Implementing Demons and Ratchets

Total Page:16

File Type:pdf, Size:1020Kb

Implementing Demons and Ratchets entropy Article Implementing Demons and Ratchets Peter M. Orem * and Frank M. Orem ThermaWatts, LLC, Renton, WA 98057, USA; [email protected] * Correspondence: [email protected]; Tel.: +1-503-635-2607 Academic Editor: Kevin H. Knuth Received: 30 November 2016; Accepted: 6 January 2017; Published: 14 January 2017 Abstract: Experimental results show that ratchets may be implemented in semiconductor and chemical systems, bypassing the second law and opening up huge gains in energy production. This paper summarizes or describes experiments and results on systems that effect demons and ratchets operating in chemical or electrical domains. One creates temperature differences that can be harvested by a heat engine. A second produces light with only heat input. A third produces harvestable electrical potential directly. These systems share creating particles in one location, destroying them in another and moving them between locations by diffusion (Brownian motion). All absorb ambient heat as they produce other energy forms. None requires an external hot and cold side. The economic and social impacts of these conversions of ambient heat to work are, of course, well-understood and huge. The experimental results beg for serious work on the chance that they are valid. Keywords: second law; thermodynamics; direct conversion; epicatalysis; semiconductor; LED; Brownian ratchet; Maxwell’s demon; ambient heat; energy 1. Introduction This paper is intended to assist understanding possible second law exceptions, so that readers might be moved to examine them carefully. The second law of thermodynamics was first expressed more than 190 years ago to show that there is an upper limit to the efficiency of a heat engine, which converts heat to mechanical energy or other work. Simply put, such conversion always suffers inefficiency. The second law has been thoroughly tested, restated and confirmed many times since then [1]. Scientists have shifted away from the notion of “laws” to ideas about “models” to explain and predict behaviors, because laws imply completeness, whereas models acknowledge their incompleteness. This gives freedom to expand our range of thinking, including that on the second law. A small set of researchers has made the transition to models as they develop experiments that point to new energy possibilities. They seem to be driven by the potentially huge value to humanity for finding such possibilities [2]. We present below three cases of systems that may be demonstrating demons and ratchets. These were chosen because: 1. They are supported by test results; 2. We believe they are conceptually clean and easily explained; and 3. They may have commercial application. We believe that if any one of these demonstrations is valid (we believe all are), it opens up a range of practical methods for turning ambient heat directly into electrical energy. This matters because such direct conversion can be perfectly sustainable, since it does not require fuels or otherwise cause environmental damage. Entropy 2017, 19, 34; doi:10.3390/e19010034 www.mdpi.com/journal/entropy Entropy 2017, 19, 34 2 of 19 Entropy 2017, 19, 34 2 of 19 The cases are: • The Epicatalysis: cases are: Tests demonstrate that opposing catalysts can create a temperature differential needed for a heat engine heat • Epicatalysis: Tests demonstrate that opposing catalysts can create a temperature differential • LEDs: Emission measurements show that unbiased light emitting diodes (LED’s) emit a needed for a heat engine heat. • LEDs:small Emission amount measurements of light. show that unbiased light emitting diodes (LED’s) emit a small •amount Doped of light.semiconductor structure: A sandwich-like structure of semiconductors presents a • Dopedpersistent, semiconductor harvestable structure: voltage. We A sandwich-likecall this an ambient structure thermal of semiconductorselectric converter presents (ATEC). a persistent, harvestable voltage. We call this an ambient thermal electric converter (ATEC). The demonstration systems have two features in common: particles are created and destroyed, and Thethese demonstration actions take place systems at different have two locations. features in common: particles are created and destroyed, and theseFigure actions 1 shows take the place general at different concept locations. for a cycle that would create an exception to the second law. Z representsFigure1 shows some potential the general or conceptwork function. for a cycle It co thatuld would be gravity, create electric an exception potential to the or secondsome other law. Zfunction. represents N represents some potential the number or work of function.particles in It the could system. be gravity, electric potential or some other function.The flow N represents is as follows: the number of particles in the system. The flow is as follows: • The bottom line represents the creation of particles at Location 1. • •The Some bottom particles line represents move across the creation the potential of particles to Lo atcation Location 2, driven 1. by thermal energy through • Some particles move across the potential to Location 2, driven by thermal energy through diffusion. diffusion. This creation process fills the role of Maxwell’s demon. This creation process fills the role of Maxwell’s demon. • Some of those particles are then destroyed • Some of those particles are then destroyed. • • RemainingRemaining particles particles return return to Location to Location 1. 