Time, direction of

2018 ◽  
Author(s):  
Jos Uffink
Keyword(s):  
Boundary Condition ◽  
General Principle ◽  
Room Temperature ◽  
Hot Water ◽  
Initial Condition ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Time Direction ◽  
James Clerk Maxwell ◽  
Ice Cube

You can pour a tumblerful of water into the sea, but you can never get that same tumblerful of water out again. James Clerk Maxwell gave this as an example of an irreversible process. There are many other homely examples: coffee and milk will mix if stirred, but white coffee does not unmix if stirred in reverse. An ice cube in a glass of hot water will melt, but we never see water at room temperature spontaneously separate into ice and hot water. Physical theories like thermodynamics or hydrodynamics, which codify this type of irreversible phenomenon, do not allow the same kind of behaviour in the forward and backward direction of time. There is thus a striking asymmetry in the two temporal directions. This is usually referred to as the ‘direction of time’ (or ‘time asymmetry’ or ‘anisotropy’ or the ‘arrow of time’). The source of this asymmetry has been sought in various theories of physics, both classical and quantum. Some explanations appeal to some sort of boundary condition, typically an initial condition, which the explanation admits to be, not a law of the theory, but a matter of happenstance. Other explanations advocate some additional general principle about, for example, temporally asymmetric notions of causality or randomness.

Ice Cubes and Hot Water Bottles

Fractals ◽  
1997 ◽  
Vol 05 (01) ◽  
pp. 145-151 ◽  
Author(s):  
Susie Vrobel
Keyword(s):  
Open Systems ◽  
Thought Experiment ◽  
Fractal Model ◽  
Hot Water ◽  
Water Bottle ◽  
Arrow Of Time ◽  
Empirical Knowledge ◽  
Ice Cube ◽  
The Moment ◽  
The Individual

Can the arrow of time we seem to perceive be explained by an overall increase in entropy? Several models suggest that the one macroscopic arrow of time which is associated with an overall increase in entropy may be identical to the arrows of time which are subject to our empirical knowledge. These models turn out to be difficult to maintain if one considers a freeze-frame picture (or one containing a minimal period of time) of nested systems of decreasing and increasing entropy. An observer who determines an arrow of time by measuring an increase or decrease in entropy must obviously be located somewhere. This observer position is in no case arbitrary — the individual situation of the observer determines, in each case, the outcome of the measurement. A fractal model suggests that the direction-generating agent is not to be found in a system's increase in entropy, but rather in the choice of the observer's position. A thought experiment involving infinitely nested ice cubes and hot water bottles leads to the conclusion that for such freeze-frames involving a minimal time span, the concepts of isolated and open systems (which otherwise are indispensable concepts for the discussion of entropy) are unsuitable. If one considers observers placed within different nested levels of the ice cube and hot water bottle universe, it will be impossible for these observers to determine whether the embedding systems add up to a total increase or decrease of entropy: we will never know whether the "outermost embedding nest" is an ice cube or a hot water bottle. An identification of the arrows of time which are subject to our empirical knowledge with an overall increase in entropy would not be plausible since there is no conceivable observer capable of monitoring the system as a whole. A fractal nested model suggests that there are nested arrows of time with differing directions. What direction we experience depends, in each case, entirely on the observer position chosen, i.e., the system we participate in. The only way to find out which arrow of time we are experiencing at the moment, say, in an ice cube, is to make contact with an observer in a hot water bottle — either with an observer in the hot water bottle embedding my ice cube or with one in the hot water bottle nested in my ice cube. The question: "Is there a way out?" must be discussed elsewhere. The arrow of time defined by an overall increase in entropy is not congruent with the arrows of time of our empirical knowledge.

scholarly journals Defining Arrow of Time at The Start of Inflation Using Traditional Cosmology Initially as an Example and Finally Penrose Cyclic Conformal Cosmology with Singular versus Nonsingular Starting Points?

2021 ◽  
Author(s):  
Andrew W Beckwith
Keyword(s):  
Quantum Information ◽  
Initial Conditions ◽  
Axiomatic Approach ◽  
Cosmological Models ◽  
Arrow Of Time ◽  
Time Asymmetry ◽  
Conformal Cosmology ◽  
Definition Of ◽  
Initial Starting

We first of all define the arrow of time. Definition of the arrow of time will allow choosing different initial starting points. One of the issues we will also discuss is the interconnection be-tween the arrow of time, entropy and quantum information. Seth Lloyd in his 2001 work made a linkage between entropy, bits, and information via an axiomatic approach involving time in-tervals. Our take is a bit more general. We will discuss as well the t’Hooft’s statement as to in-itial conditions and times arrow, and how different cosmological models may influence initial conditions. Spoilers alert, if a nonsingular start to expansion existed, this would provide the most straightforward way to avoid a datum from classical relativity. That is, that in the actual equations of classical GR, there is no reason to have time asymmetry. Time asymmetry is built into initial conditions and we will detail several candidates. The first half of the paper brings up cosmology models and forming the arrow of time. The second is related to entropy itself and the problem of information. .

