Ribbons are a class of slender structures whose length, width, and thickness are widely separated... more Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a unive...
Chaos: An Interdisciplinary Journal of Nonlinear Science
The controllability of complex networks may be applicable for understanding how to control a comp... more The controllability of complex networks may be applicable for understanding how to control a complex social network, where members share their opinions and influence one another. Previous works in this area have focused on controllability, energy cost, or optimization under the assumption that all nodes are compliant, passing on information neutrally without any preferences. However, the assumption on nodal neutrality should be reassessed, given that in networked social systems, some people may hold fast to their personal beliefs. By introducing some stubborn agents, or zealots, who hold steadfast to their beliefs and seek to influence others, the control energy is computed and compared against those without zealots. It was found that the presence of zealots alters the energy cost at a quadratic rate with respect to their own fixed beliefs. However, whether or not the zealots’ presence increases or decreases the energy cost is affected by the interplay between different parameters s...
Thermally activated escape processes in multi-dimensional potentials are of interest to a variety... more Thermally activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape-or the mean first-passage time (MFPT)-is important. Unlike in one dimension, there is no general, exact formula for the MFPT. However, Langer's formula, a multi-dimensional generalization of Kramers's one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers's and Langer's formulas are related to one another by the potential of mean force (PMF): when calculated along a particular direction (the unstable mode at the saddle point) and substituted into Kramers's formula, the result is Langer's formula. We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, although discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point.
In one-dimension, the diffusion of particles along a line is slowed by the addition of energy bar... more In one-dimension, the diffusion of particles along a line is slowed by the addition of energy barriers. The same is true in two-dimensions, provided that the confining channel in which the particles move doesn't change shape. However, if the shape changes then this is no longer necessarily true; adding energy barriers can enhance the rate of diffusion, and even restore free diffusion. We explore these effects for a channel with a sinusoidally varying curvature.
Bulletin of the American Physical Society, Mar 4, 2020
The simplicity principle states that the human visual system prefers the simplest interpretation.... more The simplicity principle states that the human visual system prefers the simplest interpretation. However, conventional coding models could not resolve the incompatibility between predictions from the global minimum principle and the local minimum principle. By quantitatively evaluating the total information content of all possible visual interpretations, we show that the perceived pattern is always the one with the simplest local completion as well as the least total surprisal globally, thus solving this apparent conundrum. Our proposed framework consist of (1) the information content of visual contours, (2) direction of visual contour, and (3) the von Mises distribution governing human visual expectation. We used it to explain the perception of prominent visual illusions such as Kanizsa triangle, Ehrenstein cross, and Rubin's vase. This provides new insight into the celebrated simplicity principle and could serve as a fundamental explanation of the perception of illusory boundaries and the bi-stability of perceptual grouping.
in recent years, fullerenes and their derivatives have attracted much attention in drug delivery ... more in recent years, fullerenes and their derivatives have attracted much attention in drug delivery and photodynamic therapy due to their antioxidant behavior and biocompatible nature. The increasing usage of fullerene nanoparticles have raised concern about their possible impact on health and environment. in this context, many studies have been conducted and both positive and negative impacts on biological processes have been determined depending upon various factors. Although the toxicity of fullerenes is still a topic of discussion, lipid peroxidation has been pointed out as the major toxicity mechanism induced by fullerene nanoparticles. For this reason, it is important to understand the interactions between fullerenes and peroxidized membranes. In the present study, pristine and janus fullerene nanoparticles are compared through their interactions with various lipid bilayers, and their different levels of peroxidized forms. The translocation of fullerenes reveal that pristine fullerenes reside close to the bilayer center while janus models shift towards to the head-groups. in all cases, fullerenes permeate into the fully peroxidized membranes faster than into the regular phospholipid bilayers. No damage to the membrane integrity is observed.
In order to understand controlling a complex system, an estimation of the required effort needed ... more In order to understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time dynamics. However, continuous-time modelling is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modelling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward towards developing realistic control of complex social systems.
