Abstract Understanding how a stressor applied on a biological system shapes its evolution is key to achieving targeted evolutionary control. Here we present a toy model of two interacting lattice proteins to quantify the response to the selective pressure defined by the binding energy. We generate sequence data of proteins and study how the sequence and structural properties of dimers are affected by the applied selective pressure, both during the evolutionary process and in the stationary regime. In particular we show that internal contacts of native structures lose strength, while inter-structure contacts are strengthened due to the folding-binding competition. We discuss how dimerization is achieved through enhanced mutability on the interacting faces, and how the designability of each native structure changes upon introduction of the stressor.
{"title":"Evolutionary dynamics of a lattice dimer: a toy model for stability vs. affinity trade-offs in proteins","authors":"Emanuele Loffredo, Elisabetta Vesconi, Rostam Razban, Orit Peleg, Eugene Shakhnovich, Simona Cocco, Remi Monasson","doi":"10.1088/1751-8121/acfddc","DOIUrl":"https://doi.org/10.1088/1751-8121/acfddc","url":null,"abstract":"Abstract Understanding how a stressor applied on a biological system shapes its evolution is key to achieving targeted evolutionary control. Here we present a toy model of two interacting lattice proteins to quantify the response to the selective pressure defined by the binding energy. We generate sequence data of proteins and study how the sequence and structural properties of dimers are affected by the applied selective pressure, both during the evolutionary process and in the stationary regime. In particular we show that internal contacts of native structures lose strength, while inter-structure contacts are strengthened due to the folding-binding competition. We discuss how dimerization is achieved through enhanced mutability on the interacting faces, and how the designability of each native structure changes upon introduction of the stressor.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135805983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1088/1751-8121/ad02cc
Lorenzo Caprini, Hartmut Lowen, Umberto Marini Bettolo Marconi
Abstract The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered structures. Motivated by recent numerical investigations concerning the nonuniform distribution of entropy production and its relation to the configurational properties of active systems, we study theoretically and numerically the spatial profile of the entropy production rate when an active solid contains an isotopic mass defect. The theoretical study of such an imperfect active crystal is conducted by employing a perturbative analysis that considers the perfectly ordered harmonic solid as a reference system. The perturbation theory predicts a nonuniform profile of the entropy production extending over large distances from the position of the impurity. The entropy production rate decays exponentially to its bulk value with a typical healing length that coincides with the correlation length of the spatial velocity correlations characterizing
the perfect active solids in the absence of impurities. The theory is validated against numerical simulations of an active Brownian particle crystal in two dimensions with Weeks-Chandler-Andersen repulsive interparticle potential.
{"title":"Inhomogeneous entropy production in active crystals with point imperfections","authors":"Lorenzo Caprini, Hartmut Lowen, Umberto Marini Bettolo Marconi","doi":"10.1088/1751-8121/ad02cc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad02cc","url":null,"abstract":"Abstract The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered structures. Motivated by recent numerical investigations concerning the nonuniform distribution of entropy production and its relation to the configurational properties of active systems, we study theoretically and numerically the spatial profile of the entropy production rate when an active solid contains an isotopic mass defect. The theoretical study of such an imperfect active crystal is conducted by employing a perturbative analysis that considers the perfectly ordered harmonic solid as a reference system. The perturbation theory predicts a nonuniform profile of the entropy production extending over large distances from the position of the impurity. The entropy production rate decays exponentially to its bulk value with a typical healing length that coincides with the correlation length of the spatial velocity correlations characterizing
the perfect active solids in the absence of impurities. The theory is validated against numerical simulations of an active Brownian particle crystal in two dimensions with Weeks-Chandler-Andersen repulsive interparticle potential.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014644","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1088/1751-8121/ad02ce
Ivan Nikolaevich Burenev, Filippo Colomo, Andrea Maroncelli, Andrei Georgievich Pronko
Abstract We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states, boxed plane partitions, and fishnet diagrams in quantum field theory. In the scaling limit, the model exhibits the emergence of an arctic curve separating a central disordered region from six frozen `corners' of ferroelectric or anti-ferroelectric type. We determine the analytic expression of the interface by means of the Tangent Method. We supplement this heuristic method with an alternative, rigorous derivation of the arctic curve. This is based on the exact evaluation of suitable correlation functions, devised to detect spatial transition from order to disorder, in terms of the partition function of some discrete log-gas associated to the orthogonalizing measure of the Hahn polynomials. As a by-product, we also deduce that the arctic curve's fluctuations are governed by the Tracy-Widom distribution.
