Time constant

About: Time constant is a research topic. Over the lifetime, 3287 publications have been published within this topic receiving 40768 citations. The topic is also known as: τ.

Closure temperature in cooling geochronological and petrological systems

Abstract: Closure temperature (Tc) of a geochronological system may be defined as its temperature at the time corresponding to its apparent age. For thermally activated diffusion (D=Doe−E/RT it is given by $$T_c = R/[E ln (A \tau D_0 /a^2 )]$$ (i) in which R is the gas constant, E the activation energy, τ the time constant with which the diffusion coefficient D diminishes, a is a characteristic diffusion size, and A a numerical constant depending on geometry and decay constant of parent. The time constant τ is related to cooling rate by $$\tau = R/(Ed T^{ - 1} /dt) = - RT^2 /(Ed T/dt).$$ (ii) Eq. (i) is exact only if T−1 increases linearly with time, but in practice a good approximation is obtained by relating τ to the slope of the cooling curve at Tc.

Voltage clamp analysis of acetylcholine produced end-plate current fluctuations at frog neuromuscular junction

Abstract: 1. Acetylcholine produced end-plate current (e.p.c.) noise is shown to be the results of statistical fluctuations in the ionic conductance of voltage clamped end-plates of Rana pipiens. 2. These e.p.c. fluctuations are characterized by their e.p.c. spectra which conform to a relation predicted from a simple model of end-plate channel gating behaviour. 3. The rate constant of channel closing α is determined from e.p.c. spectra and is found to depend on membrane potential V according to the relation α = BeAV (B = 0·17 msec−1±0·04 S.E., A = 0·0058 mV−1±0·0009 S.E. at 8° C) and to vary with temperature T with a Q10 = 2·77, at −70 mV. A and B in this expression both vary with T and therefore produce a membrane potential dependent Q10 for α. 4. Nerve-evoked e.p.c.s and spontaneous miniature e.p.c.s decay exponentially in time with a rate constant which depends exponentially on V. The magnitude and voltage dependence of this decay constant is exactly that found from e.p.c. spectra for the channel closing rate α. 5. The conductance γ of a single open end-plate channel has been estimated from e.p.c. spectra and is found not to be detectibly dependent on membrane potential, temperature and mean end-plate current. γ = 0·32±0·0045 ( S.E.) × 10−10 mhos. Some variation in values for γ occurs from muscle to muscle. 6. It is concluded that the relaxation kinetics of open ACh sensitive ionic channels is the rate limiting step in the decay of synaptic current and that this channel closing has a single time constant. The relaxation rate is independent of how it is estimated (ACh produced e.p.c. fluctuations, e.p.c., m.e.p.c.), and is consistent with the hypothesis that individual ionic channels open rapidly to a specific conductance which remains constant for an exponentially distributed duration. 7. The voltage and temperature dependence of the channel closing rate constant agree with the predictions of a simple dipole-conformation change model.

