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Book ; Online: Significance of chiral three-nucleon force contact terms for understanding of elastic nucleon-deuteron scattering

Witała, H. / Golak, J. / Skibiński, R.

2022

Abstract: We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$ ...

Abstract	We investigate the importance of the three-nucleon (3N) force contact terms in elastic nucleon-deuteron (Nd) scattering by applying the N$^4$LO$^+$ chiral semi-local momentum space (SMS) regularized nucleon-nucleon (NN) chiral potential supplemented by N$^2$LO and all subleading N$^4$LO three-nucleon force (3NF) contact terms. Strength parameters of the contact terms were obtained by least squares fitting of theoretical predictions to cross section and analyzing powers data at three energies of the impinging nucleon. Although the N$^3$LO contributions to the 3N force were completely neglected, the results calculated with the contact terms multiplied by the fitted strength parameters yield an improved description of the elastic Nd scattering observables in a wide range of incoming nucleon energies below the pion production threshold. Comment: 43 pages, 13 figures
Keywords	Nuclear Theory
Subject code	621
Publishing date	2022-03-16
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Envy-free dynamic pricing schemes

Bérczi, Kristóf / Codazzi, Laura / Golak, Julian / Grigoriev, Alexander

2023

Abstract: A combinatorial market consists of a set of indivisible items and a set of agents, where each agent has a valuation function that specifies for each subset of items its value for the given agent. From an optimization point of view, the goal is usually to ...

Abstract	A combinatorial market consists of a set of indivisible items and a set of agents, where each agent has a valuation function that specifies for each subset of items its value for the given agent. From an optimization point of view, the goal is usually to determine a pair of pricing and allocation of the items that provides an efficient distribution of the resources, i.e., maximizes the social welfare, or is as profitable as possible for the seller, i.e., maximizes the revenue. To overcome the weaknesses of mechanisms operating with static prices, a recent line of research has concentrated on dynamic pricing schemes. In this model, agents arrive in an unspecified sequential order, and the prices can be updated between two agent-arrivals. Though the dynamic setting is capable of maximizing social welfare in various scenarios, the assumption that the agents arrive one after the other eliminates the standard concept of fairness. In this paper, we study the existence of optimal dynamic prices under fairness constraints in unit-demand markets. We propose four possible notions of envy-freeness of different strength depending on the time period over which agents compare themselves to others: the entire time horizon, only the past, only the future, or only the present. For social welfare maximization, while the first definition leads to Walrasian equilibria, we give polynomial-time algorithms that always find envy-free optimal dynamic prices in the remaining three cases. In contrast, for revenue maximization, we show that the corresponding problems are APX-hard if the ordering of the agents is fixed. On the positive side, we give polynomial-time algorithms for the setting when the seller can choose the order in which agents arrive. Comment: 19 pages, 3 figures
Keywords	Computer Science - Computer Science and Game Theory ; Computer Science - Discrete Mathematics
Subject code	330
Publishing date	2023-01-04
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Book ; Online: Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

Fischer, David / Golak, Julian / Mnich, Matthias

2022

Abstract: We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times t}$ on a ... ...

Abstract	We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times t}$ on a horizontal, and $n$ arbitrary matrices $B^{(j)} \in \mathbb Z^{s\times t} on a diagonal line. Several recent works design fixed-parameter algorithms for $N$-fold IPs by taking as parameters the numbers of rows and columns of the $A$- and $B$-matrices, together with the largest absolute value $\Delta$ over their entries. These advances provide fast algorithms for several well-studied combinatorial optimization problems on strings, on graphs, and in machine scheduling. In this work, we extend this research by proposing algorithms that additionally harness a partition structure of submatrices $A^{(i)}$ and $B^{(j)}$, where row indices of non-zero entries do not overlap between any two sets in the partition. Our main result is an algorithm for solving any $N$-fold IP in time $nt log(nt)L^2(S_A)^{O(r+s)}(p_Ap_B\Delta)^{O(rp_Ap_B+sp_Ap_B)}$, where $p_A$ and $p_B$ are the size of the largest set in such a partition of $A^{(i)}$ and $B^{(j)}$, respectively, $S_A$ is the number of parts in the partition of $A = (A^{(1)},., A^{(n)}), and $L = (log(\|\|u - \ell\|\|_\infty)\cdot (log(max_{x:\ell \leq x \leq u} \|c^Tx\|))$ is a measure of the input. We show that these new structural parameters are naturally small in high-multiplicity scheduling problems, such as makespan minimization on related and unrelated machines, with and without release times, the Santa Claus objective, and the weighted sum of completion times. In essence, we obtain algorithms that are exponentially faster than previous works by Knop et al. (ESA 2017) and Eisenbrand et al./Kouteck{\'y} et al. (ICALP 2018) in terms of the number of job types.
Keywords	Computer Science - Data Structures and Algorithms
Subject code	519
Publishing date	2022-03-07
Publishing country	us
Document type	Book ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Three-nucleon reactions with chiral dynamics*

Witała H. / Golak J. / Skibiński R. / Topolnicki K.