{"title":"Arctic curves of the four-vertex model","authors":"Ivan Nikolaevich Burenev, Filippo Colomo, Andrea Maroncelli, Andrei Georgievich Pronko","doi":"10.1088/1751-8121/ad02ce","DOIUrl":"https://doi.org/10.1088/1751-8121/ad02ce","url":null,"abstract":"Abstract We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states, boxed plane partitions, and fishnet diagrams in quantum field theory. In the scaling limit, the model exhibits the emergence of an arctic curve separating a central disordered region from six frozen `corners' of ferroelectric or anti-ferroelectric type. We determine the analytic expression of the interface by means of the Tangent Method. We supplement this heuristic method with an alternative, rigorous derivation of the arctic curve. This is based on the exact evaluation of suitable correlation functions, devised to detect spatial transition from order to disorder, in terms of the partition function of some discrete log-gas associated to the orthogonalizing measure of the Hahn polynomials. As a by-product, we also deduce that the arctic curve's fluctuations are governed by the Tracy-Widom distribution.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135968606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1088/1751-8121/acfbcb
Markus Frembs, Andreas Döring
Abstract Gleason’s theorem (Gleason 1957 J. Math. Mech. 6 885) is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice extend to positive linear functionals on the algebra of bounded operators . Over many years, and by the effort of various authors, the theorem has been broadened in its scope from type I to arbitrary von Neumann algebras (without type I2 factors). Here, we prove a generalisation of Gleason’s theorem to composite systems. To this end, we strengthen the original result in two ways: first, we extend its scope to dilations in the sense of Naimark (1943 Dokl. Akad. Sci. SSSR 41 359) and Stinespring (1955 Proc. Am. Math. Soc. 6 211) and second, we require consistency with respect to dynamical correspondences on the respective (local) algebras in the composition (Alfsen and Shultz 1998 Commun. Math. Phys. 194 87). We show that neither of these conditions changes the result in the single system case, yet both are necessary to obtain a generalisation to bipartite systems.
{"title":"Gleason’s theorem for composite systems","authors":"Markus Frembs, Andreas Döring","doi":"10.1088/1751-8121/acfbcb","DOIUrl":"https://doi.org/10.1088/1751-8121/acfbcb","url":null,"abstract":"Abstract Gleason’s theorem (Gleason 1957 J. Math. Mech. 6 885) is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice <?CDATA $mathcal{P}(mathcal{H})$?> extend to positive linear functionals on the algebra of bounded operators <?CDATA $mathcal{B}(mathcal{H})$?> . Over many years, and by the effort of various authors, the theorem has been broadened in its scope from type I to arbitrary von Neumann algebras (without type <?CDATA $text{I}_2$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:msub> <mml:mtext>I</mml:mtext> <mml:mn>2</mml:mn> </mml:msub> </mml:math> factors). Here, we prove a generalisation of Gleason’s theorem to composite systems. To this end, we strengthen the original result in two ways: first, we extend its scope to dilations in the sense of Naimark (1943 Dokl. Akad. Sci. SSSR 41 359) and Stinespring (1955 Proc. Am. Math. Soc. 6 211) and second, we require consistency with respect to dynamical correspondences on the respective (local) algebras in the composition (Alfsen and Shultz 1998 Commun. Math. Phys. 194 87). We show that neither of these conditions changes the result in the single system case, yet both are necessary to obtain a generalisation to bipartite systems.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135923565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-12DOI: 10.1088/1751-8121/acff9b
A Restuccia, A Sotomayor
Abstract We consider the Becchi, Rouet, Stora and Tyutin (BRST) invariant effective action of the non-abelian BF topological theory in two dimensions with gauge group Sl(2,R) . By considering different gauge fixing conditions, the zero-curvature field equation gives rise to several well known integrable equations. We prove that each integrable equation together with the associated ghost field evolution equation, obtained from the BF theory, is a BRST invariant system with an infinite sequence of BRST invariant conserved quantities. We construct explicitly the systems and the BRST transformation laws for the Korteweg-de Vries (KdV) sequence (including the KdV, mKdV and CKdV equations) and Harry Dym integrable equation.