1. FigureFigure 1.1. AA cyclecycle thatthat wouldwould createcreate aa secondsecond lawlaw exception.exception. TheThe changingchanging numbernumber ofof particlesparticles fillsfills thethe rolerole ofof aa BrownianBrownian ratchet.ratchet. ThereThere isis muchmuch flexibilityflexibility inin implementingimplementing thisthis cycle,cycle, asas describeddescribed below.below. The The directional directional bias bias is is essential. essential. TheThe overalloverall cyclecycle convertsconverts thermalthermal energyenergy intointo somesome otherother formform ofof energyenergy andand thenthen preventsprevents thethe reversereverse transitiontransition by by removing removing the the particles particles involved. involved. Cheating Cheating the laws the oflaws physics of physics once is notonce enough; is not weenough; have towe do have it twice: to do bothit twice: Maxwell’s both Maxwell’s demon and demon a Brownian and a Brownian ratchet are ratchet required. are required. TheThe generalgeneral conceptconcept thatthat capturescaptures thethe objectionobjection to the cyclecycle of FigureFigure1 1 is is “detailed “detailed balance”. balance”. TheThe principleprinciple of of detailed detailed balance balance says says that that both both paths paths between between 1 and 1 and 2 should 2 should be in be equilibrium. in equilibrium. In that In regard,that regard, the principle the principle of detailed of detailed balance balance is the mostis the narrowly most narrowly focused focused reason whyreason such why cycles such should cycles notshould work. not In work. other In words, other thewords, principle the principle of detailed of detailed balance balance is a corollary is a corollary to the second to the law.second law. Note:Note: this paper only summarizes the methodsmethods andand resultsresults ofof epicatalysis,epicatalysis, partpart ofof thethe LEDLED emissionsemissions experimentsexperiments andand thethe dopeddoped semiconductorsemiconductor structure (ATEC) toto permitpermit thethe readerreader toto seesee thethe similaritiessimilarities ofof thethe systemssystems withoutwithout gettinggetting lostlost inin thethe details.details. Thus,Thus, thethe readerreader isis encouragedencouraged toto examineexamine thethe SupplementalSupplemental MaterialsMaterials andand referencesreferences forfor furtherfurther depthdepth of of understanding. understanding. 2. Materials and Methods Entropy 2017, 19, 34 3 of 19 2.Entropy MaterialsEntropy 2017 2017, 19, and19, 34, 34 Methods 3 3of of 19 19 TheTheThe subsectionssubsections subsections belowbelow below describe describe the thethe setup setupsetup and and processes processes we we we used used used to to totest test test the the the hypotheses hypotheses hypotheses that that that certaincertaincertain systems systems systems convert convert convert heat heat heat to to workto work work without without without a colda acold cold side. side. side. We We intendWe intend intend that that thethat the information the information information in this in in thissection this andsectionsection our “A andand Report ourour on“A“A Testing ReportReport of onon ThermaWatts TestingTesting ofof PrototypeThermaWattsThermaWatts Ambient PrototypePrototype Thermal AmbientAmbient Electric ThermalThermal Converter ElectricElectric Devices” document,ConverterConverter accessibleDevices” Devices” document, throughdocument, the accessible accessible Supplementary through through Materials, the the Supplementary Supplementary are sufficient Materials, Materials, for replication are are sufficient sufficient of our for workfor byreplicationreplication others. of of our our work work by by others. others. 2.1.2.1.2.1. LEDs LEDs LEDs TwoTwoTwo methods methods methods are are are describeddescribed described that that we we used used to toto captur capturecapture ethe the effect effect of of unbiased unbiased unbiased LEDs LEDs LEDs emitting emitting emitting light. light. light. 2.1.1.2.1.1.2.1.1. Direct Direct Direct Film Film Film ExposureExposure Exposure InInIn 2007–2008, 2007–2008, 2007–2008, Peter Peter Peter
Recommended publications
  • 1 / C\% Cellular Motions and Thermal Fluctuations: the Brownian Ratchet
    1 / C\% 316 Biophysical Journal Volume 65 July 1993 316-324 ” Cellular Motions and Thermal Fluctuations: The Brownian Ratchet Charles S. Peskin,* Garrett M. Odell,* and George F. Osters l Courant Institute of Mathematical Sciences, New York, New York 10012; *Department of Zoology, University of Washington, Seattle, Washington 98195; SDepartments of Molecular and Cellular Biology, and Entomology, University of California, Berkeley, California 94720 USA ABSTRACT We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Wisteria, and protein translocation. INTRODUCTION Many types of cellular protrusions, including filopodia, This is the speed of a perfect BR. Note that as the ratchet lamellipodia, and acrosomal extension do not appear to in- interval, 8, decreases, the ratchet velocity increases. This is volve molecular motors. These processes transduce chemical because the frequency of smaller Brownian steps grows more bond energy into directed motion, but they do not operate in rapidly than the step size shrinks (when 6 is of the order of a mechanochemical cycle and need not depend directly upon a mean free path, then this formula obviously breaks down). nucleotide hydrolysis. In this paper we describe several such Several ingredients must be added to this simple expres- processes and present simple formulas for the velocity and sion to make it useful in real situations. First, the ratchet force they generate. We shall call these machines “Brownian cannot be perfect: a particle crossing a ratchet boundary may ratchets” (BR) because rectified Brownian motion is funda- occasionally cross back.