The simplicity principle states that the human visual system prefers the simplest interpretation.... more The simplicity principle states that the human visual system prefers the simplest interpretation. However, conventional coding models could not resolve the incompatibility between predictions from the global minimum principle and the local minimum principle. By quantitatively evaluating the total information content of all possible visual interpretations, we show that the perceived pattern is always the one with the simplest local completion as well as the least total surprisal globally, thus solving this apparent conundrum. Our proposed framework consist of (1) the information content of visual contours, (2) direction of visual contour, and (3) the von Mises distribution governing human visual expectation. We used it to explain the perception of prominent visual illusions such as Kanizsa triangle, Ehrenstein cross, and Rubin's vase. This provides new insight into the celebrated simplicity principle and could serve as a fundamental explanation of the perception of illusory bound...
The energy needed in controlling a complex network is a problem of practical importance. Recent w... more The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, how target nodes are arranged with respect to control energy has yet been explored. Here, we propose an iterative method based on stiefel manifold optimization of selectable target node matrix to reduce control energy. We derived the matrix derivative gradient needed for the search algorithm in a general way, and searched for target nodes which result in reduced control energy, given that driver nodes placement is fixed. Our findings reveal that when the path distances from driver nodes to target nodes are minimised, control energy is optimal. We also applied the algorithm to various model and real networks. The simulation results show that when compared to heuristic selection strategies of choosing target nodes, the control en...
Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a ... more Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply morphometric, mechanistic, and macroevolutionary analyses to the egg shapes of 1400 bird species. We characterize egg-shape diversity in terms of two biologically relevant variables, asymmetry and ellipticity, allowing us to quantify the observed morphologies in a two-dimensional morphospace. We then propose a simple mechanical model that explains the observed egg-shape diversity based on geometric and material properties of the egg membrane. Finally, using phylogenetic models, we show that egg shape correlates with flight ability on broad taxonomic scales, suggesting that adaptations for flight may have been critical drivers of egg-shape variation in birds.
Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated ... more Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.
We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential ener... more We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U (x), where the height Q of each section is obtained from the exponential distribution p(Q) = aβexp(−aβQ), where β is the reciprocal thermal energy, and a > 0. The averaged effective diffusion coefficient D eff is introduced to characterize the diffusive motion: x 2 = 2 D eff t. A general expression for D eff in terms of U (x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a = 1, and a reduction to free diffusion as a → ∞. The behavior of D eff around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.
The energy needed in controlling a complex network is a problem of practical importance. Recent w... more The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, optimizing control energy with respect to target nodes selection has yet been considered. In this work, we propose an iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy. We derive the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed. Our findings reveal that the control energy is optimal when the path distances from driver nodes to target nodes are minimized. We corroborate our algorithm with extensive simulations on elementary network topologies, random and scale-free networks, as well as various real networks. The sim...
We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) ... more We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p = 0, the dynamics remain invariant in each renormalizationgroup (RG) transformation. Two fully attractive fixed points, ρ * c = 0 and 1, and one unstable fixed point, ρ * c = 1/(v max + 1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various v max. The critical exponent appears to decrease weakly with v max from ν = 1.62 to the asymptotical value of 1.00. For the random case p > 0, the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p → 0 is studied with simulation, and the RG flow in the ρ−p plane is obtained. The fixed points p = 0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.
Following the recent work by Deffner and Saxena [1], where the Jarzynski equality is generalised ... more Following the recent work by Deffner and Saxena [1], where the Jarzynski equality is generalised to non-Hermitian quantum mechanics, we prove in this work a stronger form of Jarzynski equality, the Crooks fluctuation theorem, also in the non-Hermitian formalism when the system is in the unbroken PTsymmetric phase.
Quantum Walk (QW) has very different transport properties to its classical counterpart due to int... more Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on t...
Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a ... more Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply morphometric, mechanistic, and macroevolutionary analyses to the egg shapes of 1400 bird species. We characterize egg-shape diversity in terms of two biologically relevant variables, asymmetry and ellipticity, allowing us to quantify the observed morphologies in a two-dimensional morphospace. We then propose a simple mechanical model that explains the observed egg-shape diversity based on geometric and material properties of the egg membrane. Finally, using phylogenetic models, we show that egg shape correlates with flight ability on broad taxonomic scales, suggesting that adaptations for flight may have been critical drivers of egg-shape variation in birds.