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

scholarly journals Effect of pre-sowing treatments and growing media on seed germination and seedling growth of Albizia lebbeck (L.) Benth

2018 ◽  
Vol 10 (3) ◽  
pp. 860-863
Author(s):  
Naresh Kumar ◽  
A. K. Handa ◽  
Inder Dev ◽  
Asha Ram ◽  
A. R. Uthappa ◽  
...  
Keyword(s):  
Seedling Growth ◽  
Room Temperature ◽  
Cold Water ◽  
Hot Water ◽  
Albizia Lebbeck ◽  
Physical Dormancy ◽  
Growing Media ◽  
Hard Seed ◽  
Collar Diameter ◽  
Hard Seed Coat

The seeds of Albizia lebbeck have been observed to exhibit physical dormancy due to presence of hard seed-coat. To overcome this problem, the seeds were subjected to seven pre-sowing treatments viz., T1-immersion of seeds in cold water for 12 h; T2-immersion of seeds in cold water for 24 h; T3-immersion of seeds in hot water (100 °C) and subsequent cooling at room temperature for 12 h; T4-immersion of seeds in hot water (100 °C) and subsequent cooling at room temperature for 24 h; T5-immersion of seeds in cold water for 12 h followed by immersion in hot water (100 °C) and allowed to cool for 1 h; T6-immersion of seeds in cold water for 24 h followed by immersion in hot water (100 °C) and allowed to cool for 1 h. Untreated seeds served as control (T0). Treatment T3 gave highest germination (96%) which was comparable with T5 (95 %), T4 (94 %) and T6 (93%). Nine growing media viz., T1: soil,  T2: soil+sand (2:1), T3: soil+perlite (2:1), T4: soil+Farm Yard Manure (FYM) (2:1), T5: soil+vermicompost (2:1), T6: soil+sand+FYM (1:1:1), T7: soil+sand+vermicompost (1:1:1), T8: soil+perlite+FYM (1:1:1) and T9: soil+perlite+ vermicompost (1:1:1) were, also, studied for their effect on seedling growth of A. lebbeck. Among these media, maximum values of shoot length (23.82 cm), root length (21.14 cm), collar diameter (3.59 mm) and seedling quality index (0.350) were observed in T7.

scholarly journals On the evolution of solutions of Burgers equation on the positive quarter-plane

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

scholarly journals The effect of temperature change on fluoride uptake from a mouthrinse by enamel specimens

2012 ◽  
Vol 06 (04) ◽  
pp. 361-369 ◽  
Author(s):  
Serdar Baglar ◽  
Adil Nalcaci ◽  
Mustafa Tastekin
Keyword(s):  
Body Temperature ◽  
Room Temperature ◽  
Hot Water ◽  
Effect Of Temperature ◽  
Distilled Water ◽  
Fluoride Solution ◽  
Fluoride Uptake ◽  
Significant Difference ◽  
Human Body Temperature ◽  
Different Temperatures

ABSTRACTObjective: The aim of this study was to examine the effect of temperature on fluoride uptake by enamel specimens from a 0.05% NaF-fluoridated mouthrinse (Oral-B Advantage; Oral-B Laboratories, Newbridge, UK).Methods: Enamel specimens were prepared from extracted human maxillary central incisors. A fluoride-specific ion electrode was used to measure the uptake from a 2 ppm fluoride solution containing 50.0 mL of distilled water, total ion strength adjustment buffer, and fluoridated rinse at 3 different temperatures (room temperature, 25°C; human body temperature, 37°C; hyper-fever temperature, 43°C). One-way analysis of variance and least significant difference were used to assess intragroup and intergroup differences (P<.05).Results: The study found that both the amount and the rate of fluoride uptake increased significantly with increase in temperature. This effect was particularly noticeable at 43°C.Conclusions: The temperature of the NaF mouthrinse may easily and safely be increased beyond room temperature by placing a container of the NaF mouthrinse in a bowl of hot water, allowing greater fluoride penetration into the enamel from the mouthrinse when used at home as a routine prophylactic agent. (Eur J Dent 2012;6:361-369)

scholarly journals The Sedov Blast Wave as a Radial Piston Verification Test

2016 ◽  
Vol 1 (3) ◽  
Author(s):  
Clark Pederson ◽  
Bart Brown ◽  
Nathaniel Morgan
Keyword(s):  
Energy Source ◽  
Boundary Condition ◽  
Point Source ◽  
Blast Wave ◽  
Time Varying ◽  
Initial Condition ◽  
Piston Problem ◽  
Great Utility ◽  
Verification Problem ◽  
Verification Test

The Sedov blast wave is of great utility as a verification problem for hydrodynamic methods. The typical implementation uses an energized cell of finite dimensions to represent the energy point source. This approximation can be avoided by directly finding the effects of the energy source as a boundary condition (BC). The proposed method transforms the Sedov problem into an outward moving radial piston problem with a time-varying velocity. A portion of the mesh adjacent to the origin is removed and the boundaries of this hole are forced with the velocities from the Sedov solution. This verification test is implemented on two types of meshes, and convergence is shown. The results from the typical initial condition (IC) method and the new BC method are compared.

scholarly journals Blow-Up of Solutions for a Class of Nonlinear Pseudoparabolic Equations with a Memory Term

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Huafei Di ◽  
Yadong Shang
Keyword(s):  
Boundary Condition ◽  
Relaxation Function ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Initial Energy ◽  
Memory Term ◽  
Initial Condition ◽  
Pseudoparabolic Equation ◽  
Pseudoparabolic Equations ◽  
Nonlinear Pseudoparabolic Equation

We consider the nonlinear pseudoparabolic equation with a memory termut-Δu-Δut+∫0tλt-τΔuτdτ=div∇up-2u+u1+α,x∈Ω,t>0, with an initial condition and Dirichlet boundary condition. Under negative initial energy and suitable conditions onp,α, and the relaxation functionλ(t), we prove a finite-time blow-up result by using the concavity method.

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