    [Show full text]
  • On Control of Transport in Brownian Ratchet Mechanisms
    Journal of Process Control 27 (2015) 76–86 Contents lists available at ScienceDirect Journal of Process Control j ournal homepage: www.elsevier.com/locate/jprocont On control of transport in Brownian ratchet mechanisms a,∗ a b a Subhrajit Roychowdhury , Govind Saraswat , Srinivasa Salapaka , Murti Salapaka a Department of Electrical and Computer Engineering, University of Minnesota-Twin Cities, 2-270 Keller Hall, Minneapolis, MN 55455, USA b Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA a r t i c l e i n f o a b s t r a c t Article history: Engineered transport of material at the nano/micro scale is essential for the manufacturing platforms of Received 1 April 2014 the future. Unlike conventional transport systems, at the nano/micro scale, transport has to be achieved Received in revised form in the presence of fundamental sources of uncertainty such as thermal noise. Remarkably, it is possible 15 September 2014 to extract useful work by rectifying noise using an asymmetric potential; a principle used by Brownian Accepted 26 November 2014 ratchets. In this article a systematic methodology for designing open-loop Brownian ratchet mechanisms Available online 23 December 2014 that optimize velocity and efficiency is developed. In the case where the particle position is available as a measured variable, closed loop methodologies are studied. Here, it is shown that methods that strive Keywords: to optimize velocity of transport may compromise efficiency. A dynamic programming based approach Flashing ratchet is presented which yields up to three times improvement in efficiency over optimized open loop designs Stochastic systems Dynamic programming and 35% better efficiency over reported closed loop strategies that focus on optimizing velocities.
    [Show full text]
  • Brownian Ratchets in Physics and Biology
    Contemporary Physics, 1997, volume 38, number 6, pages 371 ± 379 Brownian ratchets in physics and biology M ARTIN BIER Thirty years ago Feynman et al. presented a paradox in the Lectures on Physics: an imagined device could let Brownian motion do work by allowing it in one direction and blocking it in the opposite direction. In the chapter Feynman et al. eventually show that such ratcheting can only be achieved if there is, in compliance with the basic conservation laws, some energy input from an external source. Now that technology is going into ever smaller dimensions, ratcheting Brownian motion seems to be a real possibility in nanotechnological applications. Furthermore, Brownian motion plays an essential role in the action of motor proteins (individual molecules that convert chemical energy into motion). 1. The thermodynamic consistency of a Brownian microscopic engine is not necessarily the microscopic ratchet equivalent of an e cient macroscopic engine. At the Technology is reaching into ever smaller dimensions microscopic level it is possible to `ratchet’ Brownian nowadays. Many research groups are shrinking labs onto motion, i.e. to allow Brownian motion in one direction tiny squares of silicon or glass. On these `labs on chips’ and block it in the opposite direction so net displacement individual bacteria viruses and macromolecules (like occurs. It appears that a lot of biological systems at the proteins or DNA strands) are identi® ed and/or manipu- molecular level operate like this [3]. Systems that convert lated [1]. On the micrometre scale physics is diŒerent. For energy in the presence of Brownian motion are compli- motion in a ¯ uid the Reynolds number (i.e.
