(V)\! = A constant \psi_0\! is osmotic potential and \mathit(V)\! is volume of solution. This can then be manipulated to a linear relation which describes the ideal situation: \psi_0\! = \dfrac{1}V\! \times A constant (mathematics), constant Membrane biology ...
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Ecology
Ecology () is the study of the relationships between living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere level. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history. Ecology is a branch of biology, and it is not synonymous with environmentalism. Among other things, ecology is the study of: * The abundance, biomass, and distribution of organisms in the context of the environment * Life processes, antifragility, interactions, and adaptations * The movement of materials and energy through living communities * The successional development of ecosystems * Cooperation, competition, and predation within and between species * Patterns of biodiversity and its effect on ecosystem processes Ecology has practical applications in conservation biology, wetland management, natural resource managemen ...
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Water Potential
Water potential is the potential energy of water per unit volume relative to pure water in reference conditions. Water potential quantifies the tendency of water to move from one area to another due to osmosis, gravity, mechanical pressure and matrix effects such as capillary action (which is caused by surface tension). The concept of water potential has proved useful in understanding and computing water movement within plants, animals, and soil. Water potential is typically expressed in potential energy per unit volume and very often is represented by the Greek letter ψ. Water potential integrates a variety of different potential drivers of water movement, which may operate in the same or different directions. Within complex biological systems, many potential factors may be operating simultaneously. For example, the addition of solutes lowers the potential (negative vector), while an increase in pressure increases the potential (positive vector). If the flow is not restricte ...
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Water Content
Water content or moisture content is the quantity of water contained in a material, such as soil (called soil moisture), rock, ceramics, crops, or wood. Water content is used in a wide range of scientific and technical areas, and is expressed as a ratio, which can range from 0 (completely dry) to the value of the materials' porosity at saturation. It can be given on a volumetric or mass (gravimetric) basis. Definitions Volumetric water content, θ, is defined mathematically as: :\theta = \frac where V_w is the volume of water and V_\text = V_s + V_w + V_a is equal to the total volume of the wet material, i.e. of the sum of the volume of solid host material (e.g., soil particles, vegetation tissue) V_s, of water V_w, and of air V_a. Gravimetric water content is expressed by mass (weight) as follows: :u = \frac where m_w is the mass of water and m_s is the mass of the solids. For materials that change in volume with water content, such as coal, the gravimetric water content, ''u' ...
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Organism
In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fungi; or unicellular microorganisms such as protists, bacteria, and archaea. All types of organisms are capable of reproduction, growth and development, maintenance, and some degree of response to stimuli. Beetles, squids, tetrapods, mushrooms, and vascular plants are examples of multicellular organisms that differentiate specialized tissues and organs during development. A unicellular organism may be either a prokaryote or a eukaryote. Prokaryotes are represented by two separate domains – bacteria and archaea. Eukaryotic organisms are characterized by the presence of a membrane-bound cell nucleus and contain additional membrane-bound compartments called organelles (such as mitochondria in animals and plants ...
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Turgor
Turgor pressure is the force within the cell that pushes the plasma membrane against the cell wall. It is also called ''hydrostatic pressure'', and is defined as the pressure in a fluid measured at a certain point within itself when at equilibrium. Generally, turgor pressure is caused by the osmotic flow of water and occurs in plants, fungi, and bacteria. The phenomenon is also observed in protists that have cell walls. This system is not seen in animal cells, as the absence of a cell wall would cause the cell to lyse when under too much pressure. The pressure exerted by the osmotic flow of water is called turgidity. It is caused by the osmotic flow of water through a selectively permeable membrane. Movement of water through a semipermeable membrane from a volume with a low solute concentration to one with a higher solute concentration is called osmotic flow. In plants, this entails the water moving from the low concentration solute outside the cell into the cell's vacuole. Mech ...
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Osmosis
Osmosis (, ) is the spontaneous net movement or diffusion of solvent molecules through a selectively-permeable membrane from a region of high water potential (region of lower solute concentration) to a region of low water potential (region of higher solute concentration), in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a selectively permeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations. Osmosis can be made to do work. Osmotic pressure is defined as the external pressure required to be applied so that there is no net movement of solvent across the membrane. Osmotic pressure is a colligative property, meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity. Osmosis is a vital process in biological systems, as biological membranes are semiperm ...