{"title":"Integrability and BRST invariance from BF topological theory","authors":"A Restuccia, A Sotomayor","doi":"10.1088/1751-8121/acff9b","DOIUrl":"https://doi.org/10.1088/1751-8121/acff9b","url":null,"abstract":"Abstract We consider the Becchi, Rouet, Stora and Tyutin (BRST) invariant effective action of the non-abelian BF topological theory in two dimensions with gauge group <?CDATA $Sl(2,mathbb{R})$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mi>S</mml:mi> <mml:mi>l</mml:mi> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> <mml:mo stretchy=\"false\">)</mml:mo> </mml:math> . By considering different gauge fixing conditions, the zero-curvature field equation gives rise to several well known integrable equations. We prove that each integrable equation together with the associated ghost field evolution equation, obtained from the BF theory, is a BRST invariant system with an infinite sequence of BRST invariant conserved quantities. We construct explicitly the systems and the BRST transformation laws for the Korteweg-de Vries (KdV) sequence (including the KdV, mKdV and CKdV equations) and Harry Dym integrable equation.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-11DOI: 10.1088/1751-8121/acfe62
Joscha Henheik, Roderich Tumulka
Abstract Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process (Qt)t∈R in the configuration space of a variable number of particles that is |ψt|2 -distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell’s jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).
{"title":"Creation rate of Dirac particles at a point source","authors":"Joscha Henheik, Roderich Tumulka","doi":"10.1088/1751-8121/acfe62","DOIUrl":"https://doi.org/10.1088/1751-8121/acfe62","url":null,"abstract":"Abstract Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process <?CDATA $(Q_t)_{tinmathbb{R}}$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mo stretchy=\"false\">(</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:mrow> <mml:msub> <mml:mo stretchy=\"false\">)</mml:mo> <mml:mrow> <mml:mi>t</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow> <mml:mi mathvariant=\"double-struck\">R</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> in the configuration space of a variable number of particles that is <?CDATA $|psi_t|^2$?> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" overflow=\"scroll\"> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:msub> <mml:mi>ψ</mml:mi> <mml:mi>t</mml:mi> </mml:msub> <mml:msup> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:math> -distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell’s jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136058253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1088/1751-8121/acfe63
Kazuo Takatsuka
Abstract Studying possible laws, rules, and mechanisms of time-evolution of quantum wavefunctions leads to deeper understanding about the essential nature of the Schrödinger dynamics and interpretation on what the quantum wavefunctions are. As such, we attempt to clarify the mechanical and geometrical processes of deformation and bifurcation of a Gaussian wavepacket of the Maslov type from the viewpoint of length-scale hierarchy in the wavepacket size relative to the range of relevant potential functions. Following the well-known semiclassical view that (1) Newtonian mechanics gives a phase space geometry, which is to be projected onto configuration space to determine the basic amplitude of a wavefunction (the primitive semiclassical mechanics), our study proceeds as follows. (2) The quantum diffusion arising from the quantum kinematics makes the Gaussian exponent complex-valued, which consequently broadens the Gaussian amplitude and brings about a specific quantum phase. (3) The wavepacket is naturally led to bifurcation (branching), when the packet size gets comparable with or larger than the potential range. (4) Coupling between the bifurcation and quantum diffusion induces the Huygens-principle like wave dynamics. (5) All these four processes are collectively put into a path integral form. We discuss some theoretical consequences from the above analyses, such as (i) a contrast between the δ -function-like divergence of a wavefunctions at focal points and the mesoscopic finite-speed shrink of a Gaussian packet without instantaneous collapse, (ii) the mechanism of release of the zero-point energy to external dynamics and that of tunneling, (iii) relation between the resultant stochastic quantum paths and wave dynamics, and so on.