EPJ Web of Conferences, Vol 66, p

2014 Volume 03096

Abstract: Faddeev calculations using the chiral three-nucleon force at next-to-next-to-next-to-leading-order show that this force is not able to provide an explanation for the low-energy Ay puzzle. Also the large discrepancies between data and theory for the ... ...

Abstract	Faddeev calculations using the chiral three-nucleon force at next-to-next-to-next-to-leading-order show that this force is not able to provide an explanation for the low-energy Ay puzzle. Also the large discrepancies between data and theory for the symmetric-space-star and for the neutron-neutron quasi-free-scattering cross sections in low energy neutron-deuteron breakup cannot be explained by that three-nucleon force. The discrepancy for the neutron-neutron quasi-free-scattering cross section seems to require a modification of the 1S0 neutron-neutron force.
Keywords	Physics ; QC1-999 ; Science ; Q
Language	English
Publishing date	2014-03-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: The proton-proton scattering without Coulomb force renormalization

Glöckle W. / Witała H. / Golak J. / Skibiński R.

EPJ Web of Conferences, Vol 3, p

2010 Volume 05014

Abstract: We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional ... ...

Abstract	We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for an exponentially screened Coulomb potential. For the limit of large screening radii we conﬁrm analytically predicted properties for oﬀ-shell, half-shell and on-shell elements of the Coulomb t-matrix.
Keywords	Physics ; QC1-999 ; Science ; Q ; DOAJ:Physics (General) ; DOAJ:Physics and Astronomy
Language	English
Publishing date	2010-04-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: A novel treatment of the proton-proton Coulomb force in proton-deuteron Faddeev calculations

Glöckle W. / Skibiński R. / Golak J. / Witała H.

EPJ Web of Conferences, Vol 3, p

2010 Volume 05003

Abstract: We present resently introduced novel approach to include th e proton-proton (pp) Coulomb force into the momentum space three-nucleon (3N) Faddeev calculations. It is based on a standard formulation for short range forces and relies on a screening of the ... ...

Abstract	We present resently introduced novel approach to include th e proton-proton (pp) Coulomb force into the momentum space three-nucleon (3N) Faddeev calculations. It is based on a standard formulation for short range forces and relies on a screening of the long-range Coul omb interaction. In order to avoid all uncertainties connected with an application of the partial wave expansion, unsuitable when working with long-range forces, we apply directly the 3-dimensional pp screened Coulomb t-matrix. That main new ingredient, the 3-dimensional screened pp Coulomb t-matrix, is obtained by a numerical sol ution of the 3-dimensional Lippmann-Schwinger (LS) equation. Using a simple dynamical model for the nuclear part of the interaction we demonstrate the feasibility of that approach. The physical elastic pd scattering amplitude has a well deﬁned screening limit and does not require renormalisation. Well converged elastic pd cro ss sections are obtained at ﬁnite screening radii. Also the proton-deuteron (pd) breakup observables can be determ ined from the resulting on-shell 3N amplitudes increasing the screening radius. However, contrary to the pd e lastic scattering, the screening limit exists only after renormalisation of the pp t-matrices.
Keywords	Physics ; QC1-999 ; Science ; Q ; DOAJ:Physics (General) ; DOAJ:Physics and Astronomy
Subject code	539
Language	English
Publishing date	2010-04-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Approximate Three-Dimensional Wave Function and the T-Matrix for the Sharply Cut Off Coulomb Potential

Witała H. / Skibiński R. / Glöckle W. / Golak J.

EPJ Web of Conferences, Vol 3, p

2010 Volume 05017

Abstract: For a sharply cut-oﬀ Coulomb potential we derive analytically the asymptotic form of the threedimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid ...

Abstract	For a sharply cut-oﬀ Coulomb potential we derive analytically the asymptotic form of the threedimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid for any type of screening. We obtain also the asymptotic form of the corresponding three-dimensional half-shell t-matrix. Our results are fully supported by the numerical solutions of the three-dimensional Lippmann-Schwinger equation.
Keywords	Physics ; QC1-999 ; Science ; Q ; DOAJ:Physics (General) ; DOAJ:Physics and Astronomy
Language	English
Publishing date	2010-04-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Dominance of Tensor Correlations in High-Momentum Nucleon Pairs Studied by (p,pd) Reaction.

