BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

BAR-Based Multi-dimensional Nonequilibrium Pulling for Indirect Construction of QM/MM Free Energy Landscape: From Semi-Empirical to Ab Initio

<p>The indirect method for the construction of Quantum mechanics (QM)/ molecular mechanics (MM) free energy landscapes provides a cheaper alternative of free energy simulations at QM level. The indirect method features a direct calculation of the free energy profile at a relatively cheap low-level Hamiltonian and a low-level to high-level correction. In the thermodynamic cycle, the direct low-level calculation along the physically meaningful reaction coordinate is corrected via the alchemical method, which is often achieved with perturbation-based techniques. Often the indirect method can lead to about an order of magnitude speedup in free energy simulation. In our previous work, a multi-dimensional nonequilibrium pulling framework is proposed for the indirect construction of QM/MM free energy landscapes. The method relies on bidirectional nonequilibrium pulling and bidirectional reweighting with the statistically optimal estimator. In the previous work, we focus on obtaining semi-empirical QM (SQM) results indirectly from direct MM simulations and MM<->SQM corrections. In this work, we apply this method to obtain results under ab initio QM Hamiltonians by combining direct SQM results and SQM<->QM corrections. The indirect nonequilibrium scheme is tested on a dihedral flipping case and a series of SQM and QM Hamiltonians are benchmarked. It is observed that PM6 achieves the best performance among the low-level Hamiltonians, while AM1 and MNDO perform less well. Therefore, we recommend using PM6 as the low-level theory in the indirect free energy simulation. The comparison between the indirect results from different SQM Hamiltonians could also provide some hints on the development of charge models. As AM1 can be corrected with the bond charge correction (BCC) to provide a cheap and accurate charge model, which is able to accurately reproduce the electrostatic potential (ESP) at HF level, PM6 would be able to do the same thing. Considering its higher similarity to the high-level Hamiltonians, the PM6-BCC model could be more accurate than the existing AM1-BCC model. Another central result in the current work is a basic protocol of choosing the strength of restraints and an appropriate time step in nonequilibrium free energy simulation at the stiff spring limit. We provide theoretical derivations to emphasize the importance of using a sufficiently large force constant and choosing an appropriate time step. It is worth noting that a general rule of thumb for choosing the time step, according to our derivation, is that a time step of 1 fs or smaller should be used, as long as the stiff spring approximation is employed, even in simulations with constraints on bonds involving hydrogen atoms. </p>

Evolution of mantis shrimp telson armour and its role in ritualized fighting

Mantis shrimp possess both formidable weapons and impact-resistant armour that clash during ritualized combat. The telson is one of few biological structures known to withstand the repeated high impact forces of smashing mantis shrimp strikes, and it is hypothesized that this pairing of armour and weapon is associated with the evolution of telson sparring. We carried out a comparative analysis of telson impact mechanics across 15 mantis shrimp species to assess if the telsons of sparring species (i) are consistently specialized for impact-resistance, (ii) are more impact-resistant than those of non-sparring species, and (iii) have impact parameters that correlate with body size, and thereby useful for assessment. Our data from ball drop tests show that the telsons of all species function like a stiff spring that dissipates most of the impact energy, but none of the measured impact parameters are correlated with the occurrence of sparring behaviour. Impact parameters were correlated with body mass for only some species, suggesting that it is not broadly useful for size assessment during ritualized fighting. Contrary to expectation, sparring mantis shrimp do not appear to have coevolved telson armour that is more robust to impact than non-sparring species. Rather, telson structure is inherently impact-resistant.

Including Housing–Casing Fluid in a Lateral Rotordynamics Analysis on Electric Submersible Pumps

Stability and synchronous-response predictions, which were presented by Childs et al. (2014, “A Lateral Rotordynamics Primer on Electric Submersible Pumps (ESPs) for Deep Subsea Applications,” 43th International Pump Users Symposium, Texas A&M University, College Station, TX, pp. 1–18), are re-evaluated to include the effect of the fluid between the pump housing and well casing. Conclusions are made based on these new findings. The same two-line rotor–housing model is used to model the pump's rotor and its housing. The model dimensions are based on direct measurements of an ESP. The pump rotor and pump housing are only connected together at each stage by reaction forces and moments from seals and bushings. The rotor model is pinned to the housing at the rotor's ends. The housing model is pinned to ground at its ends. Synchronous response predictions are presented for: (1) relative rotor–housing motion and (2) housing velocity-response amplitudes. When handling viscosity of water, the rotor–housing model is predicted to be stable at new (centered) 1× clearances but rapidly becomes unstable with enlarged clearances (2× and 3×), primarily due to rapidly dropping rotor–housing natural frequencies. The impact of introducing effective swirl brakes for the stages' wear ring seals was investigated for a pump running at 3600 rpm. Their predicted impact on stability and synchronous response was: (1) Onset speeds of instabilities (OSIs) were elevated well above running speed and (2) synchronous response amplitudes were reduced modestly. Housing-response amplitudes varied considerably with the choice of housing-termination locations. For a pump rotor length of Lr, varying the lengths of a centered housing over 1.5 Lr, 2 Lr, and 3 Lr changes the housing's natural frequency. This natural frequency can coincide with the running speed with proper termination conditions. If the running speed and natural frequency coincide, large housing vibration amplitudes associated with resonance would exceed most vibration regulations; however, relative rotor–stator response amplitudes were a small fraction of clearances for all the cases. When handling emulsions at markedly higher viscosities, with a pump speed of 3600 rpm and new centered clearances, the predicted OSI was below 300 rpm. The OSI rapidly increased as the seals were displaced eccentrically, quickly elevating the first rotor–stator natural frequency above 1800 rpm and the OSI above 3600 rpm. With the model stabilized at 0.2 eccentricity, the synchronous relative rotor–housing amplitudes were a small fraction of seal clearances. Swirl brakes were not predicted to be effective in elevating pump OSIs for high viscosity fluids with new clearances; however, they became effective as clearances were increased. An ESP housing can contact the well casing in many possible scenarios (axial locations, contact-area length or girth, etc.). A midspan, point radial contact was examined and modeled as a stiff-spring connection from the housing to ground. For both water and oil–water emulsions, a stiff housing-to-casing contact produced major elliptical housing motion (versus circular motion without contact). However, it had a comparably minor impact on relative rotor–housing response amplitudes or rotordynamic stability.