    [Show full text]
  • Session 15 Thermodynamics
    Session 15 Thermodynamics Cheryl Hurkett Physics Innovations Centre for Excellence in Learning and Teaching CETL (Leicester) Department of Physics and Astronomy University of Leicester 1 Contents Welcome .................................................................................................................................. 4 Session Authors .................................................................................................................. 4 Learning Objectives .............................................................................................................. 5 The Problem ........................................................................................................................... 6 Issues .................................................................................................................................... 6 Energy, Heat and Work ........................................................................................................ 7 The First Law of thermodynamics................................................................................... 8 Work..................................................................................................................................... 9 Heat .................................................................................................................................... 11 Principal Specific heats of a gas ..................................................................................... 12 Summary ..........................................................................................................................
    [Show full text]
  • Artificial Brownian Motors: Controlling Transport on the Nanoscale
    Artificial Brownian motors: Controlling transport on the nanoscale Peter H¨anggi1, 2, ∗ and Fabio Marchesoni3, 4, y 1Institut f¨urPhysik, Universit¨atAugsburg, Universit¨atsstr.1, D-86135 Augsburg, Germany 2Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117542 3Dipartimento di Fisica, Universit`adi Camerino, I-62032 Camerino, Italy 4School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea (Dated: September 24, 2008) In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with unbiased external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases, one speaks of \Brownian motors". In this review the constructive role of Brownian motion is exemplified for various physical and technological setups, which are inspired by the cell molecular machinery: working principles and characteristics of stylized devices are discussed to show how fluctuations, either thermal or extrinsic, can be used to control diffusive particle transport. Recent experimental demonstrations of this concept are surveyed with particular attention to transport in artificial, i.e. non-biological nanopores and optical traps, where single particle currents have been first measured. Much emphasis is given to two- and three-dimensional devices containing many interacting particles of one or more species; for this class of artificial motors, noise rectification results also from the interplay of particle Brownian motion and geometric constraints. Recently, selective control and optimization of the transport of interacting colloidal particles and magnetic vortices have been successfully achieved, thus leading to the new generation of microfluidic and superconducting devices presented hereby.
    [Show full text]
  • A Stochastic Analysis of a Brownian Ratchet Model for Actin-Based Motility
    Copyright c 2004 Tech Science Press MCB, vol.1, no.4, pp.267-278, 2004 A Stochastic Analysis of a Brownian Ratchet Model for Actin-Based Motility Hong Qian1 Abstract: In recent single-particle tracking (SPT) ical models [Oosawa and Asakura (1975); Hill (1981); measurements on Listeria monocytogenes motility in Hill and Kirschner (1982); Hill (1987); Peskin, Odell, cells [Kuo and McGrath (2000)], the actin-based stochas- and Oster (1993); Mogilner and Oster (1996)]. Interac- tic dynamics of the bacterium movement has been ana- tions between experimental observations and theoretical lyzed statistically in terms of the mean-square displace- ideas have generated exciting research in both biophysics ment (MSD) of the trajectory. We present a stochastic and mathematical biology [Mogilner and Oster (2003)]. analysis of a simplified polymerization Brownian ratchet The molecular theory of actin polymerization also pro- (BR) model in which motions are limited by the bac- vides a unique opportunity in which the mechanics and terium movement. Analytical results are obtained and chemistry of a biological system are integrated. At the statistical data analyses are investigated. It is shown mesoscopic level, mechanics and chemistry are often two that the MSD of the stochastic bacterium movement is perspectives of a single physical process we call chemo- a monotonic quadratic function while the MSD for de- mechanics [Qian and Shapiro (1999); Qian (2000a); Qian trended trajectories is linear. Both the short-time relax- (2002b)]. ation and the long-time kinetics in terms the mean veloc- Following the seminal work of Peskin, Odell, and Os- ity and effective diffusion constant of the propelled bac- ter (1993), a sizable literature now exists on mathemat- terium are obtained from the MSD analysis.