{"title":"Schrödinger dynamics in length-scale hierarchy: From spatial rescaling to Huygens-like proliferation of Gaussian wavepackets","authors":"Kazuo Takatsuka","doi":"10.1088/1751-8121/acfe63","DOIUrl":"https://doi.org/10.1088/1751-8121/acfe63","url":null,"abstract":"Abstract Studying possible laws, rules, and mechanisms of time-evolution of quantum wavefunctions leads to deeper understanding about the essential nature of the Schrödinger dynamics and interpretation on what the quantum wavefunctions are. As such, we attempt to clarify the mechanical and geometrical processes of deformation and bifurcation of a Gaussian wavepacket of the Maslov type from the viewpoint of length-scale hierarchy in the wavepacket size relative to the range of relevant potential functions. Following the well-known semiclassical view that (1) Newtonian mechanics gives a phase space geometry, which is to be projected onto configuration space to determine the basic amplitude of a wavefunction (the primitive semiclassical mechanics), our study proceeds as follows. (2) The quantum diffusion arising from the quantum kinematics makes the Gaussian exponent complex-valued, which consequently broadens the Gaussian amplitude and brings about a specific quantum phase. (3) The wavepacket is naturally led to bifurcation (branching), when the packet size gets comparable with or larger than the potential range. (4) Coupling between the bifurcation and quantum diffusion induces the Huygens-principle like wave dynamics. (5) All these four processes are collectively put into a path integral form. We discuss some theoretical consequences from the above analyses, such as (i) a contrast between the δ -function-like divergence of a wavefunctions at focal points and the mesoscopic finite-speed shrink of a Gaussian packet without instantaneous collapse, (ii) the mechanism of release of the zero-point energy to external dynamics and that of tunneling, (iii) relation between the resultant stochastic quantum paths and wave dynamics, and so on.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1088/1751-8121/acfe65
Zi Xi Hu, Li Guang Jiao, Aihua Liu, Yuan Cheng Wang, Henry E Montgomery, Yew Kam Ho, Stephan Fritzsche
Abstract We perform benchmark calculations of resonance states in the Hulthén potential by employing the uniform complex-scaling generalized pseudospectral method. Complex resonance energies for states with the lowest four orbital angular momenta are reported for a wide range of screening parameters where their positions lie above the threshold. Our results are in good agreement with previous J -matrix predictions, but differ significantly from the complex-scaling calculations based on oscillator basis set. By tracing the resonance poles via bound-resonance transition as the screening parameter increases, we successfully identify the electronic configurations of the numerically obtained resonances. The asymptotic laws for resonance position and width near the critical transition region are extracted, and their connections with the bound-state asymptotic law and Wigner threshold law, respectively, are disclosed. We further find that the birth of a new resonance will distort the trajectories of adjacent higher-lying resonances, while even if two resonances are exactly degenerate in real energy position, they can still be treated as near-isolated resonances provided their widths are significantly different in magnitude.
{"title":"Resonances in the Hulthén potential: benchmark calculations, critical behaviors, and interference effects","authors":"Zi Xi Hu, Li Guang Jiao, Aihua Liu, Yuan Cheng Wang, Henry E Montgomery, Yew Kam Ho, Stephan Fritzsche","doi":"10.1088/1751-8121/acfe65","DOIUrl":"https://doi.org/10.1088/1751-8121/acfe65","url":null,"abstract":"Abstract We perform benchmark calculations of resonance states in the Hulthén potential by employing the uniform complex-scaling generalized pseudospectral method. Complex resonance energies for states with the lowest four orbital angular momenta are reported for a wide range of screening parameters where their positions lie above the threshold. Our results are in good agreement with previous J -matrix predictions, but differ significantly from the complex-scaling calculations based on oscillator basis set. By tracing the resonance poles via bound-resonance transition as the screening parameter increases, we successfully identify the electronic configurations of the numerically obtained resonances. The asymptotic laws for resonance position and width near the critical transition region are extracted, and their connections with the bound-state asymptotic law and Wigner threshold law, respectively, are disclosed. We further find that the birth of a new resonance will distort the trajectories of adjacent higher-lying resonances, while even if two resonances are exactly degenerate in real energy position, they can still be treated as near-isolated resonances provided their widths are significantly different in magnitude.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"2014 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136254321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-10DOI: 10.1088/1751-8121/ad01ff
Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci
Abstract We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies.