Including Housing-Casing Fluid in a Lateral Rotordynamics Analysis on Electric Submersible Pumps

Stability and synchronous-response predictions, which were presented in the paper “A Lateral Rotordynamics Primer on Electric Submersible Pumps (ESPs) for Deep Subsea Applications” [1], are reevaluated to include the effect of the fluid between the pump housing and well casing. Conclusions are made based on these new findings. The same two-line rotor-housing model is used to model the pump’s rotor and its housing. The model dimensions are based on direct measurements of an ESP. The pump rotor and pump housing are only connected together at each stage by reaction forces and moments from seals and bushings. The rotor model is pinned to the housing at the rotor’s ends. The housing model is pinned to ground at its ends. Synchronous response predictions are presented for: (1) relative rotor-housing motion, and (2) housing velocity-response amplitudes. When handling viscosity of water, the rotor-housing model is predicted to be stable at new (centered) 1X clearances but rapidly becomes unstable with enlarged clearances (2X, 3X), primarily due to rapidly dropping rotor-housing natural frequencies. The impact of introducing effective swirl brakes for the stages’ wear ring seals was investigated for a pump running at 3600 rpm. Their predicted impact on stability and synchronous response were: (1) Onset speeds of instabilities (OSIs) were elevated well above running speed, and (2) Synchronous response amplitudes were reduced modestly. Housing-response amplitudes varied considerably with the choice of housing-termination locations. For a pump rotor length of Lr, varying the lengths of a centered housing over 1.5Lr, 2Lr, and 3Lr changes the housing’s natural frequency. This natural frequency can coincide with the running speed with proper termination conditions. If the running speed coincided large housing vibration amplitudes associated with resonance would exceed most vibration regulations; however, relative rotor-stator-response amplitudes were a small fraction of clearances for all cases. When handling emulsions at markedly higher viscosities, with a pump speed of 3600 rpm and new centered clearances, the predicted OSI was below 300 rpm. The OSI rapidly increased as the seals were displaced eccentrically, quickly elevating the 1st rotor-stator natural frequency above 1800 rpm and the OSI above 3600 rpm. With the model stabilized at 0.2 eccentricity, the synchronous relative rotor-housing amplitudes were a small fraction of seal clearances. Swirl brakes were not predicted to be effective in elevating pump OSIs for high viscosity fluids with new clearances; however, they became effective as clearances were increased. An ESP housing can contact the well casing in many possible scenarios (axial locations, contact-area length or girth, etc.). A mid-span, point radial contact was examined and modeled as a stiff-spring connection from the housing to ground. For both water and oil-water emulsions, a stiff housing-to-casing contact produced major elliptical housing motion (versus circular motion without contact). However, it had a comparably minor impact on relative rotor-housing response amplitudes or rotordynamic stability.

Design and analysis of a gravity-based passive tracking mechanism to a linear solar concentrating collector

A novel gravity-based power-free solar tracking mechanism has been developed to track a linear solar concentrating collector. Multireflector compound parabolic collectors having three parabolic segments and two flat surfaces is chosen due to its high intercept factor and suitability to the current tracking. The working of tracking mechanism is studied to find the tracking loads in the east and the west sides of collector. A generalized mathematical model is derived to simulate the tracking motion from the sunrise to sunset. The identified design variants are sprocket wheel diameter, spring stiffness, solar collector’s weight, counter balance, and tracking wheel radius. The spring length is derived from the constraints. To make a compact product, the tracking load has been minimized at large sprocket wheel, low stiff spring, lighter collector weight, and small radius of tracking. For a typical collector load of 50 kg, the designed tracking load is 50 kg with 620 mm spring length, 250 mm of sprocket wheel diameter and 60 mm tracking radius.