Terashima, S / Yu, L / Ong, H J / Tanihata, I / Adachi, S / Aoi, N / Chan, P Y / Fujioka, H / Fukuda, M / Geissel, H / Gey, G / Golak, J / Haettner, E / Iwamoto, C / Kawabata, T / Kamada, H / Le, X Y / Sakaguchi, H / Sakaue, A /

Scheidenberger, C / Skibiński, R / Sun, B H / Tamii, A / Tang, T L / Tran, D T / Topolnicki, K / Wang, T F / Watanabe, Y N / Weick, H / Witała, H / Zhang, G X / Zhu, L H

Physical review letters

2019 Volume 121, Issue 24, Page(s) 242501

Abstract: The isospin character of p-n pairs at large relative momentum has been observed for the first time in the ^{16}O ground state. A strong population of the J,T=1,0 state and a very weak population of the J,T=0,1 state were observed in the neutron pickup ... ...

Abstract	The isospin character of p-n pairs at large relative momentum has been observed for the first time in the ^{16}O ground state. A strong population of the J,T=1,0 state and a very weak population of the J,T=0,1 state were observed in the neutron pickup domain of ^{16}O(p,pd) at 392 MeV. This strong isospin dependence at large momentum transfer is not reproduced by the distorted-wave impulse approximation calculations with known spectroscopic amplitudes. The results indicate the presence of high-momentum protons and neutrons induced by the tensor interactions in the ground state of ^{16}O.
Language	English
Publishing date	2019-01-04
Publishing country	United States
Document type	Journal Article
ZDB-ID	208853-8
ISSN	1079-7114 ; 0031-9007
ISSN (online)	1079-7114
ISSN	0031-9007
DOI	10.1103/PhysRevLett.121.242501
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Treatment of Two Nucleons in Three Dimensions

Glöckle W. / Skibiński R. / Golak J. / Elster Ch. / Fachruddin I. / Witała H.

EPJ Web of Conferences, Vol 3, p

2010 Volume 05021

Abstract: We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators analytically. We apply ...

Abstract	We extend a new treatment proposed for two-nucleon (2N) and three-nucleon (3N) bound states to 2N scattering. This technique takes momentum vectors as variables, thus, avoiding partial wave decomposition, and handles spin operators analytically. We apply the general operator structure of a nucleon-nucleon (NN) potential to the NN T-matrix, which becomes a sum of six terms, each term being scalar products of spin operators and momentum vectors multiplied with scalar functions of vector momenta. Inserting this expansions of the NN force and T-matrix into the Lippmann-Schwinger equation allows to remove the spin dependence by taking traces and yields a set of six coupled equations for the scalar functions found in the expansion of the T-matrix.
Keywords	Physics ; QC1-999 ; Science ; Q ; DOAJ:Physics (General) ; DOAJ:Physics and Astronomy
Language	English
Publishing date	2010-04-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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Article ; Online: Calculations of the Triton Binding Energy with a Lorentz Boosted Nucleon-Nucleon Potential

Elster Ch. / Polyzou W.N. / Skibiński R. / Golak J. / Witała H. / Glöckle W. / Kamada H.

EPJ Web of Conferences, Vol 3, p

2010 Volume 05025

Abstract: We study the binding energy of the three-nucleon system in relativistic models that use two diﬀerent relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that ... ...

Abstract	We study the binding energy of the three-nucleon system in relativistic models that use two diﬀerent relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that relates the non-relativistic center-of-mass Hamiltonian to the relativistic mass (rest energy) operator and the other uses a non-linear equation that relates the interaction in the relativistic mass operator to the non-relativistic interaction. In both cases Lorentz-boosted interactions are used in the relativistic Faddeev equation to solve for the three-nucleon binding energy. Using the same realistic NN potentials as input, the solution of the relativistic three-nucleon Faddeev equation for 3H shows slightly less binding energy than the corresponding nonrelativistic result. The eﬀect of the Wigner spin rotation on the binding is very small.
Keywords	Physics ; QC1-999 ; Science ; Q ; DOAJ:Physics (General) ; DOAJ:Physics and Astronomy
Subject code	115
Language	English
Publishing date	2010-04-01T00:00:00Z
Publisher	EDP Sciences
Document type	Article ; Online
Database	BASE - Bielefeld Academic Search Engine (life sciences selection)

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