The crumpling of spherical crystalline lattices where the topological defects are frozen is studi... more The crumpling of spherical crystalline lattices where the topological defects are frozen is studied. The geometry of the crumpled membrane is found to depend on the set of topological defects and more exotic defect sets can result in crumpled shapes resembling that of the Platonic and Archimedean solids. The phase diagram of the crumpled spheres can be categorized by two dimensionless numbers h/R (aspect ratio) and R/a (lattice ratio), where h is the thickness of the shell, R is the radius of the initial sphere and a is the average bond length of the triangulation. The shapes of the crumpled membrane can be understood using rotationally invariant quantities formed from spherical harmonics coefficients and a Landau free energy can be written, involving quadratic and cubic rotational invariants. Shells with different topological defects have qualitatively different hysteresis behaviors and the transitions appear to be first order in general.
Ribbons are a class of slender structures whose length, width, and thickness are widely separated... more Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a unive...
Chaos: An Interdisciplinary Journal of Nonlinear Science
The controllability of complex networks may be applicable for understanding how to control a comp... more The controllability of complex networks may be applicable for understanding how to control a complex social network, where members share their opinions and influence one another. Previous works in this area have focused on controllability, energy cost, or optimization under the assumption that all nodes are compliant, passing on information neutrally without any preferences. However, the assumption on nodal neutrality should be reassessed, given that in networked social systems, some people may hold fast to their personal beliefs. By introducing some stubborn agents, or zealots, who hold steadfast to their beliefs and seek to influence others, the control energy is computed and compared against those without zealots. It was found that the presence of zealots alters the energy cost at a quadratic rate with respect to their own fixed beliefs. However, whether or not the zealots’ presence increases or decreases the energy cost is affected by the interplay between different parameters s...
Thermally activated escape processes in multi-dimensional potentials are of interest to a variety... more Thermally activated escape processes in multi-dimensional potentials are of interest to a variety of fields, so being able to calculate the rate of escape-or the mean first-passage time (MFPT)-is important. Unlike in one dimension, there is no general, exact formula for the MFPT. However, Langer's formula, a multi-dimensional generalization of Kramers's one-dimensional formula, provides an approximate result when the barrier to escape is large. Kramers's and Langer's formulas are related to one another by the potential of mean force (PMF): when calculated along a particular direction (the unstable mode at the saddle point) and substituted into Kramers's formula, the result is Langer's formula. We build on this result by using the PMF in the exact, one-dimensional expression for the MFPT. Our model offers better agreement with Brownian dynamics simulations than Langer's formula, although discrepancies arise when the potential becomes less confining along the direction of escape. When the energy barrier is small our model offers significant improvements upon Langer's theory. Finally, the optimal direction along which to evaluate the PMF no longer corresponds to the unstable mode at the saddle point.
In one-dimension, the diffusion of particles along a line is slowed by the addition of energy bar... more In one-dimension, the diffusion of particles along a line is slowed by the addition of energy barriers. The same is true in two-dimensions, provided that the confining channel in which the particles move doesn't change shape. However, if the shape changes then this is no longer necessarily true; adding energy barriers can enhance the rate of diffusion, and even restore free diffusion. We explore these effects for a channel with a sinusoidally varying curvature.
Bulletin of the American Physical Society, Mar 4, 2020
The simplicity principle states that the human visual system prefers the simplest interpretation.... more The simplicity principle states that the human visual system prefers the simplest interpretation. However, conventional coding models could not resolve the incompatibility between predictions from the global minimum principle and the local minimum principle. By quantitatively evaluating the total information content of all possible visual interpretations, we show that the perceived pattern is always the one with the simplest local completion as well as the least total surprisal globally, thus solving this apparent conundrum. Our proposed framework consist of (1) the information content of visual contours, (2) direction of visual contour, and (3) the von Mises distribution governing human visual expectation. We used it to explain the perception of prominent visual illusions such as Kanizsa triangle, Ehrenstein cross, and Rubin's vase. This provides new insight into the celebrated simplicity principle and could serve as a fundamental explanation of the perception of illusory boundaries and the bi-stability of perceptual grouping.