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Elastic Deformation
In engineering, deformation refers to the change in size or shape of an object. ''Displacements'' are the ''absolute'' change in position of a point on the object. Deflection is the relative change in external displacements on an object. Strain is the ''relative'' internal change in shape of an infinitesimally small cube of material and can be expressed as a non-dimensional change in length or angle of distortion of the cube. Strains are related to the forces acting on the cube, which are known as stress, by a stress-strain curve. The relationship between stress and strain is generally linear and reversible up until the yield point and the deformation is elastic. The linear relationship for a material is known as Young's modulus. Above the yield point, some degree of permanent distortion remains after unloading and is termed plastic deformation. The determination of the stress and strain throughout a solid object is given by the field of strength of materials and for a structure ...
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Plant Tissue
In biology, tissue is a biological organizational level between cells and a complete organ. A tissue is an ensemble of similar cells and their extracellular matrix from the same origin that together carry out a specific function. Organs are then formed by the functional grouping together of multiple tissues. The English word "tissue" derives from the French word "tissu", the past participle of the verb tisser, "to weave". The study of tissues is known as histology or, in connection with disease, as histopathology. Xavier Bichat is considered as the "Father of Histology". Plant histology is studied in both plant anatomy and physiology. The classical tools for studying tissues are the paraffin block in which tissue is embedded and then sectioned, the histological stain, and the optical microscope. Developments in electron microscopy, immunofluorescence, and the use of frozen tissue-sections have enhanced the detail that can be observed in tissues. With these tools, the clas ...
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Osmotic Potential
Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in a pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane. Osmosis occurs when two solutions containing different concentrations of solute are separated by a selectively permeable membrane. Solvent molecules pass preferentially through the membrane from the low-concentration solution to the solution with higher solute concentration. The transfer of solvent molecules will continue until equilibrium is attained. Theory and measurement Jacobus van 't Hoff found a quantitative relationship between osmotic pressure and solute concentration, expressed in the following equation: :\Pi = icRT where \Pi is osmotic pr ...
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Solute
In chemistry, a solution is a special type of homogeneous mixture composed of two or more substances. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. If the attractive forces between the solvent and solute particles are greater than the attractive forces holding the solute particles together, the solvent particles pull the solute particles apart and surround them. These surrounded solute particles then move away from the solid solute and out into the solution. The mixing process of a solution happens at a scale where the effects of chemical polarity are involved, resulting in interactions that are specific to solvation. The solution usually has the state of the solvent when the solvent is the larger fraction of the mixture, as is commonly the case. One important parameter of a solution is the concentration, which is a measure of the amount of solute in a given amount of solution or solvent. The term "aqueous solution" is used when ...
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Linear Relation
In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution. More precisely, if e_1,\dots,e_n are elements of a (left) module over a ring (the case of a vector space over a field is a special case), a relation between e_1,\dots,e_n is a sequence (f_1,\dots, f_n) of elements of such that :f_1e_1+\dots+f_ne_n=0. The relations between e_1,\dots,e_n form a module. One is generally interested in the case where e_1,\dots,e_n is a generating set of a finitely generated module , in which case the module of the relations is often called a syzygy module of . The syzygy module depends on the choice of a generating set, but it is unique up to the direct sum with a free module. That is, if S_1 and S_2 are syzygy modules corresponding to two generating sets of the same module, then they are stably isomorphic, which means that there exist two free modules L_1 and L_2 such that S_1\oplus ...
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Constant (mathematics)
In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings: * A fixed and well-defined number or other non-changing mathematical object. The terms '' mathematical constant'' or '' physical constant'' are sometimes used to distinguish this meaning. * A function whose value remains unchanged (i.e., a constant function). Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question. For example, a general quadratic function is commonly written as: :a x^2 + b x + c\, , where , and are constants (or parameters), and a variable—a placeholder for the argument of the function being studied. A more explicit way to denote this function is :x\mapsto a x^2 + b x + c \, , which makes the function-argument status of (and by extension the constancy of , and ) clear. In this example , and are co ...
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