    [Show full text]
  • Brownian Motors: Noisy Transport Far from Equilibrium
    Physics Reports 361 (2002) 57–265 www.elsevier.com/locate/physrep Brownian motors:noisy transport far from equilibrium Peter Reimann Institut fur Physik, Universitat Augsburg, Universitatsstr. 1, 86135 Augsburg, Germany Received August 2001; Editor:I : Procaccia Contents 1. Introduction 59 4.6. Biological applications:molecular 1.1. Outline and scope 59 pumps and motors 130 1.2. Historical landmarks 60 5. Tilting ratchets 133 1.3. Organization of the paper 61 5.1. Model 133 2. Basic concepts and phenomena 63 5.2. Adiabatic approximation 133 2.1. Smoluchowski–Feynman ratchet 63 5.3. Fast tilting 135 2.2. Fokker–Planck equation 67 5.4. Comparison with pulsating ratchets 136 2.3. Particle current 68 5.5. Fluctuating force ratchets 137 2.4. Solution and discussion 69 5.6. Photovoltaic e5ects 143 2.5. Tilted Smoluchowski–Feynman ratchet 72 5.7. Rocking ratchets 144 2.6. Temperature ratchet and ratchet e5ect 75 5.8. In=uence of inertia and Hamiltonian 2.7. Mechanochemical coupling 79 ratchets 148 2.8. Curie’s principle 80 5.9. Two-dimensional systems and entropic 2.9. Brillouin’s paradox 81 ratchets 150 2.10. Asymptotic analysis 82 5.10. Rocking ratchets in SQUIDs 152 2.11. Current inversions 83 5.11. Giant enhancement of di5usion 154 3. General framework 86 5.12. Asymmetrically tilting ratchets 156 3.1. Working model 86 6. Sundry extensions 159 3.2. Symmetry 90 6.1. Seebeck ratchets 160 3.3. Main ratchet types 91 6.2. Feynman ratchets 162 3.4. Physical basis 93 6.3. Temperature ratchets 164 3.5.
    [Show full text]
  • On the Feynman Ratchet and the Brownian Motor
    Open Journal of Biophysics, 2018, 8, 22-30 http://www.scirp.org/journal/ojbiphy ISSN Online: 2164-5396 ISSN Print: 2164-5388 On the Feynman Ratchet and the Brownian Motor Gyula Vincze1, Gyula Peter Szigeti2, Andras Szasz1 1Department of Biotechnics, St. Istvan University, Budapest, Hungary 2Institute of Human Physiology and Clinical Experimental Research, Semmelweis University, Budapest, Hungary How to cite this paper: Vincze, Gy., Szige- Abstract ti, Gy.P. and Szasz, A. (2018) On the Feyn- man Ratchet and the Brownian Motor. Open We study the Brownian ratchet conditions starting with Feynman’s proposal. Journal of Biophysics, 8, 22-30. We show that this proposal is incomplete, and is in fact non-workable. We https://doi.org/10.4236/ojbiphy.2018.81003 give the correct model for this ratchet. Received: October 18, 2017 Accepted: January 7, 2018 Keywords Published: January 10, 2018 Brownian Motor, Feynman Ratchet, Self-Sustaining Oscillation Copyright © 2018 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International 1. Introduction License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ The theory of material transport driven by fluctuations was worked out to ex- Open Access plain motor proteins [1]. These molecular motors constrain the motion domi- nantly in one-dimensional surmount energy wells and barriers. While the ob- stacles limit diffusion, thermal noise is a part of the thermal activation [2]. The directed motion is energized by the fluctuations of the height of the barrier, de- pending on the external modulation, and is coupled to the ATP-hydrolysis as a chemical energy source.
    [Show full text]
  • Machines of Life: Catalogue, Stochastic Process Modeling, Probabilistic
    Machines of life: catalogue, stochastic process modeling, probabilistic reverse engineering and the PIs- from Aristotle to Alberts Debashish Chowdhury1,2, ∗ 1Department of Physics, Indian Institute of Technology, Kanpur 208016, India 2Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA. (Dated: July 2, 2018) Molecular machines consist of either a single protein or a macromolecular complex composed of protein and RNA molecules. Just like their macroscopic counterparts, each of these nano-machines has an engine that “transduces” input energy into an output form which is then utilized by its cou- pling to a transmission system for appropriate operations. The theory of heat engines, pioneered by Carnot, rests on the second law of equilibrium thermodynamics. However, the engines of molecular machines, operate under isothermal conditions far from thermodynamic equilibrium. Moreover, one of the possible mechanisms of energy transduction, popularized by Feynman and called Brownian ratchet, does not even have any macroscopic counterpart. But, molecular machine is not synony- mous with Brownian ratchet; a large number of molecular machines actually execute a noisy power stroke, rather than operating as Brownian ratchet. The man-machine analogy, a topic of intense philosophical debate in which many leading philosophers like Aristotle and Descartes participated, was extended to similar analogies at the cellular and subcellular levels after the invention of opti- cal microscope. The idea of molecular machine, pioneered by Marcelo Malpighi, has been pursued vigorously in the last fifty years. It has become a well established topic of current interdisciplinary research as evident from the publication of a very influential paper by Alberts towards the end of the twentieth century.