On the one hand, when the prey is uniformly distributed, the best possible strategy for the forager is to be stationary and uniformly distributed in the same region.

On the other hand, in several biological settings, foragers cannot be completely stationary, therefore we investigate the best seeking strategy for L'evy foragers in terms of the corresponding L'evy exponent. In this case, we show that the best strategy depends on the region size in which the prey is located: large regions exhibit optimal seeking strategies close to Gaussian random walks, while
small regions favor L'evy foragers with small fractional exponent.

We also consider optimal strategies in view of the Fourier transform of the distribution of a stationary prey. When this distribution is supported in a suitable volume, then the foraging efficiency functional is monotone increasing with respect to the L'evy exponent
and accordingly the optimal strategy is given by the Gaussian dispersal.
If instead the Fourier transform of the distribution of a stationary prey is supported in the complement of a suitable volume, then the foraging efficiency functional is monotone decreasing with respect to the L'evy exponent and therefore the optimal strategy is given by a null fractional exponent (which in turn corresponds, from a biological standpoint, to a strategy of ``ambush'' type).

We will devote a rigorous quantitative analysis also to emphasize some specific differences between the one-dimensional and the higher-dimensional cases.
{"title":"The Lévy flight foraging hypothesis: comparison between stationary distributions and anomalous diffusion","authors":"Serena Dipierro, Giovanni Giacomin, Enrico Valdinoci","doi":"10.1088/1751-8121/ad01ff","DOIUrl":"https://doi.org/10.1088/1751-8121/ad01ff","url":null,"abstract":"Abstract We consider a stationary prey in a given region of space and we aim at detecting optimal foraging strategies.&#xD;&#xD;On the one hand, when the prey is uniformly distributed, the best possible strategy for the forager is to be stationary and uniformly distributed in the same region.&#xD;&#xD;On the other hand, in several biological settings, foragers cannot be completely stationary, therefore we investigate the best seeking strategy for L'evy foragers in terms of the corresponding L'evy exponent. In this case, we show that the best strategy depends on the region size in which the prey is located: large regions exhibit optimal seeking strategies close to Gaussian random walks, while&#xD;small regions favor L'evy foragers with small fractional exponent.&#xD;&#xD;We also consider optimal strategies in view of the Fourier transform of the distribution of a stationary prey. When this distribution is supported in a suitable volume, then the foraging efficiency functional is monotone increasing with respect to the L'evy exponent&#xD;and accordingly the optimal strategy is given by the Gaussian dispersal.&#xD;If instead the Fourier transform of the distribution of a stationary prey is supported in the complement of a suitable volume, then the foraging efficiency functional is monotone decreasing with respect to the L'evy exponent and therefore the optimal strategy is given by a null fractional exponent (which in turn corresponds, from a biological standpoint, to a strategy of ``ambush'' type).&#xD;&#xD;We will devote a rigorous quantitative analysis also to emphasize some specific differences between the one-dimensional and the higher-dimensional cases.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-09DOI: 10.1088/1751-8121/acf96b
Nickolay Izmailian, Ralph Kenna, Vladimir Papoyan
Abstract We derive exact finite-size corrections for the free energy F of the Ising model on the square lattice with Brascamp–Kunz boundary conditions. We calculate ratios rp(ρ) of p th coefficients of F for the infinitely long cylinder ( ) and the infinitely long Brascamp–Kunz strip ( ) at varying values of the aspect ratio . Like previous studies have shown for the two-dimensional dimer model, the limiting values p→∞ of rp(ρ) exhibit abrupt anomalous behavior at certain values of ρ . These critical values of ρ and the limiting values of the finite-size-expansion-coefficient ratios differ, however, between the two models.
摘要我们在具有Brascamp-Kunz边界条件的方形晶格上，导出了Ising模型的自由能F的精确有限尺寸修正。我们计算了无限长圆柱体()和无限长布拉斯坎普-昆兹带()在不同宽高比值下的系数r p (ρ)。就像以前的研究表明的二维二聚体模型一样，r p (ρ)的极限值p→∞在某些ρ值下表现出突然的异常行为。然而，在两种模型之间，ρ的临界值和有限尺寸-膨胀-系数比值的极限值是不同的。
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