in recent years, fullerenes and their derivatives have attracted much attention in drug delivery ... more in recent years, fullerenes and their derivatives have attracted much attention in drug delivery and photodynamic therapy due to their antioxidant behavior and biocompatible nature. The increasing usage of fullerene nanoparticles have raised concern about their possible impact on health and environment. in this context, many studies have been conducted and both positive and negative impacts on biological processes have been determined depending upon various factors. Although the toxicity of fullerenes is still a topic of discussion, lipid peroxidation has been pointed out as the major toxicity mechanism induced by fullerene nanoparticles. For this reason, it is important to understand the interactions between fullerenes and peroxidized membranes. In the present study, pristine and janus fullerene nanoparticles are compared through their interactions with various lipid bilayers, and their different levels of peroxidized forms. The translocation of fullerenes reveal that pristine fullerenes reside close to the bilayer center while janus models shift towards to the head-groups. in all cases, fullerenes permeate into the fully peroxidized membranes faster than into the regular phospholipid bilayers. No damage to the membrane integrity is observed.
In order to understand controlling a complex system, an estimation of the required effort needed ... more In order to understand controlling a complex system, an estimation of the required effort needed to achieve control is vital. Previous works have addressed this issue by studying the scaling laws of energy cost in a general way with continuous-time dynamics. However, continuous-time modelling is unable to capture conformity behavior, which is common in many complex social systems. Therefore, to understand controlling social systems with conformity, discrete-time modelling is used and the energy cost scaling laws are derived. The results are validated numerically with model and real networks. In addition, it is shown through simulations that heterogeneous scale-free networks are less controllable, requiring a higher number of minimum drivers. Since conformity-based model relates to various complex systems, such as flocking, or evolutionary games, the results of this paper represent a step forward towards developing realistic control of complex social systems.
The simplicity principle states that the human visual system prefers the simplest interpretation.... more The simplicity principle states that the human visual system prefers the simplest interpretation. However, conventional coding models could not resolve the incompatibility between predictions from the global minimum principle and the local minimum principle. By quantitatively evaluating the total information content of all possible visual interpretations, we show that the perceived pattern is always the one with the simplest local completion as well as the least total surprisal globally, thus solving this apparent conundrum. Our proposed framework consist of (1) the information content of visual contours, (2) direction of visual contour, and (3) the von Mises distribution governing human visual expectation. We used it to explain the perception of prominent visual illusions such as Kanizsa triangle, Ehrenstein cross, and Rubin's vase. This provides new insight into the celebrated simplicity principle and could serve as a fundamental explanation of the perception of illusory bound...
The energy needed in controlling a complex network is a problem of practical importance. Recent w... more The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, how target nodes are arranged with respect to control energy has yet been explored. Here, we propose an iterative method based on stiefel manifold optimization of selectable target node matrix to reduce control energy. We derived the matrix derivative gradient needed for the search algorithm in a general way, and searched for target nodes which result in reduced control energy, given that driver nodes placement is fixed. Our findings reveal that when the path distances from driver nodes to target nodes are minimised, control energy is optimal. We also applied the algorithm to various model and real networks. The simulation results show that when compared to heuristic selection strategies of choosing target nodes, the control en...
Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a ... more Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply morphometric, mechanistic, and macroevolutionary analyses to the egg shapes of 1400 bird species. We characterize egg-shape diversity in terms of two biologically relevant variables, asymmetry and ellipticity, allowing us to quantify the observed morphologies in a two-dimensional morphospace. We then propose a simple mechanical model that explains the observed egg-shape diversity based on geometric and material properties of the egg membrane. Finally, using phylogenetic models, we show that egg shape correlates with flight ability on broad taxonomic scales, suggesting that adaptations for flight may have been critical drivers of egg-shape variation in birds.
Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated ... more Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.
We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential ener... more We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U (x), where the height Q of each section is obtained from the exponential distribution p(Q) = aβexp(−aβQ), where β is the reciprocal thermal energy, and a > 0. The averaged effective diffusion coefficient D eff is introduced to characterize the diffusive motion: x 2 = 2 D eff t. A general expression for D eff in terms of U (x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a = 1, and a reduction to free diffusion as a → ∞. The behavior of D eff around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.