    [Show full text]
  • Experimental Realization of Feynman's Ratchet
    Experimental realization of Feynman's ratchet Jaehoon Bang,1, ∗ Rui Pan,2, ∗ Thai M. Hoang,3, y Jonghoon Ahn,1 Christopher Jarzynski,4 H. T. Quan,2, 5, z and Tongcang Li1, 3, 6, 7, x 1School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA 2School of Physics, Peking University, Beijing 100871, China 3Department of Physics and Astronomy, Purdue University, West Lafayette, IN 47907, USA 4Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742 USA 5Collaborative Innovation Center of Quantum Matter, Beijing 100871, China 6Purdue Quantum Center, Purdue University, West Lafayette, IN 47907, USA 7Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA (Dated: March 16, 2018) 1 Abstract Feynman's ratchet is a microscopic machine in contact with two heat reservoirs, at temperatures TA and TB, that was proposed by Richard Feynman to illustrate the second law of thermody- namics. In equilibrium (TA = TB), thermal fluctuations prevent the ratchet from generating directed motion. When the ratchet is maintained away from equilibrium by a temperature differ- ence (TA 6= TB), it can operate as a heat engine, rectifying thermal fluctuations to perform work. While it has attracted much interest, the operation of Feynman's ratchet as a heat engine has not been realized experimentally, due to technical challenges. In this work, we realize Feynman's ratchet with a colloidal particle in a one dimensional optical trap in contact with two heat reser- voirs: one is the surrounding water, while the effect of the other reservoir is generated by a novel feedback mechanism, using the Metropolis algorithm to impose detailed balance.
    [Show full text]
  • Cellular Motions and Thermal Fluctuations: the Brownian Ratchet
    316 Biophysical Journal Volume 65 July 1993 316-324 Cellular Motions and Thermal Fluctuations: The Brownian Ratchet Charles S. Peskin,* Garrett M. Odell,* and George F. Oster§ *Courant Institute of Mathematical Sciences, New York, New York 10012; tDepartment of Zoology, University of Washington, Seattle, Washington 98195; §Departments of Molecular and Cellular Biology, and Entomology, University of California, Berkeley, California 94720 USA ABSTRACT We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Listeria, and protein translocation. INTRODUCTION Many types of cellular protrusions, including filopodia, This is the speed of a perfect BR. Note that as the ratchet lamellipodia, and acrosomal extension do not appear to in- interval, 8, decreases, the ratchet velocity increases. This is volve molecular motors. These processes transduce chemical because the frequency of smaller Brownian steps grows more bond energy into directed motion, but they do not operate in rapidly than the step size shrinks (when 8 is of the order of a mechanochemical cycle and need not depend directly upon a mean free path, then this formula obviously breaks down). nucleotide hydrolysis. In this paper we describe several such Several ingredients must be added to this simple expres- processes and present simple formulas for the velocity and sion to make it useful in real situations. First, the ratchet force they generate. We shall call these machines "Brownian cannot be perfect: a particle crossing a ratchet boundary may ratchets" (BR) because rectified Brownian motion is funda- occasionally cross back.
    [Show full text]
  • Confined Brownian Ratchets Paolo Malgaretti, Ignacio Pagonabarraga, and J
    Confined Brownian ratchets Paolo Malgaretti, Ignacio Pagonabarraga, and J. Miguel Rubi Citation: J. Chem. Phys. 138, 194906 (2013); doi: 10.1063/1.4804632 View online: http://dx.doi.org/10.1063/1.4804632 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v138/i19 Published by the American Institute of Physics. Additional information on J. Chem. Phys. Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors THE JOURNAL OF CHEMICAL PHYSICS 138, 194906 (2013) Confined Brownian ratchets Paolo Malgaretti,a) Ignacio Pagonabarraga, and J. Miguel Rubi Department de Fisica Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain (Received 8 March 2013; accepted 29 April 2013; published online 21 May 2013) We analyze the dynamics of Brownian ratchets in a confined environment. The motion of the parti- cles is described by a Fick-Jakobs kinetic equation in which the presence of boundaries is modeled by means of an entropic potential. The cases of a flashing ratchet, a two-state model, and a ratchet under the influence of a temperature gradient are analyzed in detail. We show the emergence of a strong cooperativity between the inherent rectification of the ratchet mechanism and the entropic bias of the fluctuations caused by spatial confinement. Net particle transport may take place in situa- tions where none of those mechanisms leads to rectification when acting individually. The combined rectification mechanisms may lead to bidirectional transport and to new routes to segregation phe- nomena. Confined Brownian ratchets could be used to control transport in mesostructures and to engineer new and more efficient devices for transport at the nanoscale.
    [Show full text]