Core Conductor Theory and Cable Properties of Neurons

Abstract: The sections in this article are: 1 Introduction 1.1 Core Conductor Concept 1.2 Perspective 1.3 Comment 1.4 Reviews and Monographs 2 Brief Historical Notes 2.1 Early Electrophysiology 2.2 Electrotonus 2.3 Passive Membrane Electrotonus 2.4 Passive Versus Active Membrane 2.5 Cable Theory 2.6 Core Conductor Concept 2.7 Core Conductor Theory 2.8 Estimation of Membrane Capacitance 2.9 Resting Membrane Resistivitiy 2.10 Passive Cable Parameters of Invertebrate Axons 2.11 Importance of Single Axon Preparations 2.12 Estimation of Parameters for Myelinated Axons 2.13 Space and Voltage Clamp 3 Dendritic Aspects of Neurons 3.1 Axon-Dendrite Contrast 3.2 Microelectrodes in Motoneurons 3.3 Theoretical Neuron Models and Parameters 3.4 Class of Trees Equivalent to Cylinders 3.5 Motoneuron Membrane Resistivity and Dendritic Dominance 3.6 Dendritic Electrotonic Length 3.7 Membrane Potential Transients and Time Constants 3.8 Spatiotemporal Effects with Dendritic Synapses 3.9 Excitatory Postsynaptic Potential Shape Index Loci 3.10 Comments on Extracellular Potentials 3.11 Additional Comments and References 4 Cable Equations Defined 4.1 Usual Cable Equation 4.2 Steady-state Cable Equations 4.3 Augmented Cable Equations 4.4 Comment: Cable Versus Wave Equation 4.5 Modified Cable Equation for Tapering Core 4.6 General Solution of Steady-state Cable Equation 4.7 Basic Transient Solutions of Cable Equation 4.8 Solutions Using Separation of Variables 4.9 Fundamental Solution for Instantaneous Point Charge 5 List of Symbols 6 Assumptions and Derivation of Cable Theory 6.1 One Dimensional in Space 6.2 Intracellular Core Resistance 6.3 Ohm's Law for Core Current 6.4 Conservation of Current 6.5 Relation of Membrane Current to Vi 6.6 Effect of Assuming Extracellular Isopotentiality 6.7 Passive Membrane Model 6.8 Resulting Cable Equation for Simple Case 6.9 Physical Meaning of Cable Equation Terms 6.10 Physical Meaning of τ 6.11 Physical Meaning of λ 6.12 Electrotonic Distance, Length, and Decrement 6.13 Effect of Placing Axon in Oil 6.14 Effect of Applied Current 6.15 Comment on Sign Conventions 6.16 Effect of Synaptic Membrane Conductance 6.17 Effect of Active Membrane Properties 7 Input Resistance and Steady Decrement with Distance 7.1 Note on Correspondence with Experiment 7.2 Cable of Semi-infinite Length 7.3 Comments about R∞, G∞, Core Current, and Input Current 7.4 Doubly Infinite Length 7.5 Case of Voltage Clamps at X1 and X2 7.6 Relations Between Axon Parameters 7.7 Finite Length: Effect of Boundary Condition at X= X1 7.8 Sealed End at X= X1: Case of B1 = 0 7.9 Voltage Clamp(V1 = 0) at X = X1: Case of B1 = ∞ 7.10 Semi-infinite Extension at X = X1: Case of B1 = 1 7.11 Input Conductance for Finite Length General Case 7.12 Branches at X = X1 7.13 Comment on Branching Equivalent to a Cylinder 7.14 Comment on Membrane Injury at X = X1 7.15 Comment on Steady Synaptic Input at X= X1 7.16 Case of Input to One Branch of Dendritic Neuron Model 8 Passive Membrane Potential Transients and Time Constants 8.1 Passive Decay Transients 8.2 Time Constant Ratios and Electrotonic Length 8.3 Effect of Large L and Infinite L 8.4 Transient Response to Applied Current Step, for Finite Length 8.5 Applied Current Step with L Large or Infinite 8.6 Voltage Clamp at X = 0, with Infinite L 8.7 Voltage Clamp with Finite Length 8.8 Transient Response to Current Injected at One Branch of Model 9 Relations Between Neuron Model Parameters 9.1 Input Resistance and Membrane Resistivity 9.2 Dendritic Tree Input Resistance and Membrane Resistivity 9.3 Results for Trees Equivalent to Cylinders 9.4 Result for Neuron Equivalent to Cylinder 9.5 Estimation of Motoneuron Parameters

Exponential analysis in physical phenomena

Abstract: Many physical phenomena are described by first-order differential equations whose solution is an exponential decay. Determining the time constants and amplitudes of exponential decays from the experimental data is a common task in semiconductor physics (deep level transient spectroscopy), biophysics (fluorescence decay analysis), nuclear physics and chemistry (radioactive decays, nuclear magnetic resonance), chemistry and electrochemistry (reaction kinetics) and medical imaging. This review article discusses the fundamental mathematical limitations of exponential analysis, outlines the critical aspects of acquisition of exponential transients for subsequent analysis, and gives a comprehensive overview of numerical algorithms used in exponential analysis. In the first part of the article the resolution of exponential analysis as a function of noise in input decays is discussed. It is shown that two exponential decays can be resolved in a transient only if the ratio of their time constants is greater than t...