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1. Proceedings of the 29th International Conference on DNA Computing and Molecular Programming (DNA 29)

   https://doi.org/10.4230/LIPIcs.DNA.29.8  

   Petrack, Joshua; Soloveichik, David; Doty, David (January 2023, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Chen, Ho-Lin; Evans, Constantine G. (Ed.)

   The field of chemical computation attempts to model computational behavior that arises when molecules, typically nucleic acids, are mixed together. By modeling this physical phenomenon at different levels of specificity, different operative computational behavior is observed. Thermodynamic binding networks (TBNs) is a highly abstracted model that focuses on which molecules are bound to each other in a "thermodynamically stable" sense. Stability is measured based only on how many bonds are formed and how many total complexes are in a configuration, without focusing on how molecules are binding or how they became bound. By defocusing on kinetic processes, TBNs attempt to naturally model the long-term behavior of a mixture (i.e., its thermodynamic equilibrium). We study the problem of signal amplification: detecting a small quantity of some molecule and amplifying its signal to something more easily detectable. This problem has natural applications such as disease diagnosis. By focusing on thermodynamically favored outcomes, we seek to design chemical systems that perform the task of signal amplification robustly without relying on kinetic pathways that can be error prone and require highly controlled conditions (e.g., PCR amplification). It might appear that a small change in concentrations can result in only small changes to the thermodynamic equilibrium of a molecular system. However, we show that it is possible to design a TBN that can "exponentially amplify" a signal represented by a single copy of a monomer called the analyte: this TBN has exactly one stable state before adding the analyte and exactly one stable state afterward, and those two states "look very different" from each other. In particular, their difference is exponential in the number of types of molecules and their sizes. The system can be programmed to any desired level of resilience to false positives and false negatives. To prove these results, we introduce new concepts to the TBN model, particularly the notions of a TBN’s entropy gap to describe how unlikely it is to be observed in an undesirable state, and feed-forward TBNs that have a strong upper bound on the number of polymers in a stable configuration. We also show a corresponding negative result: a doubly exponential upper bound, meaning that there is no TBN that can amplify a signal by an amount more than doubly exponential in the number and sizes of different molecules that comprise it. We leave as an open question to close this gap by either proving an exponential upper bound, or giving a construction with a doubly-exponential difference between the stable configurations before and after the analyte is added. Our work informs the fundamental question of how a thermodynamic equilibrium can change as a result of a small change to the system (adding a single molecule copy). While exponential amplification is traditionally viewed as inherently a non-equilibrium phenomenon, we find that in a strong sense exponential amplification can occur at thermodynamic equilibrium as well - where the "effect" (e.g., fluorescence) is exponential in types and complexity of the chemical components. 

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2. Foundations of a finite non-equilibrium statistical thermodynamics: extrinsic quantities

   https://doi.org/10.1088/1751-8121/ac798a  

   Ericok, O B; Mason, J K (July 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to conclude that statistical thermodynamics is in a state of crisis though. Indeed, the discussion about the microscopic origins of irreversibility has continued in the scientific community for more than a hundred years. This paper considers these questions while beginning to develop a statistical thermodynamics for finite non-equilibrium systems. Definitions are proposed for all of the extrinsic variables of the fundamental thermodynamic relation that are consistent with existing results in the equilibrium thermodynamic limit. The probability density function on the phase space is interpreted as a subjective uncertainty about the microstate, and the Gibbs entropy formula is modified to allow for entropy creation without introducing additional physics or modifying the phase space dynamics. Resolutions are proposed to the mixing paradox, Gibbs’ paradox, Loschmidt’s paradox, and Maxwell’s demon thought experiment. Finally, the extrinsic variables of the fundamental thermodynamic relation are evaluated as functions of time and space for a diffusing ideal gas, and the initial and final values are shown to coincide with the expected equilibrium values. 

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3. Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents

   https://doi.org/10.1145/3578579  

   Geffner, Ivan; Halpern, Joseph Y. (April 2023, Journal of the ACM)

   Abraham, Dolev, Geffner, and Halpern [ 1 ] proved that, in asynchronous systems, a (k, t)-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4( k+t ), where an equilibrium is ( k, t )-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4( k+t ) there exist ( k, t )-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing ( k, t )-robust mediators seems closely related to implementing asynchronous multiparty ( k+t )-secure computation [ 6 ], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of ( k+t )-secure computation, which we call ( k+t )-strict secure computation , to implementing ( k, t )-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be ( k+t )-strictly securely computed if n ≤ 4( k+t ). This also provides a simple alternative proof for the well-known lower bound of 4 t +1 on asynchronous secure computation in the presence of up to t malicious agents [ 4 , 8 , 10 ]. 

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4. Investigation of transcritical shock-droplet interaction using vapor-liquid equilibrium (VLE)-based CFD simulation

   Zhang, Hongyuan; Yang, Suo (May 2022, ILASS-Americas 32nd Annual Conference on Liquid Atomization and Spray Systems)

   To achieve high performance, the working pressure of liquid-fueled rocket engines, diesel engines, and gas turbines (based on deflagration or detonation) is continuously increasing, which could reach the thermodynamic critical pressure of the liquid fuel. For this reason, the studies of trans- and super-critical injection are getting more attention. However, most of the multiphase researches were mainly concentrated on single- or two-component systems, which cannot capture the multicomponent phase change in real high-pressure engines and gas turbines. The phase boundary, especially near the critical points, needs to be accurately determined to investigate the multicomponent effects in transcritical flow. This work used our previously developed thermodynamic model based on the vapor-liquid equilibrium (VLE) theory, which can predict the phase separation near the critical points. An in situ adaptive tabulation (ISAT) method was developed to accelerate the computation of the VLE model such that the expensive multicomponent VLE calculation can be cheap enough for CFD. The new thermodynamic model was integrated into OpenFOAM to build a VLE-based CFD solver. In this work, simulations are conducted using our new VLE-based CFD solver to reveal the phase change effects in transcritical flow. Specifically, shock-droplet interaction are investigated to reveal the shock-driven high pressure phase change. 

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5. An in situ adaptive tabulation based approach to multi-component transcritical flow simulation

   Zhang, Hongyuan; Yang, Suo. (May 2021, 12th U.S. National Combustion Meeting)

   null (Ed.)

   The studies of transcritical and supercritical flow have attracted much interest in the past 30 years. However, most of them mainly focus on the single-component system, whose critical point is constant. We use the vapor-liquid equilibrium (VLE) theory to capture the thermodynamic properties of the mixture and investigate transcritical flows (i.e., supercritical CO2 oxy-combustion systems). In sCO2 oxy-combustion systems, due to the presence of water from the previous cycles, the mixture critical point increases significantly, such that the phase separation could occur in both the compressor and combustor. However, the VLE solver increases the computation cost of fluid simulation significantly, which limited the size of simulations we can conduct. Naturally, tabulation methods can be used to store the VLE solutions to avoids redundant computation. However, the size of the VLE table increases exponentially with respect to the number of components. When the number of species components is greater than three, the size of the VLE table far exceeds the RAM’s limit in today’s standard computers. In this research, an online tabulation method based on In Situ Adaptive Tabulation (ISAT) is developed to accelerate the computation of multicomponent fluids based on VLE theory. Accuracy and efficiency are analyzed and discussed. The CFD solver used in this research is based on the Pressure-Implicit with Splitting of Operators (PISO) method. Peng-Robinson equation of state (EOS) is used in the calculations of phase equilibrium. 

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