The energy needed in controlling a complex network is a problem of practical importance. Recent w... more The energy needed in controlling a complex network is a problem of practical importance. Recent works have focused on the reduction of control energy either via strategic placement of driver nodes, or by decreasing the cardinality of nodes to be controlled. However, optimizing control energy with respect to target nodes selection has yet been considered. In this work, we propose an iterative method based on Stiefel manifold optimization of selectable target node matrix to reduce control energy. We derive the matrix derivative gradient needed for the search algorithm in a general way, and search for target nodes which result in reduced control energy, assuming that driver nodes placement is fixed. Our findings reveal that the control energy is optimal when the path distances from driver nodes to target nodes are minimized. We corroborate our algorithm with extensive simulations on elementary network topologies, random and scale-free networks, as well as various real networks. The sim...
We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) ... more We study the phase transition from free flow to congested phases in the Nagel-Schreckenberg (NS) model by using the dynamically driven renormalization group (DDRG). The breaking probability p that governs the driving strategy is investigated. For the deterministic case p = 0, the dynamics remain invariant in each renormalizationgroup (RG) transformation. Two fully attractive fixed points, ρ * c = 0 and 1, and one unstable fixed point, ρ * c = 1/(v max + 1), are obtained. The critical exponent ν which is related to the correlation length is calculated for various v max. The critical exponent appears to decrease weakly with v max from ν = 1.62 to the asymptotical value of 1.00. For the random case p > 0, the transition rules in the coarse-grained scale are found to be different from the NS specification. To have a qualitative understanding of the effect of stochasticity, the case p → 0 is studied with simulation, and the RG flow in the ρ−p plane is obtained. The fixed points p = 0 and 1 that govern the driving strategy of the NS model are found. A short discussion on the extension of the DDRG method to the NS model with the open-boundary condition is outlined.
Following the recent work by Deffner and Saxena [1], where the Jarzynski equality is generalised ... more Following the recent work by Deffner and Saxena [1], where the Jarzynski equality is generalised to non-Hermitian quantum mechanics, we prove in this work a stronger form of Jarzynski equality, the Crooks fluctuation theorem, also in the non-Hermitian formalism when the system is in the unbroken PTsymmetric phase.
Quantum Walk (QW) has very different transport properties to its classical counterpart due to int... more Quantum Walk (QW) has very different transport properties to its classical counterpart due to interference effects. Here we study the discrete-time quantum walk (DTQW) with on-site static/dynamic phase disorder following either binary or uniform distribution in both one and two dimensions. For one dimension, we consider the Hadamard coin; for two dimensions, we consider either a 2-level Hadamard coin (Hadamard walk) or a 4-level Grover coin (Grover walk) for the rotation in coin-space. We study the transport properties e.g. inverse participation ratio (IPR) and the standard deviation of the density function (σ) as well as the coin-position entanglement entropy (EE), due to the two types of phase disorders and the two types of coins. Our numerical simulations show that the dimensionality, the type of coins, and whether the disorder is static or dynamic play a pivotal role and lead to interesting behaviors of the DTQW. The distribution of the phase disorder has very minor effects on t...
Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a ... more Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply morphometric, mechanistic, and macroevolutionary analyses to the egg shapes of 1400 bird species. We characterize egg-shape diversity in terms of two biologically relevant variables, asymmetry and ellipticity, allowing us to quantify the observed morphologies in a two-dimensional morphospace. We then propose a simple mechanical model that explains the observed egg-shape diversity based on geometric and material properties of the egg membrane. Finally, using phylogenetic models, we show that egg shape correlates with flight ability on broad taxonomic scales, suggesting that adaptations for flight may have been critical drivers of egg-shape variation in birds.
The crumpling of spherical crystalline lattices where the topological defects are frozen is studi... more The crumpling of spherical crystalline lattices where the topological defects are frozen is studied. The geometry of the crumpled membrane is found to depend on the set of topological defects and more exotic defect sets can result in crumpled shapes resembling that of the Platonic and Archimedean solids. The phase diagram of the crumpled spheres can be categorized by two dimensionless numbers h/R (aspect ratio) and R/a (lattice ratio), where h is the thickness of the shell, R is the radius of the initial sphere and a is the average bond length of the triangulation. The shapes of the crumpled membrane can be understood using rotationally invariant quantities formed from spherical harmonics coefficients and a Landau free energy can be written, involving quadratic and cubic rotational invariants. Shells with different topological defects have qualitatively different hysteresis behaviors and the transitions appear to be first order in general.
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Papers by Ee Hou Yong